Asymmetric quantum hypothesis testing with Gaussian states

We consider the asymmetric formulation of quantum hypothesis testing, where two quantum hypotheses have different associated costs. In this problem, the aim is to minimize the probability of false negatives and the optimal performance is provided by the quantum Hoeffding bound. After a brief review of these notions, we show how this bound can be simplified for pure states. We then provide a general recipe for its computation in the case of multimode Gaussian states, also showing its connection with other easier-to-compute lower bounds. In particular, we provide analytical formulas and numerical results for important classes of one- and two-mode Gaussian states.Comment: REVTeX. Published versio

Quantum hypothesis testing: Theory and applications to quantum sensing and data readout

In this thesis we investigate the theory of quantum hypothesis testing and its potential applications for the new area of quantum technologies. We first consider the asymmetric formulation of quantum hypothesis testing where the aim is to minimize the probability of false negatives and the main tool is provided by the quantum Hoeffding bound. In this context we provide a general recipe for computing this bound in the most important scenario for continuous variable quantum information, that of Gaussian states. We then study both asymmetric and symmetric quantum hypothesis testing in the context of quantum channel discrimination. Here we show how the use of quantum-correlated light can enhance the detection of small variations of transmissivity in a sample of photodegrabable material, while a classical source of light either cannot retrieve information or would destroy the sample. This non-invasive quantum technique might be useful to realize in-vivo and real-time probing of very fragile biological samples, such as DNA or RNA. We also show that the same principle can be exploited to build next-generation memories for the confidential storage of confidential data, where information can be read only by well-tailored sources of entangled light

Optimal squeezing for quantum target detection

It is not clear if the performance of a quantum lidar or radar, without an idler and only using Gaussian resources, could exceed the performance of a semiclassical setup based on coherent states and homodyne detection. Here we prove this is indeed the case by showing that an idler-free squeezed-based setup can beat this semiclassical benchmark. More generally, we show that probes whose displacement and squeezing are jointly optimized can strictly outperform coherent states with the same mean number of input photons for both the problems of quantum illumination and reading