Bell-inequality violation versus entanglement in the presence of local decoherence

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 77, Issue 5, 2008, Pages

  Kofman, A G ^a   Korotkov, A N ^a  

^a University of California Riverside   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

SUPERCONDUCTIVITY; THERMAL EFFECTS;

BELL-INEQUALITY VIOLATION; LOCAL DECOHERENCE;

COHERENT LIGHT;

EID: 44249104739     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.77.052329     Document Type: Article

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37. Notice that when T1a T1b, the second term in Eq. 5 is maximized for a nonmaximally entangled state βπ/4 though the benefit is not significant if we need S+ 2.2.
38. The statement in Ref. that any mixed state with S+ =22C>2 is maximally entangled, is incorrect (here maximum entanglement means that C cannot be increased by any two-qubit unitary transformation). As a counterexample, consider the states ρ=f |Ψ Ψ| + (1-f) | 00 00 |, produced from the initial state 2 due to zero-temperature energy relaxation (T2 =2 T1, θ=0, f= e-t/ T1). Any two such states with the same f but different initial parameter β can obviously be connected by a unitary transformation (involving only the subspace spanned by | 01 and | 10 ), while they have different concurrence C given by Eq. 6. Finally, as follows from our analysis, there is a finite range of parameters f and β, in which S+ =22C; in this range the concurrence can still be varied by unitary transformations varying β, contradicting the statement of Ref..