Berta, Mario and Tomamichel, Marco (2016) The Fidelity of Recovery Is Multiplicative. IEEE Transactions on Information Theory, 62 (4). pp. 1758-1763. ISSN 0018-9448. https://resolver.caltech.edu/CaltechAUTHORS:20160425-151717984
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Abstract
Fawzi and Renner recently established a lower bound on the conditional quantum mutual information (CQMI) of tripartite quantum states ABC in terms of the fidelity of recovery (FoR), i.e., the maximal fidelity of the state ABC with a state reconstructed from its marginal BC by acting only on the C system. The FoR measures quantum correlations by the local recoverability of global states and has many properties similar to the CQMI. Here, we generalize the FoR and show that the resulting measure is multiplicative by utilizing semi-definite programming duality. This allows us to simplify an operational proof by Brandão et al. of the above-mentioned lower bound that is based on quantum state redistribution. In particular, in contrast to the previous approaches, our proof does not rely on de Finetti reductions.
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| Additional Information: | © 2016 IEEE. Manuscript received July 17, 2015; revised February 4, 2016; accepted February 4, 2016. Date of publication February 11, 2016; date of current version March 16, 2016. M. Berta was supported in part by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center under Grant PHY-1125565, the Gordon and Betty Moore Foundation under Grant GBMF-12500028, and the Army Research Office grant for Research on Quantum Algorithms at IQIM under Grant W911NF-12-1-0521. M. Tomamichel was supported in part by the University of Sydney Post-Doctoral Fellowship and the ARC Centre of Excellence for Engineered Quantum Systems. The authors thank Fernando Brandão, Omar Fawzi, Volkher Scholz, David Sutter, and Mark Wilde for discussions and feedback. Mario Berta thanks the University of Sydney for hosting him while part of this work was done. | ||||||||||||||
| Group: | UNSPECIFIED, Institute for Quantum Information and Matter | ||||||||||||||
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| Subject Keywords: | Quantum mechanics, quantum entanglement, information theory, entropy | ||||||||||||||
| Issue or Number: | 4 | ||||||||||||||
| Record Number: | CaltechAUTHORS:20160425-151717984 | ||||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20160425-151717984 | ||||||||||||||
| Official Citation: | M. Berta and M. Tomamichel, "The Fidelity of Recovery Is Multiplicative," in IEEE Transactions on Information Theory, vol. 62, no. 4, pp. 1758-1763, April 2016. doi: 10.1109/TIT.2016.2527683 | ||||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||||
| ID Code: | 66464 | ||||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||||
| Deposited By: | Tony Diaz | ||||||||||||||
| Deposited On: | 02 May 2016 21:03 | ||||||||||||||
| Last Modified: | 04 Jun 2020 10:14 |
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