Distances between quantum states in the tomographic-probability representation

TL;DR

This paper reviews how quantum state distances can be calculated using the tomographic-probability representation, which relies on observed probabilities and simplifies data processing for distinguishing quantum states.

Contribution

It introduces how various quantum state distance measures, including fidelity, can be expressed directly in terms of tomograms, enhancing practical data analysis.

Findings

Distances between quantum states can be represented via tomograms.

Fidelity and other measures are expressible in tomographic terms.

The approach simplifies quantum state comparison using observed probabilities.

Abstract

Distances between quantum states are reviewed within the framework of the tomographic-probability representation. Tomographic approach is based on observed probabilities and is straightforward for data processing. Different states are distinguished by comparing corresponding probability-distribution functions. Fidelity as well as other distance measures are expressed in terms of tomograms.