Unambiguous (non-orthogonal) state discrimination (USD) has a fundamental importance in quantum information and quantum cryptography. Various aspects of two-state and multiple-state USD are studied here using singular value decomposition of the evolution operator that describes a given state discriminating system. In particular, we relate the minimal angle between states to the ratio of the minimal and maximal singular values. This is supported by a simple geometrical picture in two-state USD. Furthermore, by studying the singular vectors population we find that the minimal angle between input vectors in multiple-state USD is always larger than the minimal angle in two-state USD in the same system. As an example we study what pure states can be probabilistically transformed into maximally entangled pure states in a given system .
|Journal of Physics A: Mathematical and Theoretical
|Published - 2014
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© 2014 IOP Publishing Ltd.
- entanglement distillation
- quantum information
- singular values
- state discrimination