## Abstract

We investigate the power of weak measurements in the framework of quantum state discrimination. First, we define and analyze the notion of weak consecutive measurements. Our main result is a convergence theorem whereby we demonstrate when and how a set of consecutive weak measurements converges to a strong measurement. Second, we show that for a small set of consecutive weak measurements, long before their convergence, one can separate close states without causing their collapse. We thus demonstrate a tradeoff between the success probability and the bias of the original vector towards collapse. Next, we use post-selection within the two-state vector formalism and present the non-linear expansion of the expectation value of the measurement device’s pointer to distinguish between two predetermined close vectors.

Original language | English |
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Pages (from-to) | 37-49 |

Number of pages | 13 |

Journal | Quantum Studies: Mathematics and Foundations |

Volume | 2 |

Issue number | 1 |

DOIs | |

State | Published - 1 Apr 2015 |

### Bibliographical note

Publisher Copyright:© 2015, Chapman University.

### Funding

We thank Yakir Aharonov, Niv Cohen and Ariel Landau for helpful comments and discussions. E.C was partially supported by Israel Science Foundation Grant No. 1311/14.

Funders | Funder number |
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Israel Science Foundation | 1311/14 |

## Keywords

- Quantum state discrimination
- Two-state vector formalism
- Weak measurements