### Abstract

Language | English |
---|---|

Pages | 505-523 |

Number of pages | 18 |

Journal | Journal of Modern Optics |

Volume | 51 |

Issue number | 4 |

DOIs | |

Publication status | Published - 10 Mar 2004 |

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### Keywords

- quantum
- physics
- error probability
- quantum physics

### Cite this

*Journal of Modern Optics*,

*51*(4), 505-523. https://doi.org/10.1080/09500340310001620475

}

*Journal of Modern Optics*, vol. 51, no. 4, pp. 505-523. https://doi.org/10.1080/09500340310001620475

**Comparing the states of many quantum systems.** / Jex, Igor; Andersson, Erika; Chefles, Anthony .

Research output: Contribution to journal › Article

TY - JOUR

T1 - Comparing the states of many quantum systems

AU - Jex, Igor

AU - Andersson, Erika

AU - Chefles, Anthony

PY - 2004/3/10

Y1 - 2004/3/10

N2 - We investigate how to determine whether the states of a set of quantum systems are identical or not. This paper treats both error-free comparison, and comparison where errors in the result are allowed. Error-free comparison means that we aim to obtain definite answers, which are known to be correct, as often as possible. In general, we will also have to accept inconclusive results, giving no information. To obtain a definite answer that the states of the systems are not identical is always possible, whereas in the situation considered here, a definite answer that they are identical will not be possible. The optimal universal error-free comparison strategy is a projection onto the totally symmetric and the different non-symmetric subspaces, invariant under permutations and unitary transformations. We also show how to construct optimal comparison strategies when allowing for some errors in the result, minimizing either the error probability, or the average cost of making an error. We point out that it is possible to realize universal error-free comparison strategies using only linear elements and particle detectors, albeit with less than ideal efficiency. Also minimum-error and minimum-cost strategies may sometimes be realized in this way. This is of great significance for practical applications of quantum comparison.

AB - We investigate how to determine whether the states of a set of quantum systems are identical or not. This paper treats both error-free comparison, and comparison where errors in the result are allowed. Error-free comparison means that we aim to obtain definite answers, which are known to be correct, as often as possible. In general, we will also have to accept inconclusive results, giving no information. To obtain a definite answer that the states of the systems are not identical is always possible, whereas in the situation considered here, a definite answer that they are identical will not be possible. The optimal universal error-free comparison strategy is a projection onto the totally symmetric and the different non-symmetric subspaces, invariant under permutations and unitary transformations. We also show how to construct optimal comparison strategies when allowing for some errors in the result, minimizing either the error probability, or the average cost of making an error. We point out that it is possible to realize universal error-free comparison strategies using only linear elements and particle detectors, albeit with less than ideal efficiency. Also minimum-error and minimum-cost strategies may sometimes be realized in this way. This is of great significance for practical applications of quantum comparison.

KW - quantum

KW - physics

KW - error probability

KW - quantum physics

U2 - 10.1080/09500340310001620475

DO - 10.1080/09500340310001620475

M3 - Article

VL - 51

SP - 505

EP - 523

JO - Journal of Modern Optics

T2 - Journal of Modern Optics

JF - Journal of Modern Optics

SN - 0950-0340

IS - 4

ER -