### Abstract

Arguably the deepest fact known about the von Neumann entropy, the strong subadditivity inequality is a potent hammer in the quantum information theorist's toolkit. This short tutorial describes a simple proof of strong subadditivity due to Petz [Rep. on Math. Phys. 23 (1), 57-65 (1986)]. It assumes only knowledge of elementary linear algebra and quantum mechanics.

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

Pages (from-to) | 507-513 |

Number of pages | 7 |

Journal | Quantum Information and Computation |

Volume | 5 |

Issue number | 6 |

Publication status | Published - Sep 2005 |

### Fingerprint

### Keywords

- Entropy
- Monotonicity
- Relative entropy
- Strong subadditivity

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Mathematical Physics
- Theoretical Computer Science
- Physics and Astronomy(all)
- Nuclear and High Energy Physics
- Statistical and Nonlinear Physics

### Cite this

*Quantum Information and Computation*,

*5*(6), 507-513.

**A simple proof of the strong subadditivity inequality.** / Nielsen, Michael A.; Petz, D.

Research output: Contribution to journal › Article

*Quantum Information and Computation*, vol. 5, no. 6, pp. 507-513.

}

TY - JOUR

T1 - A simple proof of the strong subadditivity inequality

AU - Nielsen, Michael A.

AU - Petz, D.

PY - 2005/9

Y1 - 2005/9

N2 - Arguably the deepest fact known about the von Neumann entropy, the strong subadditivity inequality is a potent hammer in the quantum information theorist's toolkit. This short tutorial describes a simple proof of strong subadditivity due to Petz [Rep. on Math. Phys. 23 (1), 57-65 (1986)]. It assumes only knowledge of elementary linear algebra and quantum mechanics.

AB - Arguably the deepest fact known about the von Neumann entropy, the strong subadditivity inequality is a potent hammer in the quantum information theorist's toolkit. This short tutorial describes a simple proof of strong subadditivity due to Petz [Rep. on Math. Phys. 23 (1), 57-65 (1986)]. It assumes only knowledge of elementary linear algebra and quantum mechanics.

KW - Entropy

KW - Monotonicity

KW - Relative entropy

KW - Strong subadditivity

UR - http://www.scopus.com/inward/record.url?scp=23744514592&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=23744514592&partnerID=8YFLogxK

M3 - Article

VL - 5

SP - 507

EP - 513

JO - Quantum Information and Computation

JF - Quantum Information and Computation

SN - 1533-7146

IS - 6

ER -