Local transformations of superpositions of entangled states

TL;DR

This paper investigates the conditions under which superpositions of entangled states can be transformed into other superpositions using local operations and classical communication, providing a complete characterization based on Nielsen's theorem.

Contribution

It establishes necessary and sufficient conditions for local transformations of superpositions of entangled states, extending the understanding of entanglement manipulation.

Findings

Derived conditions for superposition transformations using Nielsen's theorem

Identified when such transformations are possible or impossible

Enhanced understanding of entanglement conversion processes

Abstract

Suppose that we have two entangled states $\ket {\phi_1}$, $\ket{\psi_1}$ that cannot be converted to any of other two states $\ket{\phi_2}$, $\ket{\psi_2}$ by local operations and classical communication. We analyze the possibility of locally transforming a superposition of $\ket{\phi_1}$ and $\ket{\psi_1}$ into a superposition of $\ket{\phi_2}$ and $\ket{\psi_2}$. By using the Nielsen's theorem we find the necessary and sufficient conditions for this conversion to be performed.