Abstract
There is no doubt that Bell’s theorem [1] is a fundamental result for our understanding of quantum physics and its relation with classical physics. Before Bell, the possibility that an intuitive classical model could exist with the same predictive power as quantum physics was valid and, in a sense, justified in view of the arguments by Einstein, Podosky and Rosen (EPR) on the incompleteness of quantum physics [2]. After Bell’s work, a classical model for quantum physics is still possible but, as discussed below, requires breaking some very natural assumptions that, in a way, make it as counter-intuitive as quantum physics. In the last decade, our understanding of Bell’s theorem, for instance of the assumptions required for its derivation and its implications, has significantly improved using concepts and ideas borrowed from quantum information theory. At the same time, concepts from foundations of quantum physics have opened new approaches to quantum information applications, especially in the so-called device-independent scenario. The purpose of this text is to provide an overview over this new research direction merging quantum foundations and information theory, with an emphasis on the motivations and some of the obtained results. Our text, however, should not be understood as a review paper, but more as a rather personal selection of results in the field, unavoidably biased to some of our works. The structure of the essay is as follows: we start by presenting the assumptions required in the derivation of Bell’s theorem and its implications. We move on and show how ideas from Bell’s arguments can be used for quantum information purposes: we introduce the device-independent approach to quantum information theory and argue that it can be interpreted as a form of Bell-type quantum information theory. Then, we reverse this direction and show how ideas from information theory help us to understand quantum physics.
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Notes
- 1.
In fact, in a realistic experiment, there are 4 possible results: no detector clicks, only detector 1 clicks, only detector 2 clicks, and both detectors click. However, here we are considering an idealized scenario where photons are always detected and only one photon is sent to each observer.
- 2.
There is an implicit assumption when writing this conditional probability distribution, namely that all the rounds of the experiment represent independent and identically distributed (iid) realizations of P(ab|xy). It is however possible to derive a form of Bell’s theorem valid without the iid assumption, see for instance [3]. Here, for the sake of simplicity, we work under the iid assumption.
- 3.
It is at the moment an open problem whether a secret key, and not just a single bit, can be distributed in a realistic noisy scenario only under the assumption of the no-signalling principle.
- 4.
- 5.
The mutual information between two random variables A and B is defined as \(H(A:B)=\sum _{A,B}P(A,B)\log _2\left( \frac{P(A, B)}{P(A)P(B)}\right) \).
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Acknowledgments
This work is supported by the ERC CoG QITBOX, the AXA Chair in Quantum Information Science, Spanish MINECO (FOQUS FIS2013-46768-P and SEV-2015-0522), Fundación Cellex, the Generalitat de Catalunya (SGR 875), the John Templeton Foundation and the FQXi grant “Towards an almost quantum physical theory”.
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Acín, A., Navascués, M. (2017). Black Box Quantum Mechanics. In: Bertlmann, R., Zeilinger, A. (eds) Quantum [Un]Speakables II. The Frontiers Collection. Springer, Cham. https://doi.org/10.1007/978-3-319-38987-5_17
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