Experimentally feasible measures of distance between quantum operations

TL;DR

This paper introduces two superfidelity-based measures for quantifying distances between quantum processes, useful for diagnosing experimental imperfections and analyzing quantum channels.

Contribution

It proposes new superfidelity-based distance measures for quantum processes and provides quantum circuits to experimentally measure superfidelity.

Findings

Measures partially fulfill distance criteria for quantum processes

Quantum circuits for superfidelity measurement are provided

Statistical analysis shows measures can distinguish quantum channels

Abstract

We present two measures of distance between quantum processes based on the superfidelity, introduced recently to provide an upper bound for quantum fidelity. We show that the introduced measures partially fulfill the requirements for distance measure between quantum processes. We also argue that they can be especially useful as diagnostic measures to get preliminary knowledge about imperfections in an experimental setup. In particular we provide quantum circuit which can be used to measure the superfidelity between quantum processes. As the behavior of the superfidelity between quantum processes is crucial for the properties of the introduced measures, we study its behavior for several families of quantum channels. We calculate superfidelity between arbitrary one-qubit channels using affine parametrization and superfidelity between generalized Pauli channels in arbitrary dimensions. Statistical behavior of the proposed quantities for the ensembles of quantum operations in low dimensions indicates that the proposed measures can be indeed used to distinguish quantum processes.