Monogamy of correlations versus monogamy of entanglement
- 697 Downloads
A fruitful way of studying physical theories is via the question whether the possible physical states and different kinds of correlations in each theory can be shared to different parties. Over the past few years it has become clear that both quantum entanglement and non-locality (i.e., correlations that violate Bell-type inequalities) have limited shareability properties and can sometimes even be monogamous. We give a self-contained review of these results and present new results on the shareability of different kinds of correlations, including local, quantum and no-signalling correlations. This includes an alternative simpler proof of the Toner-Verstraete monogamy inequality for quantum correlations, as well as a strengthening thereof. Further, the relationship between sharing non-local quantum correlations and sharing mixed entangled states is investigated, and already for the simplest case of bi-partite correlations and qubits this is shown to be non-trivial. Also, a recently proposed new interpretation of Bell’s theorem by Schumacher in terms of shareability of correlations is critically assessed. Finally, the relevance of monogamy of non-local correlations for secure quantum key distribution is pointed out, and in this regard it is stressed that not all non-local correlations are monogamous.
KeywordsQuantum mechanics Entanglement Non-locality Monogamy No-signalling Shareability Cryptography
I am grateful to Jos Uffink and Marcin Pawłowski for fruitful discussions.
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
- 5.Toner, B.F., Verstraete, F.: Monogamy of bell correlations and Tsirelson’s bound. See http://arXiv.org/abs/quant-ph/0611001 (2006)
- 7.Cleve, R., Høyer, P., Toner, B., Watrous, J.: Consequences and limits of nonlocal strategies. In Proceedings of the 19th IEEE Conference on Computational Complexity, 236–249 (2004). See: http://arXiv.org/abs/quant-ph/0404076 (2004)
- 13.Schumacher, B.: Bell’s theorem and monogamy. See http://pirsa.org/08120020/ (2008)
- 15.Spekkens, R.: In defense of the epistemic view of quantum states: a toy theory, arXiv: quant-ph/0401052 (2004)Google Scholar
- 23.Seevinck, M.P.: Parts and wholes. PhD dissertation, Utrecht University, Utrecht, The Netherlands (2008). See http://arXiv.org/abs/0811.1027 (2008)
- 24.Bell, J.S.: The theory of local beables, Epistemol. Lett. 9, March 1976. Reprinted in Dialectica 39, 85 (1985)Google Scholar
- 40.Masanes, L., Renner, R., Winter, A., Barrett, J., Christandl, M.: Security of key distribution from causality constraints. http://arxiv.org/abs/quant-ph/0606049v3 (2008)
- 41.Pawłowski, M.: Security proof for cryptographic protocols based only on the monogamy of Bell’s inequality violations, http://arxiv.org/abs/0907.3778 (2009)