Southwest Quantum Information and Technology

Recovery with incomplete knowledge: fundamental bounds on real-time quantum memories

Presenting Author: Arshag Danageozian, Louisiana State University

The recovery of fragile quantum states from decoherence is the basis of building a quantum memory, with applications ranging from quantum communications to quantum computing. Many recovery techniques, such as quantum error correction, rely on the prior knowledge of the environment noise parameter to achieve their best performance. However, such parameters are likely to drift in time in the context of implementing long-time quantum memories. This necessitates the use of a "spectator" system, which makes an estimate of the noise parameter in real time, then feeds the outcome back to the recovery protocol as a classical side-information. In this article, I present information-theoretic bounds on the performance of such a spectator-based recovery. I show that there is a fundamental bound in the performance of any recovery operation, as a function of the entanglement fidelity of the overall dynamics. The lower bound for the diamond distance has a simple form, and a potentially broader range of applicability in quantum information. I provide information-theoretic characterizations of the incomplete knowledge of the noise parameter to the lower bound, using both diamond distance and quantum Fisher information. Finally, I provide fundamental bounds for multi-cycle recovery in the form of recurrence inequalities. The latter suggests that incomplete knowledge could be an advantage, as errors from various cycles can cohere. Results are illustrated for the amplitude-damping noise.

Read this article online: https://arxiv.org/abs/2208.04427

(Session 5 : Thursday from 5:00 pm - 7:00 pm)