Dynamic Quantum Tomography Model for Phase-Damping Channels

TL;DR

This paper introduces a dynamic quantum tomography model tailored for phase-damping channels in open quantum systems, aiming to reduce measurement complexity by leveraging system evolution over time.

Contribution

It presents a novel dynamic approach to quantum tomography for phase-damping channels, including algebraic criteria and a practical example for implementation.

Findings

Reduces the number of distinct measurements needed for tomography.

Provides algebraic criteria for optimal quantum state reconstruction.

Demonstrates the approach with a detailed example.

Abstract

In this article we propose a dynamic quantum tomography model for open quantum systems with evolution given by phase-damping channels. Mathematically, these channels correspond to completely positive trace-preserving maps defined by the Hadamard product of the initial density matrix with a time-dependent matrix which carries the knowledge about the evolution. Physically, there is a strong motivation for considering this kind of evolution because such channels appear naturally in the theory of open quantum systems. The main idea behind a dynamic approach to quantum tomography claims that by performing the same kind of measurement at some time instants one can obtain new data for state reconstruction. Thus, this approach leads to a decrease in the number of distinct observables which are required for quantum tomography; however, the exact benefit for employing the dynamic approach depends strictly on how the quantum system evolves in time. Algebraic analysis of phase-damping channels allows one to determine optimal criteria for quantum tomography of systems in question. General theorems and observations presented in the paper are accompanied by a specific example, which shows step by step how the theory works. The results introduced in this article can potentially be applied in experiments where there is a tendency a look at quantum tomography from the point of view of economy of measurements, because each distinct kind of measurement requires, in general, preparing a separate setup.