Performance of the quantum MaxEnt estimation in the presence of physical symmetries

TL;DR

This paper investigates how the quantum MaxEnt estimation method performs when prior symmetry information is incorporated, demonstrating improved efficiency and robustness in quantum state reconstruction through algorithms and simulations.

Contribution

It introduces a general algorithm for MaxEnt quantum state estimation with symmetries and demonstrates its effectiveness through numerical simulations on three-qubit states.

Findings

Reduces the number of measurements needed for high-fidelity state reconstruction

Maintains robustness under finite statistics and experimental noise

Provides a practical approach for symmetry-aware quantum state estimation

Abstract

When an informationally complete measurement is not available, the reconstruction of the density operator that describes the state of a quantum system can be accomplish, in a reliable way, by adopting the maximum entropy principle (MaxEnt principle), as an additional criterion, to obtain the least biased estimation. In this paper, we study the performance of the MaxEnt method for quantum state estimation when there is prior information about symmetries of the unknown state. We explicitly describe how to work with this method in the most general case, and present an algorithm that allows to improve the estimation of quantum states with arbitrary symmetries. Furthermore, we implement this algorithm to carry out numerical simulations estimating the density matrix of several three-qubit states of particular interest for quantum information tasks. We observed that, for most states, our approach allows to considerably reduce the number of independent measurements needed to obtain a sufficiently high fidelity in the reconstruction of the density matrix. Moreover, we analyze the performance of the method in realistic scenarios, showing that it is robust even when considering the effect of finite statistics, and under the presence of typical experimental noise.