Quantum channels showing superadditivity in capacity

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1、QuantumchannelsshowingsuperadditivityincapacityMasahideSasaki1,KentaroKato2,MasayukiIzutsu1,andOsamuHirota21CommunicationsResearchLaboratory,MinistryofPostsandTelecommunicationsKoganei,Tokyo184,Japan2ResearchCenterforQuantumCommunications,TamagawaUniversityTamagawa-gakuen,M

2、achida,Tokyo194,Japan(14October1997)Weconsiderachannelcodingforsendingclassicalinformationthroughaquantumchannelwithagivenensembleofquantumstates(letterstates).Aswellknown,itisgenericallypossibleinaquantumchannelthatthetransmittableinformationinblockcodingoflengthncanexceed

3、ntimesthemaximumamountthatcanbesentwithoutanycodingscheme.Thisso-calledsuperadditivityinclassicalcapacityofaquantumchannelisadistinctfeaturethatcannotbefoundinclassicalmemorylesschannel.Inthispaper,apracticalmodelofchannelcodingthatshowsthispropertyispresented.Itconsistsofa

4、simplecodewordselectionandtheoptimumdecodingofthecodewordsminimizingtheaverageerrorprobability.Atfirst,optimizationofdecodingstrategyisdiscussed.Thenthechannelcodingthatshowsthesuperadditivityinclassicalcapacityisdemonstrated.PACSnumbers:03.65.Bz,89.70.+c,42.79.Sz,89.80.+h,3

5、2.80.-tI.INTRODUCTIONTheoryofquantumcommunicationwasinitiatedmorethanthirtyyearsago,inordertoconsiderquantumnatureofsignalcarrierinopticalfrequencydomain.Inthisregion,onefacesquitedifferentfeaturesfromRFbandcommu-nication,duetoquantumnoiseofsignalcarrieritself.Thistheorywast

6、hendevelopedin1970’srevealingnewaspectsofinformationtransmissionandsignaldetection.Itnowattractsmuchattentionsincenewfieldssuchasquantumcomputationandcryptographyemerged.Beingassistedbyideasandmethodsinthesefields,significantprogresswasmadeinabasicandoldissueonchannelcapacity.

7、Inparticular,thetheoremwasestablishedthattheattainablemaximumrateofasymptoticallyerrorfreetransmissionforsendingclassicalinformationbyusingagivensourceofquantumstates(letterstates)ispreciselytheHolevobound[1,2](letuscallitthequantumchannelcoding(QCC)theorem)[3,4,5,6].Thisra

8、teistheasymptoticrateatinfiniteblocklength,n→∞,andisespeciallycalledclassicalcapaci