Constructing separable states in infinite-dimensional systems by operator matrices

TL;DR

This paper introduces semi-SSPPT states in infinite-dimensional bipartite systems using operator matrices and Cholesky decomposition, providing a new method to construct and identify separable states, especially when one subsystem is a qubit.

Contribution

It generalizes previous separability criteria to infinite-dimensional systems using operator matrices and Cholesky decomposition, offering a practical construction method.

Findings

Every semi-SSPPT state is proven to be separable.

The method simplifies the construction of separable states in infinite-dimensional systems.

The criterion is particularly effective when one subsystem is a qubit.

Abstract

We introduce a class of states so-called semi-SSPPT (semi super strong positive partial transposition) states in infinite-dimensional bipartite systems by the Cholesky decomposition in terms of operator matrices and show that every semi-SSPPT state is separable. This gives a method of constructing separable states and generalizes the corresponding results in [Phys. Rev. A \textbf{77}, 022113(2008), J. Phys. A: Math. Theor. 45 505303 (2012)]. This criterion is specially convenient to be applied when one of the subsystem is a qubit system.