Continuous Quantum Hypothesis Testing

Details Continuous Quantum Hypothesis Testing Continuous Quantum Hypothesis Testing

2011-10-23

arxiv.org/abs/1110.5058v2

Physics

Quantum Physics

v1: first draft; v2: updated and submitted

Scientific paper

I propose a general quantum hypothesis testing theory that enables one to test hypotheses about any aspect of a physical system, including its dynamics, based on a series of observations. For example, the hypotheses can be about the presence of a weak classical signal continuously coupled to a quantum sensor, or about competing quantum or classical models of the dynamics of a system. This generalization makes the theory useful for quantum detection and experimental tests of quantum mechanics in general. In the case of continuous measurements with Gaussian noise, the theory is significantly simplified to produce a compact formula for the likelihood ratio, the central quantity in statistical hypothesis testing. The likelihood ratio can then be computed efficiently in many cases of interest. Two potential applications of the theory, namely quantum detection of a classical stochastic waveform and test of harmonic-oscillator energy quantization, are discussed.

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