PROGRAMMEDESTAGED’INITIATIONALARECHERCHE AU1ERCYCLE
SIRI
UniversitédeLyon/Universitéd’Ottawa
Appelàcandidature2017
Title
RigidityofQuantumMarkovChains
Supervisor-s
Fawzi
Omar
[email protected]
http://www.omarfawzi.info
Institute
EcoleNormaleSupérieuredeLyon
Lab
LIP,ENSdeLyon
46Alleed'Italie
69364LyonCedex07
France
Context
AshortMarkovchainisatripleofrandomvariablesA,B
andCsuchthatCisindependentofAconditionedonB.
Conditionalindependenceisafundamentalpropertyandis
attheheartofprobabilisticmodelssuchasgraphical
modelsorMarkovmodels.
Thetopicofthisinternshipisaboutunderstandingbasic
propertiesofshortquantumMarkovchains,i.e.,whenA,B
andCarequantumsystems.Itisknownthatquantum
Markovchainscanhavepeculiarpropertiescomparedto
classical ones.
Prerequisites:Strongbackgroundinlinearalgebraand
discreteprobability.Knowledgeofquantuminformationisa
plus,butnotneeded.
Abstract/Objectives
Theobjectiveoftheinternshipwouldbetoprovidean
answer tothefollowingquestion:giventwosystemsAand
B,whatarethepossiblesystemsCsuchthatA,B,Cformsa
quantumMarkovchain?Thisquestionhasasimpleanswer
inthecaseofclassicalrandomvariables,namelyCcanbe
Bibliography
Location
Duration
Language
(French/English/Both)
anyrandomizedfunctionofB,butweexpectthatinthe
quantumsettingthesetofpossibilitiesismuchmore
restrictedduetoentanglementbetweenthesystemsAand
B.Inparticular,forsomestatestheonlypossiblechoicefor
CistobecompletelyindependentofthepairA,B.The
objectiveoftheprojectistodeterminewhatpropertyofthe
pairA,Bisresponsibleforsucha“rigidity”.
Structureofstateswhichsatisfystrongsubadditivityof
quantumentropywithequality
PatrickHayden,RichardJozsa,DenesPetz,AndreasWinter
CommunicationsinMathematicalPhysics,vol246,issue2,pp.
359-374,2004
Quantumconditionalmutualinformationandapproximate
Markovchains
OmarFawzi,RenatoRenner
CommunicationsinMathematicalPhysics,vol340,issue2,pp.
575-611,2015
ENSdeLyon
46Alleed'Italie
69364LyonCedex07
France
3months
Englishor both