Character of superposed states under deterministic LOCC

TL;DR

This paper explores how superposing bipartite quantum states affects their convertibility under deterministic LOCC, revealing that superposition can transform incomparable states into comparable ones and analyzing entanglement properties.

Contribution

It establishes a connection between comparable and incomparable states via superposition and provides bounds on entanglement measures based on state comparability.

Findings

Superposition can convert incomparable states into comparable states.

Entanglement measures exhibit monotone behavior under superposition.

Provided bounds for entanglement measures based on state comparability.

Abstract

In this paper we investigate the effect of superposition of states on local conversion of pure bipartite states under deterministic LOCC. We are able to form a bridge between comparable and incomparable classes of states through the linear superposition of states. For example, if we consider two pairs of incomparable states, then their superposition may result into a comparable pair of states. We investigate many such cases and provide some of the results in tabular form. We also investigate the entanglement behavior of such classes of states, specifically their monotone nature. Finally we provide some bounds of different measures of entanglement based on the idea of comparability and incomparability under deterministic LOCC.