Separability conditions based on local fine-grained uncertainty relations

TL;DR

This paper introduces new criteria for determining whether bipartite quantum states are separable, based on fine-grained uncertainty relations and spectral norms, with applications to two-qutrit systems.

Contribution

The paper develops novel separability conditions using fine-grained uncertainty relations and spectral norms, expanding the tools for entanglement detection in finite-dimensional systems.

Findings

New separability criteria based on spectral norms.

Conditions formulated using maximal probabilities of measurement outcomes.

Application demonstrated on two-qutrit entangled states.

Abstract

Many protocols of quantum information processing use entangled states. Hence, separability criteria are of great importance. We propose new separability conditions for a bipartite finite-dimensional system. They are derived by using fine-grained uncertainty relations. Fine-grained uncertainty relations can be obtained by consideration of the spectral norms of certain positive matrices. One of possible approaches to separability conditions is connected with upper bounds on the sum of maximal probabilities. Separability conditions are often formulated for measurements that have a special structure. For instance, mutually unbiased bases and mutually unbiased measurements can be utilized for such purposes. Using resolution of the identity for each subsystem of a bipartite system, we construct some resolution of the identity in the product of Hilbert spaces. Separability conditions are then formulated in terms of maximal probabilities for a collection of specific outcomes. The presented conditions are compared with some previous formulations. Our results are exemplified with entangled states of a two-qutrit system.