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Quasiprobability-based criterion for classicality and separability of states of spin-1/2 particles

Tanmay Singal

IMSc

A sufficient condition for a quantum state of a system of spin-1/2
particles to admit a local hidden variable description, i.e., to be
classical, is the separability of the density matrix characterizing its
state, but not all classical states are separable. This leads one to infer
that separability and classicality are two different concepts. These
concepts are examined here in the framework of a criterion for identifying
the classicality of a system of spin-1/2 particles based on the concept of
joint quasiprobability (JQP) for the eigenvalues of spin components [Puri,
J. Phys. A 29 5719 (1996)]. The said criterion identifies a state as
classical if a suitably defined JQP of the eigenvalues of spin components
in three suitably chosen orthogonal directions is non-negative. In
agreement with other approaches, the JQP-based criterion also leads to the
result that all nonfactorizable pure states of two spin-1/2 particles are
nonclassical. In this paper it is shown that the application of the said
criterion to mixed states suggests that the states it identifies as
classical are also separable and that there exist states which, identified
as classical by other methods, may not be identified as classical by the
criterion as it stands. However, results in agreement with the known ones
are obtained if the criterion is modified to identify as classical also
those states for which the JQP of the eigenvalues of the spin components
in two of the three prescribed orthogonal directions is non-negative. The
validity of the modified criterion is confirmed by comparing its
predictions with those arrived at by other methods when applied to several
mixed states of two spin-1/2 particles and the Werner-like state of three
spin-1/2 particles [Tòth and Acìn, Phys. Rev. A 74 030306 (2006)]. The
JQP-based approach, formulated as it is along the lines of the P-function
approach for identifying classical states of the electromagnetic field,
offers a unified approach for systems of an arbitrary number of spin-1/2
particles and the possibility of linking classicality with the nature of
the measurement process.

pra.aps.org/abstract/PRA/v86/i5/e052111