On the maximum purity of absolutely separable bipartite states

TL;DR

This paper explores the maximum purity of absolutely separable and PPT quantum states, providing an analytic solution for two qubits and conjectures for higher-dimensional states, advancing understanding of quantum state geometry.

Contribution

It offers an analytic solution for two qubits and proposes conjectures for higher-dimensional states' maximum purity, enhancing the geometric understanding of quantum states.

Findings

Analytic solution for two qubit states' maximum purity.

Numerical conjectures for qubit-qudit and qutrit-qudit states.

Geometric characterization of state sets in quantum information.

Abstract

In this study, we investigate the problem of determining the maximum purity for absolutely separable and absolutely PPT quantum states. From the geometric viewpoint, this problem is equivalent to asking for the exact Euclidean radius of the smallest ball around the maximally mixed state that encompasses the set of all absolutely separable or absolutely PPT states. Our results provide an analytic solution for two qubit states. Based on numerical computation, we propose a conjectured maximum purity for absolutely separable qubit-qudit states and absolutely PPT qutrit-qudit states.