Trends in Quantum Physics

225 Pages·2004·9.71 MB·English

by  Volodymyr Krasnoholovets, Frank Columbus, John Cortese, Zhiwei Deng, Shao-Ming Fei, Hanno Hammer, Zhiheng Lu, Matteo G. A. Paris, Lu Shan, D. A. Slavnov, Alexander Yu Vlasov

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AT eights tered. No part of tis bock may be eprudionl, seul iv risa seam oF
trnmite it any for ur hy any means. clsewoni,cletosiatc. meunotie Lape, mechs wit
huts ing, stoning aoe witout penisson fa the pubis.

ve autor rl publiher ave tea in tegration of tis Boek, but make ou express or
ingle seanarty af sry kird and essume no respnsitilty far eros 1 ons. Na
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intemal etna in chook,

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sult eter ec Tuerin, Hig sold wih the clear uderstaedy thatthe publiss & we
nanged fh ronderre les ue ay ulner poole genvses. 1 legal or any ater expt
tsisce is roger the sericee oF a compotnt pers shouis te sought RROM. A
DICLARATION OF PARTICIPANTS JOINTLY ADUPIUD AY & COMI [EE OF THE
AMERICAN BAR ASSOCIATION AND 4 COMMITTER OF PUBLISHERS,

Prone

Tt Sates ef Ameroa
CONTENTS:

Pretace

tonal Approach to Shunnon-Mviener lnfornetinn
Fiat Hane

Nowloeal Propertcs and Loca Invariants
Stace

Entangled Light und Applications
Moe tik Les

Inplermentalon of Dense Coding using the Generalized Grover'sAtgurithn
Silt Zong, Zio Ee La Shot a Zed Deng,

(Classical Communicutian Over Quantum Chines: Am Algebate Analysis
kn Contes

From Fermat's Lust Theorem to tke Quantunn Computer
sone Ya, Hla

‘Quan Mectanes and an Onjective Realty
D a Slomoe

bs

193

Preface

Volalyripe Keacnshiduses 9 sal Fri Colin

Allkeugh Une savious banc of physics fer iv their experianal etl
send theveescal aspooneliae, carts yaucrs] puiuciphes aayly Uo oil of ern. The
xref, oF eantennpareny aches i playin os L: dae sbauisrmoopic exlie,
swhethet ibe iu atoue, see waulenwalcatier, glia, pare’ phpsies,
in quatuun optics, oe even ih Ihe side of stellar strnehre. AD ane hase mp,
vant thes Ga. nena asa ey aul qua: bel Ray) ua ea

Solel .ogu: i Fen chs thseansiealtorndioas of moreen pigs, Asay phyteal
fhugsbives wheee elagsisal omencempeote vie eourinuenly uve a reat af yosble
tultes 2204 quantum sheray oanatoninad to have dieratnmyses. on isercte wales.
Vee intsnsiliy doceeranivec Cauaatex of nice! plysies is aoplavcl a yucatan
Ulwury by iatrasie ui vrtinly. Arcncding ta cuss theory: lertzomagncti cud-

rion nea nor a ane canst oF renames wuss sted ies Le vce ae
sea « ae a rollection af parci.elike photos, te ecsry aid m03.c:>
ror of ened buiug lieve pooprLiat ls le aspen Gor cel pratt
ils wave thy ploia.s sti Twasisiy, sare eacelte charsecesieres}. TEs
twee bole pecaeusy sabe of gob aekaucs ats sat Ue wo

‘The Skannou-Witcr inmotion ole peuba ely Wabeiburian "she go
jeob fs uig “9 the ald of Caseen) Iaformasioa Peony, Tee genszazatiow iat te
yoga rege, lave woe Neouunoa se ea be ee? apne 2 Quatetuy
Intonation "Pho. rm atrampe 20 ena fli desi uf eat saeleuse

ally sle

in the stone aif a aadlipaele sulaaieaeal esses Vssed
fc lageeithoie Betiemal t+ etnar to the Sanne Viewer inforsontion weassge
‘into roturals, This Mi. ielde Coe vould rule of Slisccion Wigupe nist in

ll Cosel al Quarto Informe Theney. Manno Taner iseoduces a pec

Hua wkaven aziacack bs te Soatwee WW pane inkaemstian which boc peeves
Le-prelanon fr ite Snesioral farm eee! purty all uteaaleuat

or wit n shanide vtoneture ny a now wetusis Be Uoraaiicig Le scoe

Gl iniyrnaren going, iv 4 seb thamretis| Is-enage he arviven at a vest he rally

toe structures” over u glows sel, Qu eocl Lew sbectos, &

sled, lee jay Ue dopa: ub splitting se bis ching i

1 given tree I

fir detsh the the sadniuibention of vue lve Sau jou on, pasty eousasid, ets
cl ge eleuetures ranks thi Tinekional form a: the shaven Wiener inforesrion.

Thin ean imposter: Snding. ne: ewncrtentes Hat euteupy-like iulusalivu uta
vourrs 2cay Mcnecdous Iie uudecsted a Ue aul of a animator, proces
es Velodvaare Keasniatorets and Prank Colimnbns

‘vie general wnder/ying munhowetical strseoure. in a ener, she Shanwos-Wienor
ecmroyy fs the eu’. of a0 “aeuion prireinle. fe anslogue af tie yeti Fo onal
‘elug piven fy Ree tree Feros nt the seb of Lee sloectures. ‘Thia provides a
tine we iameunctational Lratnenor to entcops-Hke aacesures 0 alors, aed
caldngkment. He snggeece caer ualutel xian Fn dining tree stmeture. which
lure at to be related 20 tle anions dese’ bing neighhorhoads 09 © tapelosival
spre, fn aes, he shone thar roemy Hracurractiane oer aul defines 9 neighbauthond
trepslogy ou Us st. ‘Hay scars minirear‘on that reudns the fuetioua “ort of the
Stamnin -Wizer izkerwatiqn from the tree fimetion then na!gus u prfirsra bop
og to the rmdderTsius a, aly ul 4 doep relation herve entree Steaua:
said preforved sighhauthaod topologies. Umno Hess expeets hat these ind
hg will eantr.saze comacrthely tw Ue probla of eranglemer qaancifation in
srolirn Quasi. 1ua Psi

As oe of th eras stehing fartnnes of cusntm paeuwuecat, quuaban cian
lomant is playing we faspersane eles a qunutuus Iuonmstion processing mie #2
deoutua Genpulatien, qpauntuin telesortscinz, douse eodice aa] quacitue ergy
raphie scvemee. Shoo Eng Te! iavealigates Uke quanti enterglemen: wud sep-
lly fa leray a Cae iavaelanis wae? local nulzury traaurcaueas, A. your
fact ‘emma of sonmuevence for high én scaiugl ~ ul ipactile euanenre mete
fa proserced, The ensagloweal of oowatign for clare of big eliwasivua wise,
{hiparsiee mannan resten weceeaced, Exes wlio. ud usossers ooze iona
for sepecni'ty of teak Lio deus as. ines nmlbipartice quantun systeaus wis
EMTevent eémensions are gees. A ueuueponalilily lug ality is algo presented, for
Phe ene alien one af Se viysasoelo

utospirtdng, ta the samzeco viral be
‘As auerally ereangied state. Ll noulcesl yeopecties af yuu rke Nos ensional Bi
parte quent ste one inseaguual. X compli get of !nvgrienes made ‘oeel
‘itary tzansformstions i preseomid, e's sleseu Te. tne geuesie wes ty net sioge
gw Zocolly squuvaleal if al yu #7911 these ineawants wee eemal vals a

tastes Ce A. Paes nevi He auueration, piopayaliey, draractarizarion 26
rossi appli paused (ix Ses ef ley wales Of radintion, with the
tain fhems om the enteal nplenentativas of gant iaxccat eu pruceia,

rose uf

Dense ending kaa boon srapleututsd ushag the gueraliced Groeur's skguitlon
ud ils iuscrse operation, Explitisg the stperposicins af seo H?sstein-Pralesky-
Howe LEP) atites, enum that are powsle le Te lewis od inerease. ‘The
selwtaw Ie Tala Bluey Zlib La, Ly Shan, sad Zhiwet Deng is demonstrated
sing amelear magnetic esmonne (NRAT. Rael a esalls eas a good age
sevet bulwo sLoviy ad exportation

ola Covtese presets beret Murecction ya elasseal comsuniention ove
vant channels. The main anatstie reeult ot a prof that for a ypuis: cass
ol gai 2
C= kegel

al hates, Jey loro Set umaciee Wesimarelac! ohanmel capacity ia
=e Eiehs, where in che dissin of the ese, Cae a,
Peostias is

ieentenind no prodent of the wae lass of unital spakt channels. Chat eopsce
Hy altisiy ie debined, nl toe rokeckonehip hetwera the sania culrapy ot th
hms rpc nel slau sais is celine he cass of sre iices
fn thie coupler,
espe the arsive ack of maccy nescouelees i Une eet af eat: compa
fin asa el oleae soc mysterious germ. Heisalsouls aa aesos! cou,
Idk, Uist_maghe mang fassoasble curren, psujects will “ade fn che fitute, ant
ome avnolutey unprudivthle sjplientiona sppenr furl, Wir ses upbia de

Dprolictivis 27% toga! here, coasite ca extreme diGeulls Ww says wet one nes
Tomine quatua algoritluu or realisre “inducing” oppicatiou Cue seuss
Is tau very dees soiteman® btercen, Heap ao only am otteealy lark

feeob o fmdecountal Udy wus pnd wh sane Seige tsi

1G application. A prvi etch noraviel wannacs of 4 (Leer — te ulead
Tinka ener difercce ‘case of our ‘“uwlalyo. Alexander Yn, Vasov'a ortice
rucaigus ose such Lez — berween appl eatin of Wey qraulastion iv te eves
fof euratn ceincritanious ead wlglreet i" he arieal eongemotins baru ined sf
IR enctary duc to e.suecvetlul Lies tn proce werrage’s Ine Corea.

1D. A, Slime shoe Hist ie priucaplar et "Ww ulijeetsce oe! sheray® and earal-
Jov‘es ef Unsstanelan? re antinn maezanicn ae no iu wu atapoulsti iuozesisinaee
ce is nan. ly atsiand, Te proposes sebewe Soc onesbe sing qanesey ech sm
ies us. bist vi ihe Millet space nad Snear opezscors ae pesiuty laueats a Ue
aes. ‘The elements of » coanonckull ve wlysra (4. the obsarenbles} snd te
a this aigabra (a. the physcal stole seryo ve Ue pe
rm, “Vs cusubles of paysicol slater mes ysesiad for
ale el quvulunn states © che standard epamtma ie’snnics, Tis silica, ie0upo
cass Fes andar mathernacizal wince ul yuou.qua wiedaais. Sos. Laneeats
fee TU bere i a uulleuualica, olsen, veh adaamecely dosesbos advidna expec
‘evr, lites arta commu tina el teu Ube acyecament of meacurabiliy of
saprulabilily pus aca Uke prin 9 ef eamplimentoritg i quiets mec ales, He
hinea Cat seme kes ft accoict Hee cequicesaes ovens Ia CAEL
fos, dav Ba aeusdty dane ot fellate the hypot:ese asl he esisteawe of
sm ahjective resis

suv Fane or

tne eis Le 4

Tree Structures; A Variational Approach to
Shanuon Wiener Information

HANNO HAMM
Depastiawot of Matherstin. LBS
P.O, Heo
‘Mauelestor 3160 10
‘Unica! Isagdo|

Bevel HsHainmnverRovnie a

1 Abstract

‘he SlonmeatWancr iuluvastou of prob striations the ecatral object
Gf study ia Une “dal Classinal information Vary. Tey gear ies she
{qramtnnn regime, Jac as vo Neuuwun elem % ot equal Fost in Quen
Eagsisation Thousy. In sy nile alnerpt to qramtify tae éno> of Lange
fn the sane of n secsiprctit: quaciam syshu, enlangienere masenres baal ns

fecal fom similar zo Hu» ShauwwueWiower iularwelign cmerge

oy Haye lie
suite -asunale.“Ubin Iighlighos th evatel cole of St mass Weer ar inforscation in
Il Classical and Qua: formation hors. Ta dae preacu wud ilu
a previanly raknewa nppruads Ww Ue Stwmmae Wierer information wed oc
provide ou “stn inlersvetatio for fee Secon fora uw wu 8 pubting ln
Frmglemenr measures wit: w salas suucure fe @ soe contests Hy formwtning
ie preaas of vnesar'on gaining in setthencties augunge we ursiew 2% 2 remclt
cone) toee aernehures” over m givan wet. Ok. aly (roy st uecine, & tee netion
au be dene, selleing he + egies of aplisting and braun ia Cae gious a We

so in detail vat the min inacion of te Lo Tiustiou ut -nosibly crust sina.
sete ud trew sutures teaers the ‘unetional form of ene Slimmuou-Wiuuer ifn
eon. ‘Uhia is = important fudig, us 1 deaousbetis rat enkoy like infonacion

ast be weston) 95 Ute fan's of a nin zation proccss un

hannar- Wear
enerony is the waull of au “activu grineiple", the aralogna of the acon feew-ocal
ein 2/sen by hve trae fntlen on the wt of sree oleae ues T3's rewiden 2 ane
feel nese Fmerpretono] eauowtn’s ba walaony “ike mesrures of irformstion andl

‘ee gonere, oneleriying rovchenatienl sisuclury, La asec, the
aus Tanne:

eneangleeacat. We suagest tras navral anions Zoe Ucn Le sieve aes, whl,
Inu. gu ly be reali bo Une axons discrl2ing nelgtbeumhonds on a “apologies!
space. In taer, we aon: that asorpraee structure uvor nt demas a suiehEouriwed
topology ou this set, The sue eaiatuieass thet reuclers the fynesions. faene of
the Shemnon-\ener inferuuntim Fromm rhe sys: fnmliam Hho assis pookcue
topoiogy Ho che mnderlvicw a, Ionting at a decp relation Detawur enlevy dike me
sites ainl prefornad vegkbmthond tapalogica. We export chat theve didings will

contrite constructively lo iw problow of eutoug eet gute jew 7, urns
Quast Pasi.

2 Introduction

Tis the pil tse caves, tat wel estab e'ceplings within Mschemation and
Physies, namely Infomation ‘Tarory see Qusamun Physic, see macraed ile 2
prospostine aw Geld ou Civic oki “Thiy grcnss wae inecigated tyr adesaoes in
Absie aim] “lecular Physies ich epened mp the possibility of contelligg the
Tebnsiony ef arstor ye acu of Tescr Ty lows Uo voty sill Keng. scales ~ fram
Ux: rang tngime, incalving merozcepie systenie, even furcher vlosat 20 the courx0)

single afomae ail mo:eccles bye moras of aggroaciate las evans. What is re
tet Lue possibile ef near te irradiating sr dem bo: anes UME
tip, sae contrelled staglephoto sources “ane been expuceuntily procsd i be
pensiite Tings ler seit these advances, ae possibly of slzing nmnesteacttees
for every single mols ist, a Hie Zulia lng Vel for Culure cust wy
compris, las arian, ‘The sty of fomnation nionesing i such a enriromace,
itz limicacions aa well a ts eapabiltiy co weocd avasivel computa ous! pretest
ea lise Lacie eine acoueding 1 the bro main pillsa counb:sing to the now
dligeiyne = Chieernm Inforraateat Man
Hocever, mame cnt char che rope of Conta TIufvrmotion Thoory is :auel
wider can thy range ef Hs pusiible aggeeav nue within Quantum Corapreatien
right waggert. ner, it has bien crnednaceslsemaeunteate: Ha. Qual au Laon
auscion Tsury provides the main oxayplaal a well 25 comeraationa!foundatien
la uacte same of the hasie nnsclved problema wthiu Churazmn Mevkunies wis
Tweve bauulsa plysicists For dards ~ dip probes uf Quast Nanlovelily [
Tis presonea signalled hy che vio.ation of appropriate Lell-iacqualtis [1 5,
the neu of Cutonglowwat bebreut: dictions quualuu ossteme. Thare questions
Luss seen sil nish rhe rivetery of ow a vagscal waele can emerge feout
mer: by Qnealacks Muwlarces i elicit ll supervosiious of states
sre snd basal cna ting aubeet af these namely thore whieh we perreive at

‘clatical’. con he oréinatily o'scrs 2 possface answer hae boat peor by the
salou o: Deealseeaie 7, 3 & 0, 21, — she daray nf guenrmn corgeatcns here.
fpsteans which are sutieened to the iuevitace antes: aise “a cairn
ick is eliaintely miderstoud vo by ty

ne # whic, Heve again, the nea!an
‘tree Strumuvess & Vaniaticual Aypcuael to Shanann-Mlenes tafoometion 3

of ents

‘Ono of the laste pre! dhans in Canton Information Tawwuy {QU is ties 29
find rnenree foe He quuutilies:Joa nf the cepree of noutdbeeieul eureatvas, or
encaglacets bolacen ten at ysioalapsteme So far. exsaxglouou lus barn shin
{o be amianlizable in toro vepiues, culled “hvie™ ame. magymptctic® [12, 19, 4:
Tho Gel wun attempts to crineify che wcccuul of vatangbum:a thin a single
egy af w-ciinmium state; fhe sion! cue Agals wih cersar pradnete of a. la:
ual of ideasioal evpitet af a given scare, “Mong of te eulaugleraunl: messmres
Dptposed 3 :n: havea close aebeicalup Wp Use ancien ha a aan-AWiener information

5.8 118] ef prolabil-y iseibntion, wld ie forally ducal (up toa 3332}

lemens oucrges ws a cee! quantiy

le Uw Ucemadynam'ral exropy of ea: sauee distritrskv2. For exnra ey the
called “madgnwuts Hasse” [12 *9, 20] aratea raat, under npprapainle cul
all eztanyglement “Yeamires wnielé co pure Lipsrt.e staves ani ave erp tt chic
fon Resenagn eamapy PU] ths y.anur anglogee at rae éagseal Shesxaon-Wiewsr

fnfonua. ou = of The eeapenvling reduced deasity epucubues. Ut be Us eeeiring
feet stich steonaly bins. dae selenve of entrapyike "ceases oF ifuramatiouy
set uy Je Shesonn Wiener informnscie, bod. i Uae classical amd" Lhe garter

TU thls wick we presere a ew az eles ciarspesiel apyrosel Uy Uae resp
of Sranmen-\Wiener inferautdou: Bre skow Uval this ganrity eam he creeerstead as
1H iserme,

Carmel f mini ation of a socalled tre fumetiun an 2 us
tele se atratare, wie. isla wl investigate in this work, WWesdare iu Dated)
{Cal Ue Shannan Woven normasrion, ak nosy up to date, zy Deobteined ag the
cnisraal wa oF ze toe fuuativn. oben the condition oF nk

sie i pov

This pals the solivwel she nan-Wier or mfbcmacenoa, 2 ka Vat al OL" PRR
fe informsion ml ednugaueal liek ono bose wpe Hts a ele wee wu
‘ehivkeaw preset 21 Unis teat. Altcomgh treme ejects ure “aro: i Jira
fie “sheers 22}. Ceauplaity Tlesny ane Diswete Mathematics, eae arcs’,
prec lane iss uo and oe ginal east of tie Teas, mad eas Ev paecivusl =
jeeponed concenta to sels n daze shat 4 ofotr el self sentained sextant
fhe weve structure iy juss Ute nom fever

{Wie rom give & Unie quaitulive wvurview gece “he new strtewsze end is soak
proper

What ave tree structures: 4 tree armen: BUX) rer give set
cf eae pom set PX of X wel iy fava hy a edacinzona splitting of fs waes
WE BOX} nla aecalee ancl ser sullen wubuctey cis wp ung ¢ vosoebed > rere
of perticemof ser, Tov shrvelues va be ln ve” sete ef axhitrary carina ty,
ceincalese we ose able, For infinite se sic tee sleactun vror X act fete
bike aajerte 23. ‘There ize Carey uashusul sa"pms governing trae autres, wie
dave nepeanden uf whether the 262 X's fice or icsatte, Thue axles g've ree ta
stave inpelagion en the ere oct X