ETD

• Quantum information
• Quantum mechanics
• Quantum state discrimination

Quantum state discrimination is a well-known problem in quantum information theory, that has already been solved optimally by Helstrom.
In quantum mechanics (QM), it is not possible to distinguish with certainty between two states, if they are non-orthogonal. Several aspects come into this statement, e.g. the no-cloning theorem and the way measurements act on states in QM.
In this master thesis, an important hypothesis of this problem is relaxed, and the new problem is studied in the context of Continuous Variables (CV) systems, in particular quantum optical states.

- An optical device, based on the Dolinar receiver, is proposed, and its performance is studied on the class of gaussian states of light. The aim of this device is not to reach the optimal Helstrom bound, that in most of the cases requires very cumbersome POVMs, but is to create an experimentally feasible device with only passive components and photon-counters/heterodyne measurements.
- Some classical algorithms allow the discrimination of two classes of objects, e.g. the perceptron algorithm. The quantization procedure of an algorithm is not unique, several attempts have already been tried. A different approach to this quantization is proposed, always in the context of CV systems, while most of the previous attempts were on finite-dimensional quantum systems. Several learning algorithms are proposed and discussed, and the performance of this algorithm is studied.