Quantum states tomography with noisy measurement channels

TL;DR

This paper develops methods for precise quantum state tomography in realistic noisy measurement environments, formalizing non-ideal measurements and analyzing information degradation to approach fundamental fidelity limits.

Contribution

It introduces a formal framework for non-ideal quantum measurements, develops a root-based reconstruction method, and analyzes information loss and fidelity in noisy quantum protocols.

Findings

Non-ideal measurements can be represented as mixtures of ideal measurements.

Fidelity analysis shows limits under various decoherence mechanisms.

Simulation results demonstrate high-fidelity quantum state reconstruction.

Abstract

We consider realistic measurement systems, where measurements are accompanied by decoherence processes. The aim of this work is the construction of methods and algorithms for precise quantum measurements with fidelity close to the fundamental limit. In the present work the notions of ideal and non-ideal quantum measurements are strictly formalized. It is shown that non-ideal quantum measurements could be represented as a mixture of ideal measurements. Based on root approach the quantum state reconstruction method is developed. Informational accuracy theory of non-ideal quantum measurements is proposed. The monitoring of the amount of information about the quantum state parameters is examined, including the analysis of the information degradation under the noise influence. The study of achievable fidelity in non-ideal quantum measurements is performed. The results of simulation of fidelity characteristics of a wide class of quantum protocols based on polyhedrons geometry with high level of symmetry are presented. The impact of different decoherence mechanisms, including qubit amplitude and phase relaxation, bit-flip and phase-flip, is considered.