Hindawi Publishing Co po a ion
Ad ances in Ma hema ical Physics
Volume 2010, A icle ID 657878, 3pages
doi:10.1155/2010/657878
Edi o ial
Quan um In o ma ion and En anglemen
Shao-Ming Fei,1Se gio Albe e io,2Adan Cabello,3
Naihuan Jing,4and Debashish Goswami5
1School o Ma hema ical Sciences, Capi al No mal Uni e si y, Beijing 100048, China
2Ins i u e o Applied Ma hema ics, Uni e si y o Bonn, 53115 Bonn, Ge many
3Depa amen o de Fisica Aplicada II, Uni e sidad de Se illa, 41012 Se illa, Spain
4Depa men o Ma hema ics, No h Ca olina S a e Uni e si y, Raleigh, NC 27695, USA
5S a is ics and Ma hema ics Uni , Indian S a is ical Ins i u e, Kolka a 700108, India
Co espondence should be add essed o Shao-Ming Fei, [email p o ec ed]
Recei ed 28 Feb ua y 2010; Accep ed 28 Feb ua y 2010
Copy igh q2010 Shao-Ming Fei e al. This is an open access a icle dis ibu ed unde he C ea i e
Commons A ibu ion License, which pe mi s un es ic ed use, dis ibu ion, and ep oduc ion in
any medium, p o ided he o iginal wo k is p ope ly ci ed.
1. In oduc ion
As a apidly expanding and c oss-disciplina y subjec , quan um in o ma ion has a ac ed
much a en ion and many leading heo is s and expe imen alis s om physics, compu e
science, in o ma ion, ma hema ics, as well as elec onic enginee ing ecen ly. Whe eas he
quan um en anglemen , which can be aced back o he EPR pa adox in 1935 and ga e ise o
he discussions on he ounda ions o quan um mechanics ela ed o eali y and locali y, plays
c ucial oles in quan um in o ma ion p ocessing such as quan um compu a ion, quan um
elepo a ion, dense coding, quan um e o co ec ion, quan um c yp og aphic schemes,
en anglemen swapping, and emo e s a es p epa a ion. Many s iking achie emen s ha e
been wi nessed o he pas en yea s.
The main ocus o his special issue is on he heo y o quan um en anglemen and
i s applica ions o quan um in o ma ion p ocessing. As an in e na ional o um o esea ches
o summa ize he mos ecen de elopmen s and ideas, o p esen new esul s and a he
same ime o aise he awa eness o such esea ches wi hin he quan um in o ma ion heo y
communi y in he ield, he issue includes o iginal esea ch a icles as well as e iew a icles
ha will s imula e he con inuing effo s in he quan um in o ma ion p ocessing, he ela ed
physicsm and he heo y o quan um en anglemen .
Among he quan um in o ma ion p ocessing quan um simula ion was in ac he i s
p oposed applica ion o which quan um compu e s migh gi e an exponen ial enhancemen
2 Ad ances in Ma hema ical Physics
o e classical compu a ion, as was no ed in 1982 by Feynman ha simula ing quan um
dynamics on a classical compu e was appa en ly in insically ha d. On he o he hand by
he e y de ini ion o nonlocali y, ha is, iola ion o a Bell inequali y, unde s anding he
nonlocal co ela ions c ea ed upon measu emen o some en angled quan um sys em is a
p oblem ha uns up agains ou common ep esen a ion o he wo ld. Bancal, B ancia d,
and Gisin p opose a amily o models ha can simula e on Neumann measu emen s in
he x-yplane o he Bloch sphe e on n-pa i e GHZ s a es using only bipa i e nonlocal
boxes. Fo he ipa i e and ou pa i e s a es, he models can be ansla ed in o classical
communica ion schemes wi h ini e a e age communica ion cos . Due o he in e ac ion wi h
he en i onmen , quan um e o co ec ion is o signi icance in in o ma ion p ocessing. Guo,
Zeng, and Lee in es iga e how o simpli y he cons uc ions o quan um e o -co ec ion
codes ia he quad a ic esidues. They p esen he quan um code ha is cons uc ed ia he
s abilize o malism o an Abelian g oup and has ad an ages o being as cons uc ed wi h
mo e efficiency han he p e ious quan um codes.
Quan um compu ing is he mos impo an subjec in quan um in o ma ion p o-
cessing. The ope a o quan um e o co ec ion encompasses ac i e e o co ec ion and
leads o imp o ed h eshold esul s in aul ole an quan um compu ing. Qiao, Liu, and
Ruda s udy he heo y o a decohe ence- ee subspaces and subsys ems in which quan um
compu ing is pe o med in a decohe ence- ee subspace, al hough he o al space s ill subjec
o a decohe ence. A o malism o quan um compu ing in he decohe ence- ee subspaces
is p esen ed. The cons uc ed subspaces a e pa ial iangula ed o he index ela ed o
he en i onmen . The quan um s a es in he subspaces a e jus p ojec ed s a es which a e
uled by a subdynamic kine ic equa ion. These p ojec ed s a es can be used o pe o m he
ideal quan um logic ope a ions wi hou decohe ence. Me kli, Be man, and Sigal desc ibe
hei ecen esul s on he esonan pe u ba ion heo y o decohe ence and elaxa ion o
quan um sys em wi h many qubi s. The app oach ep esen s a igo ous analysis o he
phenomenon o decohe ence and elaxa ion o gene al N-le el sys ems coupled o ese oi s
o he bosonic ields. The app oach does no in ol e mas e equa ion app oxima ions and
applies o a wide a ie y o sys ems which a e no explici ly sol able. The clus e s a e is a
special, highly en angled quan um s a e ha o ms he uni e sal esou ce o pe o ming
measu emen -based quan um compu a ion. Ka z and Wang gi e a b ie e iew o he
heo e ical ounda ions o clus e s a e quan um compu a ion and p opose a scheme o
he gene a ion o such en anglemen in a solid-s a e medium wi h nume ical calcula ions
on he iabili y o he scheme o he c ea ion o clus e s a es. Ano he scheme ela ed o
aul ole an quan um compu ing is he opological one. K´
ad´
a , Ma zuoli, and Rase i s udy
opological quan um ield heo ies conce ning his scheme.
Quan um do is an impo an candida e o implemen a ion o quan um in o ma ion
schemes. The heo y o quan um do has been ex ensi ely in es iga ed. In Be helo , Voisin,
Delalande, Roussignol, Fe ei a, and Cassabois’s e iew, hey p esen a gene al heo e ical
desc ip ion o he ex insic dephasing mechanism o spec al diffusion ha domina es he
decohe ence dynamics in semiconduc o quan um do s a low empe a u e. The limi s
o andom eleg aph and Gaussian s ochas ic noises a e discussed. Seigneu , Gonzalez,
Leuenbe ge , and Schoen eld in es iga e he dynamics o en anglemen be ween a quan um
do spin qubi and a single-pho on qubi inside a quan um ne wo k node. The ela ed
obus ness agains a ious decohe ence p ocesses is also s udied. Single pho on and single
pho on-pai gene a ion a e undamen al in quan um in o ma ion implemen a ion. Kumano,
Ekuni, Nakajima, Idu su, Sasaku a, and Suemune demons a e he single-pho on and
pola iza ion-co ela ed pho on pai emission om a single semiconduc o quan um do .
Ad ances in Ma hema ical Physics 3
Quan um en anglemen plays c ucial oles in quan um in o ma ion p ocessing.
Quan um en angled s a es ha e become he key ing edien in he apidly expanding ield
o quan um in o ma ion science. Li, Fei, and Li-Jos in oduce some ecen esul s in he
heo y o quan um en anglemen : he sepa abili y c i e ia based on he Bloch ep esen a ion,
co a iance ma ix, no mal o m and en anglemen wi ness; lowe bounds and subaddi i i y
p ope y o concu ence and angle; ully en angled ac ion ela ed o he op imal ideli y o
quan um elepo a ion and en anglemen dis illa ion. Baya and Bose s udy he possibili y
o using an uni o mly coupled ini e an i e omagne ic spin-1/2 Heisenbe g chain as a
channel o ansmi ing en anglemen . One membe o a pai o maximally en angled
spins is ini ially appended o one end o a chain in i s g ound s a e and he dynamical
p opaga ion o his en anglemen o he o he end is calcula ed. I is shown ha compa ed
o he analogous scheme wi h a e omagne ic chain in i s g ound s a e, in his scheme he
en anglemen is ansmi ed as e , wi h less decay, wi h a much highe pu i y. Mo eo e he
nonze o empe a u es and depola izing en i onmen s a e bo h ound o be less des uc i e
in compa ison o he e omagne ic case. Casado, Gue a, and Pl´
acido apply he Wigne
unc ion o malism o pa ial Bell-s a e analysis using pola iza ion en anglemen p oduced
in pa ame ic down con e sion. Two-pho on s a is ics a a beam-spli e a e ep oduced by a
wa elike desc ip ion wi h ze opoin luc ua ions o he elec omagne ic ield.
Quan um in o ma ion p ocessing is essen ially based on quan um mechanics.
Kh enniko discusses EPR-a gumen , one way quan um compu ing, and elepo a ion om
he wo e sions o he p ojec ion pos ula e in quan um mechanics. Rocchi in oduces a
sho su ey on ecen in o ma ion heo ies and e iews some c i ical no es conce ning he
concep ualiza ion o in o ma ion in classical and quan um physics.
The Gues Edi o s o his special issue wish o hank all he au ho s who submi ed
manusc ip s o conside a ion. Thanks also o he many indi iduals who se ed as e e ees
o he submi ed manusc ip s.
Shao-Ming Fei
Se gio Albe e io
Adan Cabello
Naihuan Jing
Debashish Goswami
Submi you manusc ip s a
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