Interconversion of pure Gaussian states using non-Gaussian operations

TL;DR

This paper explores the conditions for transforming bipartite pure Gaussian states using non-Gaussian operations, extending previous Gaussian-only frameworks and providing examples requiring non-Gaussian local operations.

Contribution

It introduces a majorization-based approach to identify when non-Gaussian operations are necessary for state interconversion, surpassing prior Gaussian-restricted conditions.

Findings

Derived sufficient conditions for Gaussian state interconversion using non-Gaussian operations

Identified simple examples of 2x2 Gaussian states needing non-Gaussian local operations

Extended the analysis to multiple modes per party

Abstract

We analyze the conditions under which local operations and classical communication enable entanglement transformations within the set of bipartite pure Gaussian states. A set of necessary and sufficient conditions had been found in [Quant. Inf. Comp. 3, 211 (2003)] for the interconversion between such states that is restricted to Gaussian local operations and classical communication. Here, we exploit majorization theory in order to derive more general (sufficient) conditions for the interconversion between bipartite pure Gaussian states that goes beyond Gaussian local operations. While our technique is applicable to an arbitrary number of modes for each party, it allows us to exhibit surprisingly simple examples of 2 x 2 Gaussian states that necessarily require non-Gaussian local operations to be transformed into each other.