## Abstract

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 .

Original language | American English |
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Article number | 165301 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Issue number | 16 |

DOIs | |

State | Published - 2014 |

### Bibliographical note

Publisher Copyright:© 2014 IOP Publishing Ltd.

## Keywords

- entanglement distillation
- quantum information
- singular values
- state discrimination