Squeezing the limit: Quantum benchmarks for the teleportation and storage of squeezed states

TL;DR

This paper establishes quantum fidelity benchmarks for the storage and teleportation of squeezed states, showing how classical limits depend on squeezing and displacement distributions, with methods applicable to broader state ensembles.

Contribution

It derives analytical fidelity benchmarks for squeezed states with fixed squeezing and Gaussian displacements, and introduces a semidefinite programming approach for general cases.

Findings

Classical fidelity limit decreases with increasing squeezing.

Analytical formula for maximum fidelity when displacement distribution is flat.

Semidefinite programming provides bounds for mixed states and general distributions.

Abstract

We derive fidelity benchmarks for the quantum storage and teleportation of squeezed states of continuous variable systems, for input ensembles where the degree of squeezing $s$ is fixed, no information about its orientation in phase space is given, and the distribution of phase space displacements is a Gaussian. In the limit where the latter becomes flat, we prove analytically that the maximal classical achievable fidelity (which is 1/2 without squeezing, for $s=1$) is given by $\sqrt{s}/(1+s)$, vanishing when the degree of squeezing diverges. For mixed states, as well as for general distributions of displacements, we reduce the determination of the benchmarks to the solution of a finite-dimensional semidefinite program, which yields accurate, certifiable bounds thanks to a rigorous analysis of the truncation error. This approach may be easily adapted to more general ensembles of input states.