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Mismatched quantum filtering and entropic information

Mankei Tsang, National University of Singapore

(Session 7 : Friday from 11:15am - 11:45am)

Quantum filtering is a signal processing technique that estimates the posterior state of a quantum system under continuous measurements and has become a standard tool in quantum information processing, with applications in quantum state preparation, quantum metrology, and quantum control. If the filter assumes a wrong model due to assumptions or approximations, however, the estimation accuracy is bound to suffer. I shall present formulas that relate the error penalty caused by quantum filter mismatch to the relative entropy between the true model and the nominal model, with one formula for Gaussian measurements, such as homodyne detection, and another for Poissonian measurements, such as photon counting. These formulas generalize recent seminal results in classical information theory and provide new operational meanings to relative entropy, mutual information, and channel capacity in the context of quantum experiments. See http://arxiv.org/abs/1310.0291 for details.