Optimizing pointer states for dynamical evolution of quantum correlations under decoherence Bo You, Li-Xiang Cen Department of Physics, SiChuan University
Optimizing pointer states for dynamical evolution of quantum correlations under decoherence Bo You,Li-xiang Cen Department of Physics, SiChuan University
Outline 1. Dissipative channels and pointer bases 2. Two different optimizations in relation to quantum discord 2. 1. Bell-diagonal state 2.2. two-qubit state of two ranks 3. Optimizing pointer bases to achieve maximal condition entropy
Outline 1.Dissipative channels and pointer bases 2. Two different optimizations in relation to quantum discord 2.1.Bell-diagonal state 2.2.two-qubit state of two ranks 3. Optimizing pointer bases to achieve maximal condition entropy
Dissipative channels and pointer bases .o Dynamical evolution under dissipative channel E(p()=∑E(O)p(0)E2() In this case of dephasing channel E1=m+)(+|+ypn)(n,E,= Pn-)(n2-| e o Pointer bases: selected by the system-environment coupling COS +e sin n=sin e cos 202
Dissipative channels and pointer bases ❖ Dynamical evolution under dissipative channel ❖ In this case of dephasing channel ❖ Pointer bases: selected by the system-environment coupling 1 2 , 1 , 1 .t E n n p n n E p n n p e + + − − − − − = + = − = − ( ) † ( ) ( ) (0) ( ) i i i = t E t E t cos 0 sin 1 2 2 sin 0 cos 1 . 2 2 i i n e n e + − = + = −
≈ Quantum discord: OD (PAB)=S(P)+min p s(pBliA-S(PAB Where S(p)=-Tr(plog2 p o Geometry measure of Quantum Discord min AB AB ZAB O e Where 2o is the set of zero-discord Entanglement of formation E(p)=min、E(v) (Pi 4 s where E(AB))=S(pA) H Ollivier and W.H. Zurek, PhysRevLett 88.017901 B. Dakic, V Vedral, and C. Brukner, Phys. Rev. Lett. 105, 190502
❖ Quantum discord: ❖ Where ❖ Geometry measure of Quantum Discord: ❖ Where is the set of zero-discord. ❖ Entanglement of formation: ❖ where ( ) ( ) min ( ) ( ) A i A A AB A i B A AB i QD S p S i S = + − S Tr ( ) = − ( log2 ) ( ) 0 2 min AB DA AB AB AB = − 0 H. Ollivier and W. H. Zurek, PhysRevLett.88.017901 B.Dakic,V.Vedral, and C. Brukner,Phys. Rev. Lett. 105, 190502 ( ) ( ) , min i i AB i AB i AB p E p E = ( ) ( ) i i E S AB A =
Schematic illustration: dependence of decoherence dynamics on pointer bases pAB=plv)(v1+(1-p)v2)(v2|12)=2(00±1) a Discord A 20 0.006 0004 0.000 0.00.5 01.520 b Information C EoF 1.0 2.0 0.8 0.6 0010 0.4 0.005 000.5 0.000 P15 2.0 0.00.5 1.5 2.0
Schematic illustration: dependence of decoherence dynamics on pointer bases