Science is all about making hypotheses and testing them, so methods for judging the validity of a hypothesis are essential tools in the kit of any researcher. In physics, the question might be “does this complex system exhibit quantum behavior?” which would be answered by quantum hypothesis testing. The formalism of quantum hypothesis testing began to gel in the 1970s, but the techniques have been limited to discriminating between hypothetical initial quantum states. Writing in Physical Review Letters, Mankei Tsang of the National University of Singapore proposes a more general way of hypothesis testing that applies to a wider range of questions about any quantum system.
Tsang builds on the foundation of statistical inference for hypothesis testing, but extends this to a comparison of different dynamical models to describe a system, rather than just initial states. The author shows how to compute a likelihood ratio, which is the ratio of probabilities of an observation record assuming one or another hypothetical model. The likelihood ratio determines which model is more likely, and Tsang applies this to two examples. In one case, Tsang considers the detection of a weak stochastic signal by a quantum sensor, such as might be needed in gravitational wave detection. The second example concerns determining whether a system is quantized, which is applicable in situations where, for instance, a macroscopic resonator is being cooled to eliminate thermal noise and elicit quantum behavior. These two examples demonstrate a more rigorous and efficient analysis of hypotheses for weak signals or when the detection task is challenging. – David Voss