### Abstract

We give an explicit characterisation of the quantum states which saturate the strong subadditivity inequality for the von Neumann entropy. By combining a result of Petz characterising the equality case for the monotonicity of relative entropy with a recent theorem by Koashi and Imoto, we show that such states will have the form of a so-called short quantum Markov chain, which in turn implies that two of the systems are independent conditioned on the third, in a physically meaningful sense. This characterisation simultaneously generalises known necessary and sufficient entropic conditions for quantum error correction as well as the conditions for the achievability of the Holevo bound on accessible information.

Original language | English |
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Pages (from-to) | 359-374 |

Number of pages | 16 |

Journal | Communications in Mathematical Physics |

Volume | 246 |

Issue number | 2 |

DOIs | |

Publication status | Published - Apr 2004 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Communications in Mathematical Physics*,

*246*(2), 359-374. https://doi.org/10.1007/s00220-004-1049-z

**Structure of States Which Satisfy Strong Subadditivity of Quantum Entropy with Equality.** / Hayden, Patrick; Jozsa, Richard; Petz, D.; Winter, Andreas.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 246, no. 2, pp. 359-374. https://doi.org/10.1007/s00220-004-1049-z

}

TY - JOUR

T1 - Structure of States Which Satisfy Strong Subadditivity of Quantum Entropy with Equality

AU - Hayden, Patrick

AU - Jozsa, Richard

AU - Petz, D.

AU - Winter, Andreas

PY - 2004/4

Y1 - 2004/4

N2 - We give an explicit characterisation of the quantum states which saturate the strong subadditivity inequality for the von Neumann entropy. By combining a result of Petz characterising the equality case for the monotonicity of relative entropy with a recent theorem by Koashi and Imoto, we show that such states will have the form of a so-called short quantum Markov chain, which in turn implies that two of the systems are independent conditioned on the third, in a physically meaningful sense. This characterisation simultaneously generalises known necessary and sufficient entropic conditions for quantum error correction as well as the conditions for the achievability of the Holevo bound on accessible information.

AB - We give an explicit characterisation of the quantum states which saturate the strong subadditivity inequality for the von Neumann entropy. By combining a result of Petz characterising the equality case for the monotonicity of relative entropy with a recent theorem by Koashi and Imoto, we show that such states will have the form of a so-called short quantum Markov chain, which in turn implies that two of the systems are independent conditioned on the third, in a physically meaningful sense. This characterisation simultaneously generalises known necessary and sufficient entropic conditions for quantum error correction as well as the conditions for the achievability of the Holevo bound on accessible information.

UR - http://www.scopus.com/inward/record.url?scp=2142702206&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2142702206&partnerID=8YFLogxK

U2 - 10.1007/s00220-004-1049-z

DO - 10.1007/s00220-004-1049-z

M3 - Article

AN - SCOPUS:2142702206

VL - 246

SP - 359

EP - 374

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -