Information recoverability of noisy quantum states

TL;DR

This paper introduces a comprehensive framework to quantify and optimize the recoverability of classical information from noisy quantum states, providing theoretical limits and practical protocols for error mitigation.

Contribution

It offers the first full characterization of information recoverability in noisy quantum systems, including a measure and efficient protocols for optimal information retrieval.

Findings

Characterizes the recoverable range of classical information from noisy quantum states.

Provides a semidefinite programming approach to compute the minimum information retrieving cost.

Demonstrates applications in error mitigation for quantum energy estimation.

Abstract

Extracting classical information from quantum systems is an essential step of many quantum algorithms. However, this information could be corrupted as the systems are prone to quantum noises, and its distortion under quantum dynamics has not been adequately investigated. In this work, we introduce a systematic framework to study how well we can retrieve information from noisy quantum states. Given a noisy quantum channel, we fully characterize the range of recoverable classical information. This condition allows a natural measure quantifying the information recoverability of a channel. Moreover, we resolve the minimum information retrieving cost, which, along with the corresponding optimal protocol, is efficiently computable by semidefinite programming. As applications, we establish the limits on the information retrieving cost for practical quantum noises and employ the corresponding protocols to mitigate errors in ground state energy estimation. Our work gives the first full characterization of information recoverability of noisy quantum states from the recoverable range to the recovering cost, revealing the ultimate limit of probabilistic error cancellation.