### Abstract

Generalized measurement {M_{s}} on a single d-level quantum system was studied. For the case when the initial state is pure and otherwise completely unknown, it was pointed out that the best estimates of the premeasurement and postmeasurement states for a given measurement readout s are the respective right and left eigenvectors of M_{s}, belonging to the (common) largest eigenvalue. The mean post-measurement estimation fidelity of the measurement device was also calculated and shown to satisfy a simple relationship with the mean premeasurement estimation fidelity. A constraint between the postmeasurement estimation fidelity and the operation fidelity of the measurement illustrated how state disturbance and information gain about the postmeasurement state are competing with each other.

Original language | English |
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Pages (from-to) | 034302/1-034302/4 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 68 |

Issue number | 3 |

Publication status | Published - Sep 1 2003 |

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

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## Cite this

*Physical Review A - Atomic, Molecular, and Optical Physics*,

*68*(3), 034302/1-034302/4.