Non-deterministic noiseless amplification via non-symplectic phase space transformations

TL;DR

This paper uses phase space methods to analyze a non-deterministic noiseless amplifier, providing formulas for multiple modes and demonstrating applications in quantum information processing.

Contribution

It introduces a phase space formalism for analyzing non-symplectic transformations of Gaussian states in noiseless amplification.

Findings

Derived closed-form expressions for multi-mode amplification effects.

Analyzed the impact on entanglement strength and purity.

Optimized amplification strategies for quantum protocols.

Abstract

We analyse the action of an ideal noiseless linear amplifier operator, $g^\hat{n}$, using the Wigner function phase space representation. In this setting we are able to clarify the gain $g$ for which a physical output is produced when this operator is acted upon inputs other than coherent states. We derive compact closed form expressions for the action of $N$ local amplifiers, with potentially different gains, on arbitrary $N$-mode Gaussian states and provide several examples of the utility of this formalism for determining important quantities including amplification and the strength and purity of the distilled entanglement, and for optimising the use of the amplification in quantum information protocols.