Quantifying entanglement of two relativistic particles via decomposable optimal entanglement witnesses

TL;DR

This paper introduces a method to quantify entanglement of two relativistic particles using decomposable optimal entanglement witnesses, revealing that entanglement is not invariant under Lorentz transformations in certain conditions.

Contribution

It develops a convex optimization-based approach to construct decomposable optimal entanglement witnesses for relativistic bipartite systems, enabling entanglement quantification.

Findings

Entanglement is not relativistically invariant when momentum and Lorentz boost are parallel.

The method effectively quantifies entanglement in two spin-half particles under Lorentz transformations.

The approach highlights the impact of relativistic effects on quantum entanglement measures.

Abstract

The study of Entanglement of Formation of a mixed state of a bipartite system in high-dimensional Hilbert space is not easy in general. So, we focus on determining the amount of entanglement for a bipartite mixed state based on the concept of decomposable optimal entanglement witness (DOEW), that can be calculated as a minimum distance of an entangled state from the edge of positive partial transpose (PPT) states which has the most negative (positive) expectation value for non-PPT (bound) entangled states. We have constructed DOEWs based on the convex optimization method, then by using of it we quantify the degree of entanglement for two spin half particles under the Lorentz transformations. For convenience, we restrict ourselves to 2D momentum subspace and under this constraint when the momentum and the Lorentz boost are parallel, we have shown that the entanglement is not relativistic invariant. Keywords : Relativistic entanglement, Measure of entanglement, Optimal entanglement witnesses, Convex optimization PACS numbers: 03.67.Hk, 03.65.Ta