Multi-state and multi-hypothesis discrimination with open quantum systems

Abstract

We show how an upper bound for the ability to discriminate any number N of candidates for the Hamiltonian governing the evolution of an open quantum system may be calculated by numerically efficient means. Our method applies an effective master equation analysis to evaluate the pairwise overlaps between candidate full states of the system and its environment pertaining to the Hamiltonians. These overlaps are then used to construct an N -dimensional representation of the states. The optimal positive-operator valued measure (POVM) and the corresponding probability of assigning a false hypothesis may subsequently be evaluated by phrasing optimal discrimination of multiple non-orthogonal quantum states as a semi-definite programming problem. We investigate the structure of the optimal POVM and we provide three realistic examples of hypothesis testing with open quantum systems.

9 pages, 5 figures

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Cited by in corpus (6)

• Searching for Lindbladians obeying local conservation laws and showing thermalization
• Hypothesis testing with a continuously monitored quantum system
• Ancilla mediated qubit readout and heralded entanglement between rare-earth dopant ions in crystals
• Binary Discrimination in Quantum Systems via Hypothesis Testing
• Semidefinite programming for understanding the limitations of Lindblad equations
• Reinforcement Learning with Neural Networks for Quantum Multiple Hypothesis Testing