Entanglement of Formation is Non-monotonic with Concurrence-A Simple Proof

TL;DR

This paper demonstrates that the entanglement of formation does not always increase with concurrence in pure bipartite states, highlighting the role of incomparable states and providing a simple proof of this non-monotonic behavior.

Contribution

It offers a straightforward proof revealing the non-monotonic relationship between entanglement of formation and concurrence in pure bipartite states.

Findings

Entanglement of formation is non-monotonic with concurrence.

Incomparable states cause non-monotonicity.

Provides a simple proof of the non-monotonic relationship.

Abstract

In this paper we explore the non-monotonic nature of entanglement of formation with respect to concurrence for pure bipartite states. For pure bipartite system, one of the basic physical reason of this non-monotonicity character is due to the existence of incomparable states, i.e., the pure bipartite states which are not convertible to each other by LOCC with certainty.