# Exploring Quantum Average-Case Distances: proofs, properties, and examples

@inproceedings{Maciejewski2021ExploringQA, title={Exploring Quantum Average-Case Distances: proofs, properties, and examples}, author={Filip B. Maciejewski and Zbigniew Puchała and Michał Oszmaniec}, year={2021} }

In this work, we present an in-depth study of average-case quantum distances introduced in [1]. The average-case distances approximate, up to the relative error, the average Total-Variation (TV) distance between measurement outputs of two quantum processes, in which quantum objects of interest (states, measurements, or channels) are intertwined with random quantum circuits. Contrary to conventional distances, such as trace distance or diamond norm, they quantify average-case statistical…

## 2 Citations

### Operational Quantum Average-Case Distances

- Computer Science, Physics
- 2021

It is argued that ACDs are better suited for assessing the quality of NISQ devices than common distance measures such as trace distance or the diamond norm.

### The Wasserstein distance of order $1$ for quantum spin systems on infinite lattices

- Physics
- 2022

We propose a generalization of the Wasserstein distance of order 1 to quantum spin systems on the lattice Z d , which we call speciﬁc quantum W 1 distance. The proposal is based on the W 1 distance…

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