Nonlocality in pure and mixed nqubit Emphasis Ty

Authors: J Batle C H Raymond Ooi Ahmed Farouk S Abdalla

Publish Date: 2015/12/21

Volume: 15, Issue: 4, Pages: 1553-1567

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Abstract

Nonlocality for general multiqubit X states is studied in detail Pure and mixed states are analyzed as far as their maximum amount of nonlocality is concerned and analytic results are obtained for important families of these states The particular form of nonzero diagonal and antidiagonal matrix elements makes the corresponding study easy enough to obtain exact results We also provide a numerical recipe to randomly generate an important family of X states endowed with a given degree of mixtureJ Batle acknowledges fruitful discussions with J Rosselló Maria del Mar Batle and Regina Batle J Batle is grateful to the villages of sa Pobla and Santa Margalida for their warm hospitality R O acknowledges support from High Impact Research MoE Grant UMC/625/1/HIR/MoE/CHAN/04 from the Ministry of Education Malaysiaregion II r in h 1 h 2 R in 32 where h 2 equiv sqrth2 c+fracD22=sqrt2over 4 denotes the radius of a sphere which is tangent to the sides of the tetrahedron T Delta Contrary to the previous case part of the surface of the sphere lies outside the tetrahedron This fact means that we are able to still generate the states rho as before provided we reject those ones with negative weights lambda iregion III r in h 2 h 3 R in 21 where h 3 equiv sqrth2 c+D2=sqrt6over 4 is the radius of a sphere passing through the vertices of T Delta The generation of states is a bit more involved in this case Again phi =2pi rand u but the available angles theta now range from theta cr to pi It can be shown that wequiv cos theta c results from solving the equation 3r2 w2 sqrtfrac32r w + frac382r2 = 0 Thus theta r=arccos wr with wr=cos theta cr + 1cos theta cr rand u Some states may be unacceptable lambda i0 still but the vast majority are accepted

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