Does there exist a super-quantum correlation in mixed-state formalism

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Discussion Overview

The discussion revolves around the existence of super-quantum correlations within the mixed-state formalism, specifically examining the conditions under which the CHSH inequality can be violated. Participants explore theoretical implications and experimental considerations related to quantum states.

Discussion Character

  • Debate/contested, Technical explanation, Exploratory

Main Points Raised

  • One participant proposes a two-point covariance defined as ##C(a,b)=\langle A\otimes B\rangle## and questions the existence of a mixed state that could yield ##CHSH=C(a,b)-C(a,b')+C(a',b)+C(a',b')>2\sqrt{2}##.
  • Another participant suggests that a slight perturbation of the density matrix of a pure state might achieve this condition.
  • There is a query regarding the possibility of violating Tsirelson's bound, indicating an interest in the implications of such a violation.
  • A later reply asserts that violations of Tsirelson's bound are indeed possible, referencing the role of imperfect polarizers in standard experiments that lead to mixed state preparations and their effects on entanglement analyses.

Areas of Agreement / Disagreement

Participants express differing views on the implications of mixed states and the potential to violate established bounds, indicating that multiple competing perspectives remain unresolved.

Contextual Notes

Participants do not clarify the specific assumptions regarding the density matrices or the definitions of the states involved, leaving some aspects of the discussion open to interpretation.

jk22
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Suppose a two point covariance : ##C(a,b)=\langle A\otimes B\rangle## with the eigenvalues of A and B in {-1,1}.

Does there exist a mixed state such that ##CHSH=C(a,b)-C(a,b')+C(a',b)+C(a',b')>2\sqrt{2}## ?
 
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Any tiny perturbation of the density matrix of a pure state with this property should do...
 
So violation of Tsirelson's bound were possible ?
 
jk22 said:
So violation of Tsirelson's bound were possible
Of course. If one uses in the standard experiments imperfect polarizers one gets preparations in mixed states; these effects are accounted for in efficiency analyses of entanglement experiments.
 

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