Retrieving maximum information of symmetric states from their corrupted copies

TL;DR

This paper develops a method to optimally extract maximum information from symmetric quantum states that have been corrupted by noise, using quantum metrology and semidefinite programming.

Contribution

It introduces a systematic approach to identify optimal measurements for corrupted symmetric states, extending prior work on symmetric structures in quantum information.

Findings

Optimal measurement can be found via semidefinite programming.

Explicit solutions for noise models covariant under symmetry groups.

Enhances information retrieval from noisy symmetric quantum states.

Abstract

Using quantum measurements to extract information from states is a matter of routine in quantum science and technologies. A recent work [Phys. Rev. Lett. 133, 040202 (2024)] reported the finding that the symmetric structures of a state can be harnessed to dramatically reduce the sample complexity in extracting information from the state. However, due to the presence of noise, the actual state at hand is often corrupted, making its symmetric structures distorted before the execution of quantum measurements. Here, using the methodology of quantum metrology, we identify the optimal measurement that can retrieve maximum information of a symmetric state from its corrupted copies. We show that this measurement can be found by solving a semidefinite program in generic cases and can be explicitly determined for a large class of noise models covariant under the symmetry group in question. The results of this study nicely complement the recent work by providing a method to optimally utilize the distorted symmetric structures of corrupted states for information retrieval.