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Nonlocality test of continuous variable state

Nonlocality test of continuous variable state. 17, Jan,2003 QIPI meeting Wonmin Son Queen’s University, Belfast. Contents I. EPR paradox vs Locality EPR argument Bohr’s reply Einstein’s Locality Bell’s inequality CHSH version CH version Bell’s inequality for N-dim. state.

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Nonlocality test of continuous variable state

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  1. Nonlocality test of continuous variable state 17, Jan,2003 QIPI meeting Wonmin Son Queen’s University, Belfast

  2. Contents I • EPR paradox vs Locality EPR argument Bohr’s reply Einstein’s Locality • Bell’s inequality CHSH version CH version • Bell’s inequality for N-dim. state

  3. Contents II • Dichotomic observable • Gisin-Pere’s vs Psudospin observable • Wigner (CHSH) vs Q-function (CH) • Continuous variable state • EPR state • Nonlocality test with Psudospin, Wigner, Q-Function Measurement • More than two outcome measurement • Summary and future work

  4. p1 p2 x1 x2 EPR paradox vs LocalityA.Einstein et al ,Phys. Rev. 47 (1935) 777 ; • “Completeness” and “Element of reality” • EPR state • “…quantum mechanical description of physical reality given by wave function is not complete.”

  5. ? p2 ? x2 EPR paradox vs LocalityN. Bhor, Phys. Rev. 48 (1935) 696 • “Principle of complementarity” ; mutually incompatible test • No conclusion can be drawn from the comparison of possible results of mutually incompatible measurements.

  6. EPR paradox vs LocalityA. Einstein, Philosopher-Scientist,(1949) …… the paradox forces us to relinquish one of the following two assertions; • The description by means of the wave function is complete • The real states of spatially separated objects are independent of each other  Einstein’s locality

  7. Bell’s inequality • D. Bohm ; EPR paradox in terms of the decay of a spinless system into a pair of spin half particles. • von Neumann ; existence of hidden variables (Cryptodeterminism ) • J. Bell ; Quantum mechanics predicts the correlation that any local hidden variable can not reproduce. Einstein’s local realistic model ??? Quantum mechanics nonlocal !!!

  8. where Bell’s inequality • CHSH version of Bell’s inequality (1969) • For the Bohm version of EPR state (cf singlet ) • maximum violation for specific measurement

  9. Bell’s inequality • CH version of Bell’s inequality (1974) where • Different measurements (different observables) • Noise robust Bell’s inequality tests

  10. Bell’s test for N-dim. system • Arbitrarily large spin • Gisin-Peres observable for Bell’s test of N-dim. System •  are block diagonal matrices and each block is comprised in pauli matrix  • is a matirx whose only non-vanishing element is NN=1 for N is odd • The maximum violation for even state. • Entangled pure state always violates the Bell’s inequality

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