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. 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 Contents II

4. EPR paradox vs Locality A.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.” x1x1 x2x2 p1p1 p2p2

5. EPR paradox vs Locality N. 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. ?x2x2 ?p2p2

6. EPR paradox vs Locality A. Einstein, Philosopher-Scientist,(1949) …… the paradox forces us to relinquish one of the following two assertions; (1)The description by means of the wave function is complete (2) 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. Bell’s inequality CHSH version of Bell’s inequality (1969) where For the Bohm version of EPR state (cf singlet ) maximum violation for specific measurement

9. CH version of Bell’s inequality (1974) Bell’s inequality 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