Positive phase space transformation incompatible with classical physics.

  title={Positive phase space transformation incompatible with classical physics.},
  author={Wonmin Son and Johannes Kofler and M. S. Kim and Vlatko Vedral and {\vC}aslav Brukner},
  journal={Physical review letters},
  volume={102 11},
Bell conjectured that a positive Wigner function does not allow violation of the inequalities imposed by local hidden variable theories. A requirement for this conjecture is "when phase space measurements are performed." We introduce the theory-independent concept of "operationally local transformations" which refers to the change of the switch on a local measurement apparatus. We show that two separated parties, performing only phase space measurements on a composite quantum system with a… 

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  • Rev. 47, 777
  • 1935
  • Rev. A 58, 4345
  • 1998
Speakable and Unspeakable in Quantum Mechanics
Bell,Speakable and Unspeakable in Quantum Mechanics (Cambridge
  • 1987
  • Rev. Lett. 10, 84
  • 1963
Methods in Theoretical Quantum Optics (Clarendon Press
  • Oxford, 1997). W11 W12 W21 4 2 0 2 4 Re β1 4 2 0 2 4 Re β2 0 0.1 0.2 W22 4 2 0 2 4 Re β1 4 2 0 2 4 Re β2 0 0.1 0.2 FIG. 1 (color online). Wigner functions Wij of the density matrix ̂ð i; ’jÞ, Eq. (7), for the transformations ( i, ’j) with i, j 1⁄4 1, 2 and ð 1; 2; ’1; ’2Þ 1⁄4 ð0;
  • 2009
A 41
  • 445303 (2008); 41, 445304
  • 2008