Volume of Separable States for Arbitrary $N$-dimensional System

TL;DR

This paper derives analytical bounds for the volume of separable states in arbitrary N-dimensional quantum systems, providing simple criteria for separability and bounds for bipartite cases.

Contribution

It introduces a general analytical lower bound for the volume of separable states applicable to any N-dimensional system, extending previous nonzero volume results.

Findings

Derived a computable lower bound for VOSS in N-dimensional systems.

Provided an upper bound for bipartite system VOSS.

Offered simple sufficient conditions for quantum state separability.

Abstract

In a celebrated paper ([Phys. Rev. A 58, 883 (1998)]), K. Zyczkowski, P. Horodecki, A. Sanpera,and M. Lewenstein proved for the frst time a very interesting theorem that the volume of separable quantum states is nonzero. Inspired by their ideas, we obtain a general analytical lower bound of the volume of separable states (VOSS) for arbitrary N-dimensional system. Our results give quite simple and computable suffcient conditions for separability. Moreover, for bipartite system, an upper bound of the VOSS is also presented.