Robustness of random-control quantum-state tomography

TL;DR

This paper investigates the robustness of a quantum-state tomography method that uses random control fields, analyzing its sensitivity to measurement errors and how this scales with system size through theoretical and numerical approaches.

Contribution

It provides a scaling law for the robustness measure in random-control quantum tomography and explores its temporal behavior in specific quantum systems.

Findings

The robustness measure scales with system size according to derived laws.

Numerical simulations show a plateau in robustness before reaching Haar-random behavior.

Robustness asymptotically approaches theoretical predictions for large systems.

Abstract

In a recently demonstrated quantum-state tomography scheme [Phys. Rev. Lett. 124, 010405 (2020)], a random control field is locally applied to a multipartite system to reconstruct the full quantum state of the system through single-observable measurements. Here, we analyze the robustness of such a tomography scheme against measurement errors. We characterize the sensitivity to measurement errors using the logarithm of the condition number of a linear system that fully describes the tomography process. Using results from random matrix theory we derive the scaling law of the logarithm of this condition number with respect to the system size when Haar-random evolutions are considered. While this expression is independent on how Haar randomness is created, we also perform numerical simulations to investigate the temporal behavior of the robustness for two specific quantum systems that are driven by a single random control field. Interestingly, we find that before the mean value of the logarithm of the condition number as a function of the driving time asymptotically approaches the value predicted for a Haar-random evolution, it reaches a plateau whose length increases with the system size.