Inequalities for thermodynamic mean values of operator products

Najla A. Altwaijry, Shigeru Furuichi, Nicuşor Minculete

Tanmoy Chakraborty, Harkirat Singh, Chiranjib Mitra

Violation of Bell’s inequality test has been established as an efficient tool to determine the presence of entanglement in quantum spin 1/2 magnets. Herein, macroscopic thermodynamic quantities, namely, magnetic susceptibility and specific heat have been employed to perform Bell’s inequality test for [NH4CuPO4, H2O], a spin 1/2 antiferromagnet with nearest neighbor interactions. The mean value of the Bell operator is quantified and plotted as a function of temperature. The threshold temperature is determined above which the Bell’s inequality is not violated and a good consistency is found between the analyses done on magnetic and thermal data.

V. V. Dodonov

Sum and product uncertainty relations, containing variances of three or four observables, but not containing explicitly their covariances, are derived. Their consequences are, in particular, inequalities, giving nonzero lower bounds for the products of two variances in the case of zero mean value of the commutator between the related operators. Explicit examples show that the bounds can be better than the known Robertson-Schr\"odinger one.

Sanket Tikare, Svetlin G. Georgiev

V. A. Andreev, Vladimir I. Man’ko

A new formalism for calculation of the spin correlation magnitude is developed. In this approach, the mean value of an operator acting in the four-dimensional space of two-particle spin states has the form of a scalar product of vectors defined in the three-dimensional direction space. A complete description of the two-particle spin states satisfying Bell inequalities is given in this formalism. It is shown that these states include both factorable and entangled states.

Giacomo De Palma, Davide Pastorello