2011/09/25 by Abhinav Somaraju, I. Dotsenko, Somaraju, Abhinav +7 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #math-ph #math.MP #quant-ph #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.1109.5344
Submitted to the American Control Conference 2012
openalex publication_date 2011/09/25 · arxiv created 2011/09/27 · arxiv updated 2011/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This work considers the theory underlying a discrete-time quantum filter recently used in a quantum feedback experiment. It proves that this filter taking into account decoherence and measurement errors is optimal and stable. We present the general framework underlying this filter and show that it corresponds to a recursive expression of the least-square optimal estimation of the density operator in the presence of measurement imperfections. By measurement imperfections, we mean in a very general sense unread measurement performed by the environment (decoherence) and active measurement performed by non-ideal detectors. However, we assume to know precisely all the Kraus operators and also the detection error rates. Such recursive expressions combine well known methods from quantum filtering theory and classical probability theory (Bayes' law). We then demonstrate that such a recursive filter is always stable with respect to its initial condition: the fidelity between the optimal filter state (when the initial filter state coincides with the real quantum state) and the filter state (when the initial filter state is arbitrary) is a sub-martingale.