Schmidt-number benchmark for genuine quantum memories and gates

TL;DR

This paper introduces a Schmidt-number benchmark to evaluate whether quantum memories and gates can preserve genuine multi-level quantum coherence, extending existing quantum benchmarks.

Contribution

It proposes a new criterion based on average gate fidelity to assess multi-level coherence, unifying and extending previous quantum benchmarking methods.

Findings

Demonstrates the coherence of quantum gates in existing experiments

Provides a simple, practical criterion for multi-level quantum coherence

Shows the Schmidt-number benchmark encompasses quantum benchmarks as a special case

Abstract

We propose to apply the notion of the Schmidt number in order to show that a quantum memory or gate process is capable of maintaining a genuine multi-level quantum coherence. We present a simple criterion in terms of an average gate fidelity with respect to the input states of two mutually unbiased bases and demonstrate the coherence of the gate operation in several existing experiments. The Schmidt-number benchmark naturally includes the quantum benchmark as a specific case.