The minimal principals of Hermitian matrices and the negativity of bipartite of qubit states

TL;DR

This paper explores how the minimal principal values of the partial transpose of bipartite qubit states can provide insights into their entanglement, offering an alternative to eigenvalue-based criteria.

Contribution

It introduces a novel approach using minimal principal values of the partial transpose to analyze entanglement in bipartite qubit states.

Findings

Minimal principal values relate to entanglement measures.

Provides an alternative criterion for bipartite qubit entanglement.

Enhances understanding of partial transpose properties in quantum states.

Abstract

Quantum entanglement is an enigmatic and powerful property that has attracted much attention due to its usefulness in new ways of communications, like quantum teleportation and quantum key distribution. Much effort has been done to quantify entanglement. Indeed, there exist some well-established separability criterion and analytical formulas for the entanglement of bipartite systems. In some of these, the crucial elements are the eigenvalues of the partial transpose of the density matrix. In this paper, we show that one can also have information about the entanglement of bipartite state, in C2xC2, looking at the minimal principals of the partial transpose.