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Volumn 77, Issue 4, 2008, Pages

Local and nonlocal content of bipartite qubit and qutrit correlations

Author keywords

[No Author keywords available]

Indexed keywords

CORRELATION METHODS; GROUND STATE; PROBABILITY DISTRIBUTIONS;

EID: 42449134009     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.77.042112     Document Type: Article
Times cited : (23)

References (37)
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    • Note that the band defined by | az |, | bz | ≤ 1-s c becomes narrower when approaching the maximally entangled state. From this perspective, the decomposition we have just found behaves in a discontinuous way: (i) for the maximally entangled state, PNL = PQ has random marginals and correlations defined by a scalar product; and (ii) for highly but nonmaximally entangled states (θ= π 4 -ε), such a simple form is, however, retained only for a narrow band of settings; the band increases when going to weakly entangled states, filling ultimately again the whole sphere for θ=0, in which case, however, the weight of PNL is zero.
    • Note that the band defined by | az |, | bz | ≤ 1-s c becomes narrower when approaching the maximally entangled state. From this perspective, the decomposition we have just found behaves in a discontinuous way: (i) for the maximally entangled state, PNL = PQ has random marginals and correlations defined by a scalar product; and (ii) for highly but nonmaximally entangled states (θ= π 4 -ε), such a simple form is, however, retained only for a narrow band of settings; the band increases when going to weakly entangled states, filling ultimately again the whole sphere for θ=0, in which case, however, the weight of PNL is zero.
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    • For the whole region 0<γ<1, the upper bound 6 obtained using the chained inequality gives a strictly positive number
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    • It is an interesting open question, whether pL max (ρ) <1 implies the possibility of checking nonlocality with a finite number of settings.
    • It is an interesting open question, whether pL max (ρ) <1 implies the possibility of checking nonlocality with a finite number of settings.


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