An operational measure for squeezing

TL;DR

This paper introduces a new mathematical measure for quantifying the minimal squeezing required to prepare continuous variable quantum states, providing an operational and computational framework with practical implications.

Contribution

It defines a novel squeezing measure, proves its mathematical properties, and demonstrates its effectiveness through bounds and numerical algorithms.

Findings

The measure is convex and superadditive.

It can be computed via convex optimization.

Preparation of some multi-mode states requires less squeezing than previously thought.

Abstract

We propose and analyse a mathematical measure for the amount of squeezing contained in a continuous variable quantum state. We show that the proposed measure operationally quantifies the minimal amount of squeezing needed to prepare a given quantum state and that it can be regarded as a squeezing analogue of the "entanglement of formation". We prove that the measure is convex and superadditive and we provide analytic bounds as well as a numerical convex optimisation algorithm for its computation. By example, we then show that the amount of squeezing needed for the preparation of certain multi-mode quantum states can be significantly lower than naive approaches suggest.