Schmidt-number benchmarks for continuous-variable quantum devices

TL;DR

This paper introduces fidelity benchmarks for continuous-variable quantum devices, enabling assessment of their ability to transmit high-dimensional quantum coherence, with practical criteria based on heterodyne and homodyne measurements.

Contribution

It establishes fundamental fidelity thresholds for CV quantum channels based on Schmidt class, extending to general quantum operations and measurement schemes.

Findings

Defined fidelity bounds for Gaussian distributed coherent states

Connected fidelity benchmarks to high-dimensional coherence transmission

Extended benchmarks to general quantum operations

Abstract

We present quantum fidelity benchmarks for continuous-variable (CV) quantum devices to outperform quantum channels which can transmit at most $k$-dimensional coherences for positive integers $k$. We determine an upper bound of an average fidelity over Gaussian distributed coherent states for quantum channels whose Schmidt class is $k$. This settles fundamental fidelity steps where the known classical limit and quantum limit correspond to the two endpoints of $k=1$ and $k= \infty $, respectively. It turns out that the average fidelity is useful to verify to what extent an experimental CV gate can transmit a high dimensional coherence. The result is also extended to be applicable to general quantum operations. While the fidelity is directly associated with heterodyne measurements in quantum optics, we can also obtain similar criteria based on mean square quadrature deviations via homodyne measurements.