Berta, Mario and Coles, Patrick J. and Wehner, Stephanie (2014) Entanglement-assisted guessing of complementary measurement outcomes. Physical Review A, 90 (6). Art. No. 062127 . ISSN 1050-2947. doi:10.1103/PhysRevA.90.062127. https://resolver.caltech.edu/CaltechAUTHORS:20150129-085700236
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Abstract
Heisenberg's uncertainty principle implies that if one party (Alice) prepares a system and randomly measures one of two incompatible observables, then another party (Bob) cannot perfectly predict the measurement outcomes. This implication assumes that Bob does not possess an additional system that is entangled to the measured one; indeed, the seminal paper of Einstein, Podolsky, and Rosen (EPR) showed that maximal entanglement allows Bob to perfectly win this guessing game. Although not in contradiction, the observations made by EPR and Heisenberg illustrate two extreme cases of the interplay between entanglement and uncertainty. On the one hand, no entanglement means that Bob's predictions must display some uncertainty. Yet on the other hand, maximal entanglement means that there is no more uncertainty at all. Here we follow an operational approach and give an exact relation—an equality—between the amount of uncertainty as measured by the guessing probability and the amount of entanglement as measured by the recoverable entanglement fidelity. From this equality, we deduce a simple criterion for witnessing bipartite entanglement and an entanglement monogamy equality.
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| Alternate Title: | An equality between entanglement and uncertainty | |||||||||
| Additional Information: | © 2014 American Physical Society. Published 22 December 2014; received 6 June 2013. P.J.C. thanks Jędrzej Kaniewski for helpful discussions. P.J.C. and S.W. acknowledge funding from the Ministry of Education (MOE) and National Research Foundation Singapore, as well as MOE Tier 3 Grant “Random numbers from quantum processes” (Grant No. MOE2012-T3-1-009). | |||||||||
| Group: | Institute for Quantum Information and Matter | |||||||||
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| Issue or Number: | 6 | |||||||||
| Classification Code: | PACS number(s): 03.65.Ta, 03.65.Ud, 03.67.−a, 89.70.Cf | |||||||||
| DOI: | 10.1103/PhysRevA.90.062127 | |||||||||
| Record Number: | CaltechAUTHORS:20150129-085700236 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20150129-085700236 | |||||||||
| Official Citation: | Berta, M., Coles, P. J., & Wehner, S. (2014). Entanglement-assisted guessing of complementary measurement outcomes. Physical Review A, 90(6), 062127. | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 54221 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | INVALID USER | |||||||||
| Deposited On: | 30 Jan 2015 00:08 | |||||||||
| Last Modified: | 10 Nov 2021 20:30 |
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