"Quantum Estimation Utilizing Bayesian Techniques and Quantum Error Correction"

Speaker: Dr. Boyu Zhou, Department of Physics, University of Arizona

Abstract: 

Quantum estimation investigates the fundamental precision limits set by quantum mechanics, offering a quadratic advantage through entanglement and non-classical states. The Bayesian framework is especially valuable when Fisherian methods, like the Cramér-Rao bound (CRB), are ill-defined—such as in uncertainty regimes or with limited data. Bayesian quantum estimation enables adaptive strategies that improve with accumulating measurements, making it ideal for practical sensing. Yet, decoherence and noise remain major obstacles, which quantum error correction (QEC) seeks to mitigate.

This thesis begins by establishing the mathematical foundation of quantum estimation, from classical theory to quantum, covering both Fisherian and Bayesian approaches.

Next, we apply Bayesian estimation to transmissivity sensing, deriving optimal probe states under various priors and analyzing trade-offs between measurement strategies.

The third part addresses phase estimation, vital for metrology and quantum computing. We examine NOON and general photon-number states under Bayesian methods, highlighting how adaptive updates enhance precision.

We then study spatial separation estimation of incoherent sources, relevant to quantum imaging. We compare direct imaging and SPADE under different priors, extending to multi-source cases and identifying when quantum methods outperform classical ones.

Finally, we explore QEC’s role in estimation. By integrating Gottesman-Kitaev-Preskill (GKP) codes and two-mode squeezing, we design noise-resilient protocols for distributed sensing, assess concatenation schemes, and examine applications in hypothesis testing and machine learning-assisted sensing.

All these results advance quantum estimation theory and its real-world utility, offering strategies for more precise and robust quantum sensing.