Separability of N-particle Fermionic States for Arbitrary Partitions

TL;DR

This paper introduces a criterion for separability in N-particle fermionic pure states across arbitrary partitions, revealing conditions under which states exhibit factorizable correlations despite antisymmetry constraints.

Contribution

It generalizes previous separability criteria to arbitrary partitions, clarifying the structure of fermionic states and associated observables with implications for quantum correlations.

Findings

Separable fermionic states have factorizable correlations for specific observables.

The criterion applies to arbitrary partitions, extending prior results.

Non-uniqueness of the orthogonal structure affects transitivity of factorizability.

Abstract

We present a criterion of separability for arbitrary s partitions of N-particle fermionic pure states. We show that, despite the superficial non-factorizability due to the antisymmetry required by the indistinguishability of the particles, the states which meet our criterion have factorizable correlations for a class of observables which are specified consistently with the states. The separable states and the associated class of observables share an orthogonal structure, whose non-uniqueness is found to be intrinsic to the multi-partite separability and leads to the non-transitivity in the factorizability in general. Our result generalizes the previous result obtained by Ghirardi et. al. [J. Stat. Phys. 108 (2002) 49] for the s = 2 and s = N case.