### Abstract

Original language | English |
---|---|

Pages (from-to) | 893-906 |

Number of pages | 13 |

Journal | Annals of Physics |

Volume | 323 |

Issue number | 4 |

DOIs | |

Publication status | Published - Apr 2008 |

### Fingerprint

### Keywords

- linear transformations
- complete positivity
- Kraus sum

### Cite this

*Annals of Physics*,

*323*(4), 893-906. https://doi.org/10.1016/j.aop.2007.06.001

}

*Annals of Physics*, vol. 323, no. 4, pp. 893-906. https://doi.org/10.1016/j.aop.2007.06.001

**Linear transformations of quantum states.** / Croke, S.; Barnett, S.M.; Stenholm, S.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Linear transformations of quantum states

AU - Croke, S.

AU - Barnett, S.M.

AU - Stenholm, S.

PY - 2008/4

Y1 - 2008/4

N2 - This paper considers the most general linear transformation of a quantum state. We enumerate the conditions necessary to retain a physical interpretation of the transformed state: hermeticity, normalization and complete positivity. We show that these can be formulated in terms of an associated transformation introduced by Choi in 1975. We extend his treatment and display the mathematical argumentation in a manner closer to that used in traditional quantum physics. We contend that our approach displays the implications of the physical requirements in a simple and intuitive way. In addition, defining an arbitrary vector, we may derive a probability distribution over the spectrum of the associated transformation. This fixes the average of the eigenvalue independently of the vector chosen. The formal results are illustrated by a couple of examples.

AB - This paper considers the most general linear transformation of a quantum state. We enumerate the conditions necessary to retain a physical interpretation of the transformed state: hermeticity, normalization and complete positivity. We show that these can be formulated in terms of an associated transformation introduced by Choi in 1975. We extend his treatment and display the mathematical argumentation in a manner closer to that used in traditional quantum physics. We contend that our approach displays the implications of the physical requirements in a simple and intuitive way. In addition, defining an arbitrary vector, we may derive a probability distribution over the spectrum of the associated transformation. This fixes the average of the eigenvalue independently of the vector chosen. The formal results are illustrated by a couple of examples.

KW - linear transformations

KW - complete positivity

KW - Kraus sum

UR - http://dx.doi.org/10.1016/j.aop.2007.06.001

U2 - 10.1016/j.aop.2007.06.001

DO - 10.1016/j.aop.2007.06.001

M3 - Article

VL - 323

SP - 893

EP - 906

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

IS - 4

ER -