Unboxing hidden correlations

This is a Perspective on "The type-independent resource theory of local operations and shared randomness" by David Schmid, Denis Rosset, and Francesco Buscemi, published in Quantum 4, 262 (2020).

By Patryk Lipka-Bartosik (University of Bristol, UK).

Quantum entanglement allows spatially separated parties to share correlations which cannot be reproduced by any classical scheme. This means that the results of measurements performed locally on a shared quantum state cannot be reproduced by any classical device, i.e. a quantum state which is not entangled. This is, in essence, the main theme of Bell non-locality [1], a phenomenon which reveals that sometimes it is not possible to describe a physical behavior using only local classical models.

However, not all entangled states can display Bell non-locality. Quantum systems can actually demonstrate other forms of non-locality which is not accessible in a Bell experiment but which may become apparent in different experimental settings. In 2007, the Einstein–Podolsky–Rosen (EPR)-steering phenomenon was introduced as a formalization of Einstein’s ‘spooky action at a distance’— the EPR effect [2,3,4]. The steering experiment does not produce correlations like the standard Bell test. Instead it outputs multiple ensembles of quantum states: a \emph{steering assemblage}. EPR-steering is demonstrated if one of the parties can remotely influence the ensemble of another party in a way which cannot be explained by any classical model.

Importantly, every state which demonstrates Bell-nonlocality also demonstrates EPR-steering (but not vice versa) and every EPR-steerable state is necessarily entangled (not vice-versa). This leads to a natural hierarchy of $types$ of nonlocal correlations. In general different experimental settings can certify different ”types” of nonlocal correlations. In the recent years a substantial effort has been made to formalize these different aspects of non-locality. Apart from Bell-type and steering-type nonlocality, other well-studied examples involve teleportation-type nonlocality which is certified by a generalized teleportation experiment [5] or Buscemi-type nonlocality which occurs in the setting of semi-quantum non-local games [6].

One of the modern tools used to study nonlocality is the framework of resource theories [7], a mathematical toolbox which allows to systematically quantify various properties of physical systems. One of the main traits pursued by resource theories of nonlocality is describing relevant settings in which nonlocal correlations can lead to a genuine advantage over their classical counterparts. In this way the outcomes of a steering experiment has been given their operational meaning in [8]. A similar study was performed for assemblages of teleported states [9] or Buscemi-nonlocal correlations [6].

The work by Shmid, Rosset and Buscemi combines these interesting insights and unifies them in a single resource-theoretic framework of Local Operations and Shared Randomness (LOSR). The main observation is that each of the different types of nonlocality described above can be thought of as being encoded by a certain ‘black box’ with a fixed number of classical or quantum inputs and outputs. The Authors formalize this intuition in their framework and show that a variety of different objects displaying nonlocal correlations can be encompassed by a single resource-theory.

One of the advantages of the approach taken by the Authors is that it allows them to construct a $\textit{type-independent}$ resource theory. This enables them to study the problem of converting between different types of nonlocal resources (boxes) and determine when boxes of one type can encode nonlocality of different types. This leads to a natural hierarchy among different types of boxes and is formalized in terms of three distinct pre-orders of nonlocal resources. The Authors also formulate a family of games which can probe nonlocal properties of the boxes and can be used to study the aforementioned hierarchy of correlations.

In addition to the technical results, the framework developed by the Authors will be valuable to the interested reader for its generality and clear conceptual message. It unifies several seminal results already present in the literature and places them all onto a single family tree. This is particularly relevant as it allows for characterizing when devices of one type can be converted into devices of another type in a ”lossless” way. The paper also offers a brief and accessible introduction to a couple of related seminal results from the literature and neatly integrates them with the bigger picture.

On a final note, the article by Shmid, Rosset and Buscemi is a valuable contribution to the field of quantum nonlocality. What was previously a collection of different concepts and interlacing results relating different aspects of quantum nonlocality has now been given a unifying framework which not only simplifies the original proofs but also provides a solid conceptual contribution to the field of quantum nonlocality.

► BibTeX data

► References

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[2] E. Schrödinger, Math. Proc. Cambridge 31, 555–563 (1935).
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[3] A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935).
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[4] H. M. Wiseman, S. J. Jones, and A. C. Doherty, Phys. Rev. Lett. 98, 140402 (2007).
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[5] C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).
https:/​/​doi.org/​10.1103/​PhysRevLett.70.1895

[6] F. Buscemi, Phys. Rev. Lett. 108 (2012), 10.1103/​physrevlett.108.200401.
https:/​/​doi.org/​10.1103/​physrevlett.108.200401

[7] E. Chitambar and G. Gour, Rev. Mod. Phys 91 (2019), 10.1103/​revmodphys.91.025001.
https:/​/​doi.org/​10.1103/​revmodphys.91.025001

[8] M. Piani and J. Watrous, Phys. Rev. Lett. 114 (2015), 10.1103/​physrevlett.114.060404.
https:/​/​doi.org/​10.1103/​physrevlett.114.060404

[9] P. Lipka-Bartosik and P. Skrzypczyk, Phys. Rev. R. 2, 023029 (2020).
https:/​/​doi.org/​10.1103/​PhysRevResearch.2.023029

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