Published April 2004
| Submitted
Journal Article
Open
Structure of States Which Satisfy Strong Subadditivity of Quantum Entropy with Equality
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.
Additional Information
© 2004 Springer-Verlag. Received 10 April 2003; Accepted 08 October 2003; Published 24 February 2004.Attached Files
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Additional details
- Eprint ID
- 101971
- DOI
- 10.1007/s00220-004-1049-z
- Resolver ID
- CaltechAUTHORS:20200318-104229836
- Created
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2020-03-18Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field