Testing foundations of quantum mechanics with photons

2.7 MB·English

by  Peter Shadbolt

Testing foundations of quantum mechanics with photons
Peter Shadbolt, Jonathan C. F. Mathews, Anthony Laing, and Jeremy L. O’Brien1
1Centre for Quantum Photonics, H. H. Wills Physics Laboratory & Department of Electrical and Electronic Engineering,
University of Bristol, Merchant Venturers Building, Woodland Road, Bristol, BS8 1UB, UK
(Dated: January 16, 2015)
Thefoundationalideasofquantummechanicscontinuetogiverisetocounterintuitivetheoriesand
physicaleffectsthatareinconflictwithaclassicaldescriptionofNature. Experimentswithlightat
thesinglephotonlevelhavehistoricallybeenattheforefrontoftestsoffundamentalquantumtheory
andnewdevelopmentsinphotonicsengineeringcontinuetoenablenewexperiments. Herewereview
recent photonic experiments to test two foundational themes in quantum mechanics: wave-particle
duality, central to recent complementarity and delayed-choice experiments; and Bell nonlocality
where recent theoretical and technological advances have allowed all controversial loopholes to be
separately addressed in different photonics experiments.
5
1
0
Light has featured in tests of foundational physics clicks never occurs, and the photon initially appears to
2
during times that witnessed major advancements in travel and arrive as a discrete particle. However, having
n
our understanding of nature. Newton’s investigation of detected many photons, the observed probability distri-
a
J the nature of light, using prisms to reveal the visible bution p(x) can only be explained by wave interference,
spectrum, is iconic of the Scientific Revolution of the due to components of the photon which travel through
5
1 16thand17thcenturies. EarlytestsofEinstein’sgeneral both slitssimultaneously. Confoundingly,whendetectors
relativity involved observations of starlight passing close areplaceddirectlyinsidethetwoslits,thephotonisonly

] to the sun during a solar eclipse. Scientific advances ever detected at one slit or the other — never at both.
h
p have led to more convincing (and striking!) observations Where was the photon when it travelled through the
- of relativistic effects with images from the Hubble space mask? If it passed through one slit and not the other,
nt telescope revealing the gravitational lensing of galactic wave interference effects would not be observed. If it
a light. And we now know how the electromagnetic passed through both slits at once, it should be possible
u spectrum extends beyond the visible range and is to detect it at both simultaneously; this never occurs.
q quantised into single photons. Since the primary detec- If it passed through neither slit, we should not detect it
[ tion apparatus in early experimental physics were the at all — but we do. In this way, the double-slit experi-
1 physicists themselves, light made a natural observable. ment reveals the inadequacy of classical language when
v As our understanding of quantum photonics deepened, describing quantum systems.
3 the utility of photons in tests of foundational concepts
In 1909, Geoffrey Taylor used a sewing needle to split
1 in physics became more evident. Photons are robust to
7 abeamoflightintotwopaths,andobservedinterference
environmental noise, have low decoherence properties,
3 fringes in the resulting pattern of light and shadow6. He
and are easily manipulated and detected. The first half
0 usedanincandescentsourceof“feeblelight”withroughly
of this review discusses tests of wave-particle duality
. the intensity of a candle held at a distance of one mile.
1 with one photon, while the second half looks at ex-
0 Since then, single photons have played a pivotal role in
perimentaltestsofnonlocalitywithtwoormorephotons.
5 tests of wave-particle duality. This is largely due to the
1 ease with which photons can be generated, manipulated
v: 1. Wave-particle duality and measured, as well as their resilience to noise, and
i The double-slit experiment has famously been said to associated room temperature/pressure operation. Many
X
contain the entire mystery of quantum mechanics. It oftheseexperimentsarebasedonaverynaturalquestion:
r provides a concise demonstration of the fact that single whatdoweknow, andhowmuchcanwemeasure, ofthe
a
quanta are neither waves nor particles, and that in gen- state of the photon as it passes through the slits?
eraltheyareneitherinonesingleplace,norintwoplaces The light source used by Taylor was thermal — it did
at once. not generate photons one-by-one — and his experiment
The experiment begins with a source of single quanta. consequently admits a classical model. The fact that
Here we will consider only photons, but qualitatively true single photons are not detected at both slits simul-
identical results have been observed in a wide variety taneously (antibunching) was confirmed experimentally
of quantum systems including electrons1–3, atoms4, and by Clauser7, who used a more sophisticated light source,
even large molecules such as C 5. Single photons are based on atomic cascades in mercury atoms. A similar
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sent towards a mask into which two slits have been cut. source was used by Grangier et al.8, who observed both
On the far side of the mask, the spatial distribution of antibunching and wave interference effects analogous to
single-photon detection events is measured by a sensi- those of the double-slit experiment.
tive detector. For each photon, the detector registers In the quantum-mechanical description, detection of
a “click” at position x. Simultaneous detection of two thephotonatoneslit“collapses”thesingle-photonwave-
2
function and precludes detection at the other slit. Col- lar significance in the de Broglie-Bohm interpretation of
lapse is instantaneous, even when the slits are very far quantum mechanics, where they are literally interpreted
apart, and it was emphasised by Einstein at the Solvay as the path taken by a single particle-like photon.
conference9 that the effect is thus seemingly nonlocal. A
recent experiment by Guerreiro et al.10 tested Einstein’s (a) (b)
thought experiment for the first time, using space-like BS1 BS1
separated (causally independent) detectors. BS
2
Wavefunction collapse belongs to the Copenhagen in-
terpretation of quantum mechanics, and encompasses
Niels Bohr’s principle of complementarity. Bohr main-
tainedthatinordertoobservecomplementaryproperties R N G C H
of a quantum system, an experimentalist must necessar-
ily employ mutually incompatible arrangements of the
measurement apparatus. In the context of the double
FIG. 1. Delayed choice experimental set-ups. (a) Wheeler’s
slit, this means that any experiment which fully reveals
delayed choice experiment. A photon is sent into a Mach-
the wave-like properties of the photon must obscure its
Zehnder interferometer. Upon arrival at the first beamsplit-
particle-like character, and vice-versa.
ter BS , it is split into a superposition across both paths. A
1
Bohr’s principle has only very recently been formal- random number generator (RNG) then toggles a fast optical
izedinuniversalcomplementarityrelations,suchasthose switch, closing or opening the interferometer by insertion or
due to Ozawa and Hall11–13. These relations formalize removalofBS2,leadingtowave-likeorparticle-likemeasure-
ment of the photon respectively. Two detectors reveal wave-
the notion that although the inaccuracy in either of two
like behaviour in the event that the interferometer is closed,
complementaryobservablescanindividuallybemadear-
otherwise particle-like statistics are seen. (b) Quantum de-
bitrarily small, one cannot simultaneously measure both
layed choice. The optical switch is replaced by a quantum-
to an arbitrary degree of accuracy. This is distinguished
controlledbeamsplitter: acontrolled-Hadamardgate. Anan-
from the Heisenberg uncertainty principle, where mea-
cilla photon controls this gate: ancilla states |0(cid:105) and |1(cid:105) lead
surementsaresequentialratherthansimultaneous. Very to presence and absence of BS respectively. By preparing
2
recently, Weston et al.14, used a spontaneous parametric the ancilla in a superposition state BS can be placed into a
2
down-conversionsourcetogetherwithalinear-opticalcir- superposition of present and absent, leading to a superposi-
cuit to experimentally test these new relations. Making tion of wave-like and particle-like measurement.
use of entanglement generated by the photon source, the
authors were able to test complementarity under condi- John Wheeler’s famous delayed-choice thought exper-
tions in which previously discovered, non-universal com- iment18,19 also addresses the question of the position or
plementarity relations fail. trajectory of the photon in a two-path setup. Consid-
Upon first encountering the double slit experiment, it ering the double slit experiment, one might attempt to
is natural to wonder about the trajectory of the photon side-steptheuncomfortableimplicationsofwave-particle
during its path from source to detector. Complemen- duality by means of a pseudo-classical explanation in
tarity implies that it is not possible to simultaneously which the photon decides in advance to behave as a par-
measure the position of the photon without irrevocably ticle or wave, depending on the choice of measurement
disturbingitsmomentum,andindeedana¨ıveexperiment setup. Ifthephotonnoticesthataparticle-likemeasure-
hoping to track the route of the photon by measurement mentisplanned,itdispenseswithallwave-likeproperties
of its position will destroy all wave-like effects. How- and passes through one slit at random, and vice-versa.
ever, Kocsis et al. recently demonstrated15,16 that quan- Wheeler proposed an elegant test of this comforting (if
tum weak measurement17 can be used to approximately pathological) model, in which the decision to measure
reconstruct the average trajectory of ensembles of pho- wavelike or particle-like behaviour is delayed until after
tonsastheyundergodouble-slitinterference. Weakmea- the photon has passed the slits, but before it reaches the
surementallowsapproximateinformationtobeobtained measuring apparatus. Delayed-choice experiments have
on a particular observable without appreciably disturb- been performed in a variety of physical systems20–23, all
ing “strong” measurement outcomes on a complemen- ofwhichconfirmthequantumpredictionsandrefutethe
tary variable. The authors sent single photons from a notion that the photon decides in advance to behave as
GaAs quantum dot through a double-slit interferometer, a particle or a wave.
in which a piece of birefringent calcite imposes a weak Ofparticularsignificanceisarecentresult24ofJacques
polarizationrotationdependingontheangleofincidence et al., in which relativistic space-like separation between
— and thus the momentum — of the photon. Then, by the random choice of measurement setting and slits was
simultaneous detection of the lateral position and polar- achieved for the first time. This ensures that there can
ization using a high-resolution CCD camera, weak mea- benocausallinkbetweenthefreechoiceofmeasurement
surement of the photon’s momentum was accomplished settingandthebehaviourofthephotonattheslits. Here,
atthesametimeasstrongmeasurementofposition. The anitrogenvacancycolourcentreindiamondwasusedas
trajectories measured in this experiment hold particu- the source of single photons, ensuring extremely close
3
approximation to the single-photon Fock state 1 . An therefore causally disconnected.
| (cid:105)
electro-optic modulator, driven by a quantum random In all of these variants on the double-slit experiment,
numbergeneratorat4.2MHz,wasusedtoimplementthe we see a fundamental trade-off between the information
choice of measurement setting. A similar experimental whichcansimultaneouslybeobtainedonparticularprop-
setup was more recently employed by the same group25 erties of quantum systems, as well as a behavioural de-
torefutethecontroversialclaimsduetoAfsharetal.26,27 pendence on the choice of measurement setting. These
that Bohr’s complementarity principle could be violated effects seem contrary to what is known as noncontex-
in a subtle variation on the double slit experiment. tual realism, the (rather natural) assumption that the
observable properties of objects are well-defined inde-
In delayed-choice experiments, the choice of measure-
pendent of measurement. Kochen and Specker (KS)37
ment setting is generally implemented using a classical
proved that there exist sets of quantum-mechanical ob-
optical switch, driven by a random number generator,
servables,towhichauniquesetofvaluesprovablycannot
whichrapidlyinsertsorremovesanopticalbeam-splitter
be consistently and simultaneously assigned — render-
inthepathofthephoton. Ifthebeam-splitterispresent,
ing noncontextuality untenable. No direct experimen-
which-way information is erased and full-contrast wave-
tal implementation has yet been reported, and indeed
like interference is observed. If the beamsplitter is in-
it is unlikely that a meaningful direct implementation
stead absent, each detection event yields full which-way
of KS is possible38,39. However, a number of theoret-
information but no interference is seen. A recent pro-
posal by Ionicioiu and Terno28 suggested that the clas- ical works40–43 have shown that noncontextual realism
can be revoked under much less demanding conditions,
sical random bit might be replaced by an ancilla qubit,
and many of these theories have since been tested us-
and the classical controlled-beamsplitter by a quantum
ing single photons. An early result by Michler et al.44
controlled-beamsplitter, or controlled-Hadamard (CH)
mimicked three-particle GHZ correlations, using entan-
gate. Bypreparingtheancillaqubitinthesuperposition
gled photon pairs generated by SPDC. Huang et al.45
statecos(α) 0 +sin(α) 1 ,thebeamsplitteriseffectively
| (cid:105) | (cid:105) testedthe“all-or-nothing”KS-liketheoryofSimon41,en-
placed into a coherent superposition of being present
coding two qubits in the path and polarization degrees
and being absent. One can then continuously tune be-
of freedom of one heralded single photon. More recently,
tween particle-like and wavelike measurement settings,
Lapkiewicz et al. reported46 an experiment using a sin-
in close analogy with the weak measurement technique
glephotonicqutrit,encodedinpathandpolarizationus-
ofRef.16. Thisideawasquicklyimplementedbyanum-
ber of groups29–31, two of which used photon pairs gen- ing calcite beam displacers, to implement the theoretical
erated by SPDC. The result of Peruzzo et al.30 exploits proposal of Klyachko et al.47. This result is notable as it
recent developments in integrated quantum photonics32, reinforces the strong incompatibility between the quan-
tum and classical pictures of physics with only a single
withWheeler’sinterferometerandtheCH gatebothim-
plemented on-chip33. In this experiment, entanglement quantumparticleandintheabsenceofmulti-particleen-
tanglement.
generated by the CH gate allows for device-independent
AfundamentaltenetofquantummechanicsistheBorn
refutationofhiddenvariablemodelsinwhichthephoton
rule, whichstatesthatgivenasystemwithwavefunction
decides in advance to behave as a particle or a wave, by
violation of the Bell-CHSH inequality34. ψ((cid:126)r,t), the probability that it is detected in the volume
element d3r at time t is given by
In the scenario of Ionicioiu and Terno, which-way in-
formationiscarriedbytheancillaryparticle. Thispossi- p((cid:126)r,t)= ψ((cid:126)r,t)2d3r. (1)
bility was previously emphasized by Scully and Dru¨hl35, | |
who pointed out that the choice of measurement basis Itcaneasilybeshownthatsincethisexpressiondepends
for theentangledancilla determines the contrastof wave only on the square of the wavefunction, probabilities
interference observed, and that this choice can be made generated by multi-particle wavefunctions can always
even after the system photon has been detected. Only a be written in terms of interference between pairs;
subset of allowed measurement settings completely and three-body interference terms never appear in the
irrevocably erase all which-way information, resulting expansion of (1). Indeed, it has been shown that almost
in high-contrast interference fringes. In 2000, Kim et all nonlinear models of quantum mechanics which
al.23 implemented this so-called delayed-choice quantum permit three-body interference have extreme and highly
eraser using single photons generated by SPDC. More unlikely consequences, such as cloning of quantum
recently, Ma et al.36 demonstrated a quantum eraser us- states and polynomial-time quantum algorithms for
ing entangled photon pairs. The authors went to great NP-complete computational tasks48. A recent exper-
lengths to rule out models in which the circumstances iment by Sinha et al.49 went in search of such effects
of the ancilla are communicated to the system photon using a triple-slit variation on the double-slit experi-
through a local, causal mechanism. The system and an- ment. Using a lithographically fabricated triple slit, a
cilla photons were sent to separate islands, 144km apart, coherent laser source, and heralded single photons from
suchthatthechoiceofmeasurementsetting,systempho- SPDC, the authors gathered strong evidence against
ton and interferometer, and measurement of the ancilla theexistenceofhigher-ordercorrectionstotheBornrule.
photon, were all mutually space-like separated — and
4
2. Nonlocality entangledphotonpairsthataresharedbetweenobservers
Locality is the concept that the behaviour of space-like AliceandBobwhoindependentlyperformmeasurements
separatedobjectsdependsonlyoneventsintheirrespec- and subsequently compare their results (Fig. 2 (a)). The
tive light-cones. Confoundingly, entangled particles ex- measurements have two possible settings, 0 or 1, and
hibitcorrelationsthatdefythisunderstanding. Manyat- have only two possible outcomes a,b 1,+1 , often
∈ {− }
tempts have been made to explain these correlations in assignedtothepolarisationofthephotons. TheClauser-
terms of local hidden variable models (LHVs) which at- Horne-Shimony-Holt(CHSH)34 versionofBell’sinequal-
tempttocaptureoureverydayexperienceoftheuniverse. ity sets an upper bound on the strength of correlations
LHVsassociatedtoeachparticlecanbeimaginedashav- allowedbyLHVmodelsusingtheasumofexpectedval-
ing been determined from some earlier local interaction. uesforab,foreachpossiblecombinationofmeasurement
This aligns with an intuitive local and realistic view of a outcome:
universe that is causally connected by locality. In 1964,
S = a b + a b + a b a b 2. (2)
John Bell described an experimentally tenable scenario 0 0 0 1 1 0 1 1
|(cid:104) (cid:105) (cid:104) (cid:105) (cid:104) (cid:105)−(cid:104) (cid:105)|≤
in which quantum mechanics predicts outcomes that are
Quantum mechanics predicts that this bound can be ex-
incompatible with all possible LHV models50—provided
perimentally violated, demonstrating the inadequacy of
the experiments are rigorously performed. The plat-
LHV models. If the two particles are entangled—for ex-
form of entangled single photons is the only platform to ample in the singlet state ψ− = √1 (01 10 )—then
haveaddressedalltheknownkeyrequirementsofaquan- | (cid:105) 2 | (cid:105)−| (cid:105)
a choice of measurement settings σ & σ for Alice, and
tumtheoryofnonlocality,albeitinseparateexperiments. z x
σ +σ & σ σ for Bob, leads to a violation of (2)
Here we review a selection of recent developments using z x z − x
with S =2√2.
entangled photons to test quantum nonlocality and ex-
The implications of rigorously violating this inequal-
ploreitsproperties. Foranexhaustivereviewofthesub-
ity have a profound effect on our intuition of how the
ject’s history we point the reader towards more in-depth
universe works, for it suggests that the two particles are
reviews on multi-photon entanglement51 and theoretical
instantaneously communicating with one another, even
developments52.
though they are far apart. Although the randomness of
Since the seminal experiments of Freedmand and
outcomestomeasurementsmeanthatnocommunication
Clauser53 in 1972, and Aspect et al.54 in 1982, nonlo-
can occur between Alice and Bob, these nonlocal effects
cality experiments have typically comprised a source of
seemtobeincontradictionwiththespirit,ifnotthelet-
ter, of special relativity. These far reaching implications
(a)" 0" 1" 0" 1" have motivated particular scrutiny on the possible ways
+1 +1 inwhichnaturemightsomehowfake nonlocality,withfo-
Alice" Source" Bob" cusmainlyfallinguponexperimentallimitations. Anap-
1 1 parent experimental violation S >2 could be attributed
� Loss?" ?Loss" � to assumptions exploited by LHV models and known as
(b)"me% (c)"me% loopholes, the more famous of which are the Locality,
Ti R R Ti
a b Detection and Freedom of Choice loopholes (Fig. 2). A
R R
a b completely unambiguous experimental demonstration of
Bell nonlocality requires the simultaneous obstruction of
Ma Mb everypossibleloophole. Whilethismilestoneisyettobe
reachedinexperimentalphysics,photonshavebeenused
C C
a b Ma Mb to address each of these loopholes individually.
The Detection Loophole—Optical tests of nonlocality
x" x" x" x"
Alice" Source" Bob" Space% C Space% Spache%ave suffered from low detection efficiency. With an ex-
a
Cb perimental efficiency of η <100% there exist, in addi-
tionto“+1”and“ 1”,non-conclusivemeasurementout-
FIG.2. Anonlocalityexperimentandassociatedloop- comes“ ”thatrep−resentthefailuretodetectanemitted
holes. (a) The detection loophole can be opened by optical photon.⊥“ ” can be ignored by including only measure-
lossifthereisasufficientlyhighproportionofnon-conclusive ⊥
ments that register photon detection. But this relies on
outcomes “⊥”. (b) A space-like separation prohibits sig-
the assumption of a fair sampling, since otherwise local
nallingbetweenthevariouseventsoccurringforeachobserver
models may skew the detection statistics of “+1” and
and closes the locality loophole. E.g. Alice’s measurement
“ 1” to falsify violation of (eq. 2). This has been illus-
M and results R are outside of the light-cone of influence
a a −
from Bob’s measurement choice C . Furthermore since C trated experimentally through the use of side channels
b a
and C are causally disconnected from detection events and tointentionallyfalsifysignaturesofnonlocalityinexper-
b
the source, Alice and Bob are free to choose their measure- imentalsetupsthatareotherwiseconsideredasstandard
ment settings without influence. (c) If the observers are not Bell-inequality experiments55–57.
space-like separated, it is possible for signalling to occur be- When including “ ” outcomes, violation of CHSH
tween events. In this example, Ma and Mb can respectively (eq. 2) only occurs w⊥hen experiment efficiencies are be-
influence R and R , and C can influence both M and R .
b a b a b yondthethresholdofη >82.8%. Remarkably, Eberhard
week ending
PRL 111, 130406 (2013) PHYSICAL REVIEW LETTERS 27 SEPTEMBER 2013 5
Here,wereportthefirstexperimentthatfullyclosesthe Inordertoavoidthecoincidence-timeloophole[17–19]
discovered that lowering the amount of entanglement by configuration63,64;Ref.60usesanon-colinearSPDCpho-
detection loophole with photons, which are then the only (oneofthesameloopholespresentinthereport(cid:112)eddatafor
controlling the r parameter in (r 01 10 )/ (1+r2) tonsourceconfiguration(Fig.3(a)). Whilebothdemon-
system in which both loopholes have been closed, albeit the previous photon experiment [1|6](cid:105)),−w|e u(cid:105)se a Pockels
reduces the threshold efficiency to η > 66.7% in test- strations are of sufficient efficiency to close the detection
not simultaneously. Moreover, we show that the source cell between crossed polarizers to periodically transmit
ing nonlocality58. Denoting n (a b ) as the number of loophole,theexperimentinRef.59isstillopentotheso-
k,l i j
quality is high enough to provide the best test to date of pshhoorttobnurpsatsirsofwthitehpouumtcpolmaseerk. Each+b1u,rst1c,orresapnodndls to called “coincidence-time” loophole65. This experiment
thequantummechanicspredictionitself.Finally,weapply a single well-defined event, easi∈ly d{istin−guis⊥he}d with th∈e
+1, 1, when using measurement settings i 0,1 (and numerous others) rely on using timing windows de-
the stronger-than-classical correlations to verify the crea- {detec−tors.⊥C}are must still be taken, however, to gu∈ar{ante}e
on one particle and j 0,1 on the other, Eberhard’s finedbysinglephotondetectioneventstoperformcoinci-
tionoftruerandomnumbers,achievingratesover4orders itnheaqtuthaleirtey i(swhnoichtehmopldos∈raflo{lyr LcHo}rVre)laistewdreitftfeenctatshat unduly dent detection analysis: when one photon detector regis-
of magnitude beyond all past experiments. affectsthemeasuredcounts.Forexample,laserpowerdrift tersasingle-photonevent,acoincidenceeventisrecorded
J=n (a ,b ) n (a ,b )+n (a ,b ) (3)
The first form of a Bell inequality that was experimen- can lea+d1,t+o1a v1iol1ati−on +w1i,t+h1no0nen0tangle+d1,p−h1oto0ns,1if the if a second single-photon event is recorded within a pre-
tally feasible and did not require assumptions such as fair ordernof+t1h,⊥e(ma0e,abs1u)re+mne−n1ts,+i1s(nao1,tbm0)ad+enra⊥n,+d1o(mal1y,b[01)9].W0e scribed window of time. The coincidence time loophole
≥
sampling was the Clauser-Horne (CH) inequality [20], addressthisissuebymeasuringeachofthetermsinEq.(2) allows the detection time to be shifted by the local mea-
Notably, each observer needs only one detector, since
which places the following constraints for any local real- multiple times while randomly choosing the detector set- surementsettingsinoroutofthecoincidencewindow,so
the decrease in efficiency of detectors responsible for
istic theory: tings, and then determine the counts and relative errors that a completely local process can match quantum me-
“ 1” outcomes causes outcomes nominally “ 1” to be
(d−ue to both finite counting statistics as well a−s multiple chanical expectation values. However, this loophole can
includedas“ ”,mappingn (a ,b )ton (a ,b )
p12 a;b p12 a;b0 p12 a0;b p12 a0;b0 amnedasnuremen(at⊥s,obf)eatcohnterm)(.+a1,,−b1)509. F1urther+m1,o⊥re,0tes1t- beavoidedbyusingacoincidencewindowdefinedaround
ð pÞþa pð b Þ; þ ð Þ$ ð Þ (1) ingFnoor−no1luo,+rc1aelnitt1aynwg0litehm(eenqt⊥.s3,o+)u1irscre1o[b1u09s]t,twoethfoecPuosisthsoen3ia5n5-nnam- asystemclock: Ref.60achievesthiswithachoppedlaser
1 2 pulsethatdrivestheSPDCtocreatephotonpairsinwell-
% ð Þþ ð Þ tpuurleseodf plahsoetrono-nctoountwtinogomrtehaosguornemalenntosnolinneSaPrDcCryssotaulrscetos
defined events.
wherea,a b;b arethesettingsfordetector1(2),p x apnroddurecmeopvoallaroifzatthioenv-aecnutaunmglevdiapphoostto-nselpeacitrisonatis71n0otnrme-,
denotes th0eð pro0bÞability of a count for any given tr1iða2ÞlðaÞt qvuiairesdp.ontaneous parametric8 down-conversion [23]. The Ref. 60 also highlights the “production-rate loophole”
deTgrweeo roefceennttaenxgpleermimenetntosf59t,6h0erdepowornt-cvoionlvaetriotendopfhEobtoenr-s where non-random drifting of the pump laser power or
detector 1 (2) with setting x, and p12ðx;yÞ denotes the achievhceada nrwdith’b sae pienrcfeeocqtnlyut araloiglniletldey rdefteoruensccieln ofrgasmeew, tSaohpvt e=e 2d.5pe4 lt±ae 0tc.e0t6si, ownthoichl oims oclaopsneh itopo lutehle.a BteeBll voatlthuhee SSNR = detection efficiency can be exploited by local realistic
probability of a coincidence count with settings x and y 0.91·2(cid:1103)(cid:1006)(cid:3)(cid:124) 2.57 that is limited only by the SNR. This agreement indicates that the polarization errors did not
models, however the experimental drifts in Ref. 59 have
for detectors 1 and 2, respectively. The inequality can be resultetpr frDrxeuoiafmpifm"en preesoprnHliatit rmsiipzpoaaotecni=oenl-npat tidmerse2diecz osguhcaweeestnreeiainorslicoleenhs..n ; ipFgsorrioh o.trhedese. u,sffia(ckaTeec oiEfep tcnhSoumce)mpy6le2petesnnaietpnsnasog,nd wllgaee hlrheiapizvdghea hpotseitrotcfooanorntmleeloedd cBfeetHltlið eoejxHcnVpteriiienmþfeg-nts us- been shown66 to be not sufficient for this loophole. Al-
violated using maximally entangled states [e.g., HH ing dififfecreinetn jspcaycie-Þtpimhe aorrtaongnemesnotsu orf cthee sreletvoants euvernpts,a aschsievEingb siegnrihficaanrt dBesll veioðffiljaticonise inni ceþaych case ternatively,aquantumrandomnumbergeneratorcanbe
VV =p2,whereHandVrepresentthepolarizatiðojnofithþe (Tabletr 2he).r iðe"sþh"olcdÞj,VVaffiffiffinidÞ=pea2c,hwohberteai"ncηis>the70re%la:tivReepf.ha5s9eupsiceksead used to randomly choose measurement settings in order
jp0h:8o2ti8oÞ;nsth],ffiiffiffisasissutmheinlgowaedreeteffictciioennceyffilcimienitcfyo!ra>ny2ðmpa2x$im1aÞl&ly Acknohuwpilegdhignemcteohnltelse cntoinonlineeffiafficrffiffiicernycsytaplhso[t2o4n].sourcebasedonaSagnac tsoaticslfoysiengthteheprmoodruectsitornin-rgaetnetloreoqpuhiorelem60e.ntFoufrtrhaenrdmomorley,
ffiffiffi
entangled two-particle system measured with a pair of The authors wish to thank F. Sanchez (Director IAC) and A. Alonso (IAC), T. Augusteijn, C. Perez and the staff of the Nordic chosen measurement settings for every entangled parti-
Optical (Teale)s$cope (NOT), J. Kuusela, Z. Sodnik and J. Perdigues of the Optical Ground Station (OGS), and J. Carlos and the cle pair in order to close the freedom of choice loophole
detectorsthateachhastwosettings[21].However,further staff of the Residence of the Observatorio del Roque de Los Muchachos for their support at the trial sites; as well as C.
Brukner for helpful discussions and an anonymous referee of an earlier manuscript draft for his/her comments on the free- simultaneously addresses production-rate loophole.
analysisbyEberhard[22]showedthatwithnonmaximally dom-of-choice loophole within deterministic theories. This work was supported by ESA (contract number 18805/04/NL/HE),
ethnetadnegtleecdtosrtaetfefis,ciee.ngc.y, jrceqruii¼remðrejnHtHciouþldjVbVeiÞr=edpu1ceþdrt2o, Etthiuoern osAp uPesraotnrgi arCanom mS cAmieSinAsscPieo. nF oQu-nEdsasetinocne ,( FaWndF )t huen dAeurs tprrioanje cRte nseuamrcbhe rP rSoFmB oF4ti0o0n8 A, gtheen cDyo (cFtFoGr)a lt hPrroouggrahm th Ceo AQuusSt,r itahne Sppraocjee cAt popfl itchae- expFerereimdoemntsofacthteomiceptaenddtloocaclliotyselotohpeholloec—alTitwyolofaomphooules
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi through space like separation by fast measurement set-
2=3, although the tolerable amount of background counts
Figures and tables tings chosen during the time of flight of the entangled
inthedetectorisverysmallinthislimit.Essentially,using photons67,68. HoweverthesettingsofRef.67werechosen
asmallvalueofr,onecanchooseaandbtonearlyblock
(b)$ using periodic sinusoids and were therefore predictable
the vertically polarized single counts [thereby decreasing FIG. 1(coloronline). Adiagramofthesystemusedtoviolate
and susceptible to influence by hidden variables created
theright-handsideofEq.(1)],whilechoosinga0 andb0 to theCHBellinequality[19].Wepulseourlaser(L)byputtinga at the source, so failed to close the freedom of choice
maximize the left-hand side [19]. For the background Pockels cell (PC) between crossed polarizers (P1 and P2). The loophole—thepossibleinfluenceofmeasurementsettings
levels in our experiment, a value of r 0:26 allows us to Pockels cell is periodically turned on for a short time to allow by either other measurement apparatus or hidden vari-
¼ 240 laser pulses to transmit through P2, thus creating event
maximally violate the CH inequality. ables created at the source of photons. The random set-
intervals that the detectors can distinguish, which we can then
In order to determine the probabilities in Eq. (1), we tings of Ref. 68 were chosen within the forwards light
use as well-defined trials. Down-conversion is produced in
normalize the measured singles and coincidence rates to cone of the emission point of the entangled photons, so
paired nonlinear BiBO crystals (NLC). The produced state is
the number of trials with the specific analyzer setting for could also have been influenced by hidden variables cre-
controlled through the half-wave plates HWP1 and HWP2,
each term. We can then write ated at the source. Improving upon these experiments
which control the relative amplitude and phase of the HH
j i the authors of Ref. 61 space-like separate their random
and VV down-conversionterms.Weattainveryhighentangle-
C a;b C a;b C a;b C a;b j i number generators to remove the possibility for trans-
B 12ð Þ 12ð 0Þ 12ð 0 Þ 12ð 0 0Þ mentqualityby compensatingtemporal decoherence caused by
¼ N a;b þ N a;b þ N a;b $ N a;b group-velocity dispersion in the down-conversion crystals [38], mitting any physical signal between entangled particle
0 0 0 0
ð Þ ð Þ ð Þ ð Þ usingaBBOcrystal(TC).Thedown-conversioncreationspotis emission and the random measurement settings. This
S a S b
1ð Þ 2ð Þ 0; (2) imagedontoasingle-modefiber(SMF).HWP3setsthebasisfor Bell test was performed between the two Canary Islands
$ N a $ N b % Figuret 1h: eExpperoimleanrtailz saettuipo. nThea Bnelal elxypesriimsen(tb waass ecadrrieod nout ibnetpwueetn fthreo ismlandQs oRf LNa PGalmad aandt aTe)nebrifye at an La Palma and Tenerife separated by 144km, with the
ð Þ ð Þ altitudFe oIfG 24.00 3m.. La PEalmxap: A e40r5i nmm laesenr tdisode f(LoD)r pumcpleod sa ipenriogdicallloy poolpedh KToP l(pepsKT.P) cr(ysata)l inH a pioglahrization-
based dtShaegetnaecBc inttrieeorfwenrosmteeeffiterrs,c toiea gnnengcerylaete cepnatoannlgalebrdi epzhioantocgnh piabeiresv iaen mdthe w(cid:663)s–p istilnhigtletteT srtaEte(S. POnBte oSph)oc.tolnoC pseuer sptatoirh mweas sent quantum random number generator used to choose mea-
where C x;y are the coincidence counts, and S x the
singlesco12uðntsfÞorthedurationoftheexperiment,N1ðx;Þy is tehr rcooungdsships eate et6d eck omctf r thlaoainlolfg-, ni acnnoditll eeqodur oaofrppetteircrh-aewlo nsailvnceeg le.pel-amfitFeosld it(egHe fWirubsePrr, e(Q(SIWMFfPFr))), o taoamn Ar eleilceeRcu t(rloosec-efoa.ptdetidc6 tano0le mx.too tdon(u tlalahyte)o srdo (SuEerOpctMeea)). ,ccA altei cp-eso’llpsai prkeiozeiclnagrti rzsbaaeetailopmlny- sapnlaitltyezr- surement bases space-like separated from the rest of the
ð Þ (PBS) aacnord antwtjoiu npghgoatottedheteecptoqhrsu o(DatTon, DntRus).. mA quFraniatnunmad lrlaoynmd,om ntnhuumemberb pgeehnreoragttooern3n0 s(eQrRaNaGtrAoe) rloscadtteehd taaet tac dtcieshtdanocoe bosfey 1.2 km, experiment (Fig. 3 (b)).
thetotalnumberoftrialswherethedetectorssettingswere cwohnicsihs tttwirnheagre eon fs saer nialittg inthoot dAenmloi-cietmet ivdniagg mad ei2o.-de4es aG e(LHsnEzuD sr)ar,o daei ro5m 0li/nd5ek0e.n Tbthteeeac mrsat ensopdtlorittmstie; nrb i(tBgtsSh sw) eaenraedo n utwsudeodt pptthouho stwtoemitscumhil tgtiphenleiea EarOssl (MusPM,r da)ee, rtmgeeernmeeirsnnaietntegnd i atfr atpnhtdeo- oinmc obmits- EPR-steering—Almost 80 years after Schr¨odinger re-
x, y, and N x is the number of trials where the channel ing phpaotaotnri wamatse um-seta,osue-redndia ignb ithtleae 2ls2.tc5°ho/1en12vl.5oe° crorta e6l7ri.5t°y(/1T5a7D.n5°Cd lin)efartre opeoldarreoizacmtoionro dbfascias.hl Alo tidimceee-ttaeegcgxintpgi ouennriti (mTeTvUe)e,n nlotctked to ferred to the effects of entanglement as “piloting” or
setting wasðx (Þregardless of the setting on the other side). the GPltSoi mtoimpee hsst.aondlaersd atndo cobmepencsaltoeds3e1 fdor. smFalil gdruiftsr uep tfor 1o0m ns, rRecoerdfe.d 6ev1er.y detection event (arrival time, detec-
“steering” of one quantum state by the measurement of
130406-2
6
LETTERS NATUREPHYSICSDOI:10.1038/NPHYS1766
another,theconceptofEPR-steeringwasformalised69,70
Alice Bob
andfollowedswiftlybyanEPR-steeringinequalitybased
onlocalmodels71. Steeringsitsstrictlybetweenentangle-
a
mentwitnesses72—thatrelyentirelyonassumptionsthat or 1
b
quantum mechanics is correct, to test for the presence
of non-seperability—and Bell-nonlocality—ideally no as- σˆk 2
sumptionsaremadeabouttheexperimentalsetuporthe
model of physics. The modern concept (Fig. 4) assumes Ak 3 4 σBk
thatonehalfofthesystem, anobserverBob, fullytrusts
Key:Classical communication: Entangled pair: Pure state:
his measurement apparatus and that any states in his
Output: Detector: Measurement: Analyser:
possession adhere to the laws of quantum mechanics. A
second party (Alice) is tasked with convincingFBiguoreb1 tThheastteeringtask.BobisscepticalthatAlicecanremotelyaffect(steer)hisstate.Bobtrustshismeasuringdevice(representedbythewhite
|
box),inparticularthatitbFehIaGves.a4cc.orEdinPgtoRtheslatweseofrqiunangtu.mmHecehraenicos,nbuetmoabkessenrovasesrum(pBtioonsba)boturtuAlsictes’sstyhsteemiranddevices(represented
she can steer a quantum state that she has alrebyathdeyblacskebnoxt).Thestepsinthetask,fromtop(1)tobottom(4)areasfollows.(1)Bobreceiveshisqubit.Heisunsurewhetherhehasreceived(a)half
system works according to quantum mechanics (denoted by
tohim. Importantly,noassumptionsaremadeaofbanoeuntatngtlehdepairor(b)apurestatesentbyAlice.(2)AfterBobreceiveshisqubit,heannouncestoAlicehischoiceofmeasurementsettingfromthe
physicstowhichAlicehasaccess,sosheisfreetsmoeatn{uy�ˆkBrsu}e.n(s3)a)thnBeoybstreeecroinrdgspaphairlsaycomwlieennteagmrrSenBa.bsIufoortehbxmis)eiwsn,tgiwrrteesahhuteltiraslte�hkaqBnaaunandacoernerttctaheuiinvemebrsouthpnsedat,reaArslttuicyleteAha(kastAnhdadeltmiAcdoleincese)tmdraietscoeldantrsesatset.se(rrk4ian)egtBdooifnbBwcgoobmi’sstbhshintaeetssect,uhaaenpdnr-etshuultssBtoobccaalcnublaetesu(orevethrat
meanstocarryouthertask. Assuminglocalmohdereeclesiv,edtah,niostb. affecthismeasurementresultsbyanymeans(blackbox). As-
experiment is constrained by the inequality71 a suminglocallawsofpbhysics,aninequalityforc thisexperiment
n 1is derived, which is vio1lated when Alice choose1s to share en-
S 1 (cid:88)(cid:10)A σB(cid:11) C (4) tanglement between herself and Bob. Figure from Ref. 73.
n ≡ n k k ≤ n 0 0 0
k=1
in which Alice and Bob compare n measurement results;
σkB is the kth of n measurements performed by Bob in ¬1¬wo1fisme0eaallsouwr1e¬tm1hee0npt1hsoettotni¬n1¬1pg.airT0shoiusr1ics¬e1tth0oei1nfiflrsutent¬¬1ic1meetha0enchoon1il¬co1e-0 1
conjunction with Alice declaring a measurement result
A 1,+1 . C isthemaximumvaluethatcanbeob- cal quadntum effect has beeneexplored whilst simultane-
k n
tain∈ed{−forthe}quantityS ,providedBobhaspre-existing ously clos1ing three major looph1oles. Collectively, these
n experiments74–76 markanimportantprogressiontowards
states known to Alice. This inequality is violated when
AliceinsteadsharesentanglementwithBob,andthrough loophole-0freedevice-independen0ttestsofBellnonlocality.
her own measurements, affects Bob’s results. Reference frame independent nonlocality tests—
demSaounnsdtrearstioentsoafl.v73iolpateirnfogrSmteeedrinthgeinfieqrsutaleitxiepserwimithenptoa-l Tshraardeidtiorne¬¬1af1ellrye,n0cenofn1ral¬om1cae0l.ity1Thtaets¬t¬1is1s ttoa0kseayp1tlah¬1caet0 Aw1liitcheinanda
larisationentangledphotons,showingthatincreFaigusrien2g|Ptlahtoneic-solidmBeoasburemaenrtescheambesl.eMeatsuoremaenltiagxensuktarhedeeifirnedmbytehaeBsluocrh-espmaceednirtectioanspthproaugrhaatnutipsodalpairsofverticesof
number of measurements n (testing up to nre=gular6fi)gureisn.a-–e,Squawre,int=h2(ar)e,asnpdtehecftourtsouitaoblnePelatoannicosotlidhs:eorct.aheTdrohn,ins=3m(ba);ycubbe,ne=p4(rco);bicolseahmedarotn,inc=6(d),and
dodecahedron,n 10(e).Thebulletsymbolsshowtheorientationsofpurestatesinoptimalcheatingensemblesfortwo-qubitWernerstates.Indande
creases the robustness of this nonlocality testttheoseestxatepsealrig-n=withthfeomreasuerexmpenetraxiems(veenrtitcess),ubustiinnag–cthleoyhnavgethoepdutaliacrraanlgemfiebntr,oenthoerfacefcreentere-ss,spimailacretothesituationin
imental noise. However, just like Bell-like ineraqnudoaml-aictcieesssc,odes28.orbital communications. One solution is to harness
local models can also exploit loopholes to explainTosdteereivre-usefuldienceqouhaleitireesnwcee-cfornesiedersumbeasspuraemceenst77, wWehrnicerhstahteas18sarbeetheenbesrt-ekcnoewnntlcylassofmixedentangled
settingsbasedaroundthefourPlatonicsolidsthathavevertices states.Forqubits,theycanbewrittenas
ing. Steering has less stringent requirementsthtahtacnomethine antipoimdalpplaeimrs e(Fnigt.e2d). Eauchsinpagir dhefyinbesriad polarisation and orbital
atthrhfoyorlreeoesmhfwotehlhndeetniooeuxnfspeiηdenrgi>nmonenn1l=o/t,3caa3lfniotdmryehcatalesossustraisnen,mgdeextunhpetees.rtiodmeTttehehncerttem4awf(ieeoiar,oihrleffi)lsainao6cnseyEwhucgxxaimreniplnempweogmedm:reneeoienmn1rc(tpedi0.teiy)i---nFdatsoDaxerlitelnstyerionaivutcgdehkaiatse,.niminnmmgtgeFhogpeiaoenqvaliureistsnnutmuberlgnrcaoaaedetunrme=lrun.tiesedtEa2nymePaRtsxnRCspsee-onceeitshartntmmiireeiinmremnnagreaensieann,ngtrdhtg(leaketwiemilxgulbaemyceyni)ebnmnputemevltswqiyneoffueoo,elesaararnlitniidiontnnttysotqgn=a=uh(fttan11hhror03a)eeege,,.fsleetbwµ((dhrBshee2eeefele.lrs[t–1e0nttqC8,|a)i1H9u.n]stT.S�ahgeHWhinseso)eiy7tswrincn8uttaeehn.noqmrWeuvssµatitoaivln=ihTtslteaigyystoaµlheeoast|lttn9riatheslsyete�tsaeiCimehntfhertl9µaaaeauna�rnq>sig|deinl+uern1,BdvI/i(Hgpr1eiiefsoe�2salrat,s-nlnµhaeden),IdoSi/dhn4ceilanmyntinoiftnoy(,tyifvaaf)innodµdlaHtw>eoh1al(ent/3r23ye)0
ments published around the same time collectinievqeulaylityaudsi-ng Wercnoermsptatlees.te(iiir)eTfehreoerneticcaellyfrsahomwethiast nBoetllirneeqquauliitryeifdµ<fo0.r65t95w(oref.r9e).mReofetreence2showedthatthese
Alice can saturate the inequality by sending Bob pure states statesarealsosteerable,withn settings,iffµ>1/2.Withn 2
dress loop-hole-free steering74–76. All three expdrearwinmbeynhtersfrom apaparrttiiceulsarteonsevmibolel.a(tive) EaxpBeriemlelntianllyequpraoljeicttyiv,emperaosuvreimdeendtstthehye!arep1sateerrtaibelesiffµ>1/p2,nobet=ter
use Sagnac entanglement sources (see Box 1) todeminocnsrtreaatese(iii) abosvheabryeneaorlnyesatmuraetiangsuthreeEmPRe-nstteeridngiretchtainothneBpelle–CrfHeScHtilnye,quatlihtye.Dyerihvinagvaenalyticalexpressionsfor
experiment efficiency and close the detectioninloeqoupalihtyoinleth;atway.high probability to violate atheBboeulnldsinCneqisuaasilmitpyleepxeercrisfeeicntglyeometry(seeMethods).
itnoras.ddiBtieonnneStmeitthale.7t4alu.7s5euuspe TtoESns=ing1le6pmhoeat8os4un6redmeteenct- wmiatxhimaallmyaxcoimmap©l ll2iy0m11 Meeanncmttilalaanrn Pyugbllisemhedrse LaimssiNtteuAdaT.r U tAeRelElm rPigHhbeYtsSn yIrCetsSes|rveVeOdai.L nc6h|NtOhVcEehMBoEpRo2ls0ai10nn|gewww.nature.com/naturephysics
settings, which they show allows them to measure vio- orthogonaltotheshareddirectionintheBlochsphere79.
lation of Eq. (4) without assuming fair sampling despite By increasing the complexity of the measurements
high loss (87% loss) induced by 1km of coiled optical each party makes, observers can always violate a Bell
fibre between the entanglement source and one of the inequality without sharing any information about their
measurement apparatus; this explores the conditions for reference frames80,81. This potentially removes the need
closing freedom of choice and locality loopholes over a of establishing reference frames for future nonlocality
lossy channel. In addition to closing the detection loop- tests, in particular taking nonlocality tests into orbit to
hole, Witmann76 enforces strict Einstein locality condi- help address the locality loophole.
tions,withspace-likeseparationover48mofopticalfibre. Multipartite locality tests—The majority of nonlocal-
This closes the locality loophole. In addition they use a ity tests have been focused towards using bi-partite en-
space-likeseparatedquantum-randomnumbergenerator, tanglement. Greenberger Horne and Zeilinger extended
closing the freedom-of-choice loophole that would other- nonlocality tests to that of three-party entanglement
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms1628 7 ARTICLE
(GHZ); this was formulated into an inequality to test (a)$ PC collection apparatus, we optimized the pump and collection spots
for multipartite nonlocality by Mermin82. The first TES LP based on ref. 19, with the optimum found at using pump spot and
3-photon GHZ entanglement was demonstrated fifteen Alice L2 TES collection mode diameters of 200 and 84 (cid:77)m in the crystal, respec-
years ago using a pulsed SPDC source83 and was then ppKTP L2 PBS SPAD tively. With these parameters, we achieved a typical pair detection
subsequentlyusedtoviolateMermin’sinequality84;four- PBS HWP efficiency of 40% measured with standard single-photon avalanche
diodes (SPADs), whose detection efficiency was estimated to be
photon GHZ states85,86 have also been used for local re- QWP BD
50% at 820 nm, implying a collection efficiency of 80%. Owing to
alism tests87. However, until recently no multi-photon HWP QWPHWP the asymmetry of the steering task, the source and detection system
experiment has succeeded in addressing loopholes that LD do not have to be symmetric. For example, in our setup Alice does
BP Bob
ctgoalerndisbsetohueerxctpeyslpo.iictReadlelcybenlyotwlLyH,bErVigr.vhTetnnheeestsmaoalf.j8mo8rurlcetopi-noptrhrtioebdtuotngineengnetrfaaanct--- PC SourLc1e LPL2 NAPTCURECOMMUNICwAwTwIO.nNaStu|reD.cOoIm:1/0s.1c0ie3n8t/ifniccroemnbcpmoiaoerscttn2s k3ceg0ym7r ocpuolnnoydd i, tnbiaourntr eordewd o-ubnca eBnsod hb e’fisr l mtleoerssas;s, utthhreuisms cienhncotr.iecaes iinngc rtehaes edse theecrti AoonvR eeTrffiaIl-Cl LE
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tion. By eliminating the transverse walk-off effect via dtieomzvnicaoefesmt.aTaishxoeiumsnyarmlelymmerentteraeincfngslrtertdui csgattuaxtreeesiri,ssinaa,l tshtoleiuopms∼rerefsusielntfoceeradothf newbsatdvayebgl eutigddheeneleeorst as-.veicstFhitigebuiprioeoll2ainrctizysaht oieoownffisfrt ohttecahtliiiogeenh tnatsnrahgcnlesaimaertisetsshidoen roopstraftotaporetrehtiSe.Ps RoI(9fsfet he5eM%reeftpehroeadnrsc)ea.tively low rates of photon-pair creation. We achieved optimal
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tcioonnfigeuffircaiteinocnyhinastobseienngledemmoodnestfirbatreedistoobotapienreadt.e Twhitihs sF(wSpuaSBiasurvCnrteihir)ogoen,euurewbimsqdghe ouipcrcglnhehiaer,oecitoltsuo-thiinastewptsns ydfiohoten hrv(tnaeiaor3ctreffeoua)tlclii, lsmeoy uwwtieitnnqthiittuehltiiehglpnrse pnaibldetieedca edapelpw QEoylvtiriItc[Phioae(cid:159)totsihacyoBrˆelsnrstaetieptmt(cid:174)oyoopeptf2A-oersdonsiitzhso]ea erfic=cfqthso uio(nepau(cid:73)v.nSredctVruetatoSm2e.h1crf.2ihP1n.i 066sfeNuThDofi0vnu00lecrn..mac1t0sieu1miohn,s)nwtwhio aos9a(hosfmtt7i5p-oaliwenn0bsattcepaahtladuiotaeinhdnderretnieertddsaifenoesf(anrfo8ev rea3ond5rtl0smecmoh-enmuuiansmtaampiflpttit-iuetcloitt oooiipmnnetnnntogghwwlr)aasiweriecruonlieiiz ctpreoohwonsrnotgaaatanhvnnfpeerregeogirdelnlureadopg.irrdeudAwihizeveanhoiectssSwxiatiPogibhtoRngiii slbnvriinrtiaetnoyl)eustVdaae,agatbagrooonhrffssaemad08oat.6nsv9are.al97aiplen,w trgtioaihranteei,wn sltpioghraes ec~siwnN 1digdb2utoN hkef Htozttl aih dotorineeofea np-sdsdrion iatmpsgiemelsrnehties oeip sowwhnonaaoflsittn hofi~ennF2idistg.ee 5.it-ne%1dcci tf..eofeTarrcheahnerec feTufinrEtsidmtSaa mecn-hedanloaytmsnaelandionenplut.(i mFcAaDeltrT mitcDhao)lidlsyes iwmoifutha-
CW or pulsed regimes90 with at least 80% coupling SCpaIENprTIoFpICmlREiPcOisRaTiStn|i2og:n81a7sl|:tDOehI:r1en0.r1a0e3t8/iasvrepe0s0i8(cid:73)fn1o7Vgr2leb>1co1ph2/ti0hNphno.mutfs.orinLengieghf-aotscbpfurssoaimoncgreabgnraeaetdnxintdegrbncyiaonlultapaesleegsrr((sur44sao())pFutiergecr.edE-1ibsx)pc2,oepuripnilmkedetrinniattnoagllt ehvse,iol7tao5tw0ioa!rnd1 s1ot0fhn eomNu2brN ssiltdieceoetenrcitnowrgar veiegngiuoeinqdue(liagilshittylsat.ur unWcctheue rdeprinforodthmueccetehdnet releoftf
Feffiorcifeuntcuyreaenxdpefroirmaentnsu,mabmeroroef cnoomnpliancetarsomuracteeroiaflse9n1-. acrocnhSaidtteuisccftyutironerg ibtsh ieca hsraeeqldluenijrgueimsntge.nb tFeso lgori wvtgtehwuneiiodt bpesmdaytc ahienlrsoq:iinumotgniaaecltoliapw oals-ntleho ct(sl us4eoa)prd fhris oneNtto onaw n=t iapc 2rIhdw scomattvhcoeeegrnaudesiiec-dat eetcs,etoastwrnhdahenfe duprrteothh leaeHrortishzp aealirnttipdiona ntthoV-en rtethelaeepcntrigrmeilcseaeodgnep )tst.i icsnFainliggmgluelrotee d she1t.odaItrnediz its|ohp(cid:90)enlatp(cid:13)yasr(cid:174)le st(cid:29)ahenne(cd|esH uvopeVfprtot(cid:174)hri(cid:13)etcea|dNlV bpsHNiongl(cid:174)talh)eri/nitzrfiae2nldm,s v,etrhsee
a local resistive “hotspot”,isdgireencteedratotaincogntraolpvoortl.tAafgterepapssuinlgseth.roughthedetector, evanescenttailoftheguidedopticalmodeiscoupledstronglyto
tangled photons would likely use an integrated archi- urement settings, an experimentaaln ytersets idouf althlieg hstteisercionllgec tiendeqinutoaliatny addpithioontaolnosu,t pruetsppeocrttivethlye, saunpedrc opnedrufoctrinmgewdir esse.pInarthaitsec amsee,tahseuorpetmicaelnfitesld isna r2e more
tecture, where stabilised path-entangled photons92 and (S3u) rpeeqruciroens,d evuecnt fionrg a pdueret eencttaonrgsle(blda baseisnlleegddlerteo ssitndautaeNl wlbigithNht vpnoisraitbniinloiFtwyig V.ir1 =be) s1.,T ohpusa-,nfodr 3th edipffuerproesnet obfasetisg h(tNly =co 2n,fi 3n,e dwittoht hmeedaesteucrtoermweinretss, aosf sXhˆo,w Yˆn ainndth eZˆi)n.s etof
polarisation-entangled photons93 can be generated. tehraatt Aelaicte ∼det4eKcts tae msigpnearl amtuorree sientshtiatimaiannlad ted(cid:72)eaa t>besrc 5oteor0pr%ctisoa cnoprefleao nstbsihnelsege, frtootihmmfeetvhpseeh oBrNtyoobnNbfi cawsicrtiTherscubeiyt dmaislelcoarswuesrtienu gpsrthotoebab(TiFhliigits.yc 1odeui)sp,tlwirniigtbhulestaiidgosnnitfio fcosatrnr otAnfigleicladbes eaonnrhpdatin oBcneomobf’estnh cteoairntrcetohlmaetiNniogbnNwsa, svied,eass.
rceoquunesttisn ag rersaptoensse.( Tuop retaochG thHeszeli) grhetaqcnuoidurpelmeldoewonuttsd,o ntahrtehk eexrcepsoeiduruinamltelsinght(ta<lp ort1Pre(lAatiiv=etao,Bthje=ligbh)t, is psrheosewntned inin Ftihgeulroeg -3palo. tForfotmhe tmhoedsael, iwnteen fisritsyt iens(tFimig.a1tce)d.F rom
Increasing detector efficiency—Single photon detec- aHpzp)a9ra5t.usN hbasN to nbae ncaorwefiurlely dopettiemceixtztoreadrcts.edcafrnomoptheeracotnetroilnpcorot.mInmtehrea-nsc aanvneinraggeedle chtreornaldtihnego petffiicacliseinmcuyla t(cid:72)io na,nwde oebnttaainn1g0le.1d± s0t.a2tdeB vaitsteinbuilaittiyo nVw ithin
tors94 underpinthemeasurementsmadebytheobservers cialcryo-coolers94. RecentNmNbibcNrNosgtrrnaupcahtunr(Feosigwa.r1ierbde,isincdesreenttiabenlecdtasaoltsrhoseSluiugphsptilnreemggaienonndtas ,rylcoocFamigte.pdSa2or)ne,dttoh petheaamtte1 n0tu-oma mtitohnleop negtrhwmeomavreeogtfuiciddaeelt ecwmtoitirhnlieNmnbgutNhm.wT ihrreeesqFuDoinrTeDmtospei,mntousrl,a t1iodnBs
in any photonic nonlocality experiment. Transition edge Eaxtprearvimelelnintagl wseatuvpe. dWees ipgenrf9o6rmhoeafdvth eoeusdirlei cemoxnpopehnroistmotnreiacnttc ierucdsuiintorgyn, -aescnhatlasionp-hidghele-igqhuteadtiionnth (e4s)e,c ionn dFigualrsoe 3rebv.e aThlneo palpoptr eicniadbilcearteeflse cat icoonn(colusi2v8ed, Bd)etfreocmtiothne-onset
seemnbsoedrsde(dTEinSa)naroeptfiacbarlicstaatcekdoufsminagtearitahlisntotuennghsatnencefitlhme gtdttaeileenoscdeintg opinuooh snfo mptNoeaenrffiebastT mscc riieteeNtwarntoieccn d ydac iornnauw oabcnw ipoacolvio rlneaervrei9eqszri0uasnti%iriozoegoeoxpnl.nmtoter1im acS6Iecap-,anntl1ingp7htth,sona soe;rsca tdetasdca,neoed msnt neFoiihecntuittigigaodgrolrucehernlresae tied cg,bee tin2orancrao.sfltet nreaThfoecrdnqmoer ugmoiisnesclnnre totoscd hsosyne-pcru(poeocRrpSahancFeiii)eplr-N-ii ,ncsoas9aesnt7l-t.soahIcoontwIppnanhadddodisenilteeaitro-dhefn,er ufetsuooeeprd pdt htteehoerme osotwtnrfeaasenvtthersrgieiatnuitomigidno eepnafsnra eoodrcmaefti rmostntsheet,reetwuerbchritane urSrrege3e.. stdhiTleiechfiouisnlntrieawsdtaha viinenrge Nsu(ui3"bdlt)Ne,o twlfaoyeteth hroeecbnoNtemaabiprNn-aa-erdcedoida vbwearitetihdc
absorption62. With the voltage biased at their super- ceoxltleecntidons etffihecieonpcey raantdi nngearw-iadveaehll aeplfnoolgaftrFihizga.ft1riboo.nm enItRangtloemveinsti.ble and theunSd3er=ly1in.7g4si0li8co(cid:111)n0la.y0e0r1gi7v,es anarearatioof1:118.Becauseof
conducting transition, absorbed photons cause a mea- redWuec efsolldoawrekd croefu. n1t7 riant ethteo bNmaATsUiiclRlE iCd-OHeMsMzigU.NnIC AoTfIO NoSu|3r:13 2s5o|DuOrI:c1e0..1 03T8/on commws2h30e7r|ew wwth.naetu reu.cnomc/enrattuareicnomtym un(ic1at siotnasndard deviation) was calculated by 3
surable change in the current flowing through the tung- maximize the conditional coupling between Alice and Bob’s &20s1t2aMnadcmarildla npPruobplisahgerastLioimnit eodf. Atlhlreig hPtosiressseorvneida.n photon-counting statistics.
sten film that is efficiently measured with a supercon-
NATURE COMMUNICATIONS | 3:625 | DOI: 10.1038/ncomms1628 | www.nature.com/naturecommunications (cid:20)
ducting quantum interference device amplifier. TES re-
© 2012 Macmillan Publishers Limited. All rights reserved.
8
Outlook tum photonics101 have developed a path to challenging
Photonicexperimentsoverthepastfourdecadeshavean- the ECT on a near term timescale, with a non-universal
swered many important debates in the fundamental the- quantum photonic device that performs a task known as
ory of quantum mechanics and new photonic technolo- Boson Sampling102–105. If experiments confirm the pre-
gies continue to create opportunities to close loopholes, diction, as we believe they will, that our universe cannot
answer old questions, and even inspire new theoretical beefficientlysimulatedbyaclassicalmachine,thenthere
research. Experimental confirmation of the predictions may be other confounding features of quantum mechan-
of quantum physics during the previous century forced ics currently hidden from us and apparent only through
a reevaluation of the understanding of the operation of simulations on a quantum computer. It is therefore pos-
the universe as a classical machine, at least at the mi- sible that, rather than confirming existing theory, future
croscopic scale. Over the coming decades, as we increase photonic experiments might be the first to reveal new
our capabilities to harness the effects of quantum me- and complex quantum phenomena, requiring innovative
chanics to build quantum computers98, we will test the theoretical explanations.
extenttowhichquantumeffectspersistatamacroscopic
scale, with further potential consequences for our under-
standingoftheuniverse. Famously,theExtendedChurch
ACKNOWLEDGMENTS
Turing Thesis (ECT) says that all computational prob-
lems that are efficiently solvable with realistic physical
systemscanbeefficientlysolvedwithaclassicalmachine TheauthorsaregratefulforfinancialsupportfromEP-
— a statement clearly in conflict with our hopes for the SRC, ERC, NSQI, NRF (SG) and MOE (SG). JCFM
capabilities of quantum computers99. While we might is supported by a Leverhulme Trust Early-Career Fel-
have to wait some time for a universal quantum com- lowship. JLOB acknowledges a Royal Society Wolfson
puter to operate at the scale which challenges the ECT, MeritAwardandaRoyalAcademyofEngineeringChair
recenttheoretical100 andtechnologicaladvancesinquan- in Emerging Technologies.
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