Second Law of Entanglement Dynamics for the Non-Asymptotic Regime

TL;DR

This paper refines the second law of entanglement dynamics to apply in the non-asymptotic regime, providing a more precise understanding of entanglement manipulation beyond the asymptotic limit.

Contribution

It introduces a new inequality that extends the second law of entanglement dynamics to finite, non-asymptotic scenarios, enhancing the theoretical framework.

Findings

Established a non-asymptotic second law of entanglement dynamics.

Provided bounds on entanglement manipulation in finite regimes.

Strengthened understanding of entanglement resource limitations.

Abstract

The distillable entanglement of a bipartite quantum state does not exceed its entanglement cost. This well known inequality can be understood as a second law of entanglement dynamics in the asymptotic regime of entanglement manipulation, excluding the possibility of perpetual entanglement extraction machines that generate boundless entanglement from a finite reserve. In this paper, I establish a refined second law of entanglement dynamics that holds for the non-asymptotic regime of entanglement manipulation.