dorsal/arxiv
View SchemaOn the power of non-local boxes
| Authors | A. Broadbent, A. A. Methot |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0504136 |
| URL | https://arxiv.org/abs/quant-ph/0504136 |
| DOI | 10.1016/j.tcs.2005.08.035 |
| Journal | Theoretical Computer Science C 358: 3-14, 2006 |
Abstract
A non-local box is a virtual device that has the following property: given that Alice inputs a bit at her end of the device and that Bob does likewise, it produces two bits, one at Alice's end and one at Bob's end, such that the XOR of the outputs is equal to the AND of the inputs. This box, inspired from the CHSH inequality, was first proposed by Popescu and Rohrlich to examine the question: given that a maximally entangled pair of qubits is non-local, why is it not maximally non-local? We believe that understanding the power of this box will yield insight into the non-locality of quantum mechanics. It was shown recently by Cerf, Gisin, Massar and Popescu, that this imaginary device is able to simulate correlations from any measurement on a singlet state. Here, we show that the non-local box can in fact do much more: through the simulation of the magic square pseudo-telepathy game and the Mermin-GHZ pseudo-telepathy game, we show that the non-local box can simulate quantum correlations that no entangled pair of qubits can in a bipartite scenario and even in a multi-party scenario. Finally we show that a single non-local box cannot simulate all quantum correlations and propose a generalization for a multi-party non-local box. In particular, we show quantum correlations whose simulation requires an exponential amount of non-local boxes, in the number of maximally entangled qubit pairs.
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"abstract": "A non-local box is a virtual device that has the following property: given\nthat Alice inputs a bit at her end of the device and that Bob does likewise, it\nproduces two bits, one at Alice\u0027s end and one at Bob\u0027s end, such that the XOR\nof the outputs is equal to the AND of the inputs. This box, inspired from the\nCHSH inequality, was first proposed by Popescu and Rohrlich to examine the\nquestion: given that a maximally entangled pair of qubits is non-local, why is\nit not maximally non-local? We believe that understanding the power of this box\nwill yield insight into the non-locality of quantum mechanics. It was shown\nrecently by Cerf, Gisin, Massar and Popescu, that this imaginary device is able\nto simulate correlations from any measurement on a singlet state. Here, we show\nthat the non-local box can in fact do much more: through the simulation of the\nmagic square pseudo-telepathy game and the Mermin-GHZ pseudo-telepathy game, we\nshow that the non-local box can simulate quantum correlations that no entangled\npair of qubits can in a bipartite scenario and even in a multi-party scenario.\nFinally we show that a single non-local box cannot simulate all quantum\ncorrelations and propose a generalization for a multi-party non-local box. In\nparticular, we show quantum correlations whose simulation requires an\nexponential amount of non-local boxes, in the number of maximally entangled\nqubit pairs.",
"arxiv_id": "quant-ph/0504136",
"authors": [
"A. Broadbent",
"A. A. Methot"
],
"categories": [
"quant-ph"
],
"doi": "10.1016/j.tcs.2005.08.035",
"journal_ref": "Theoretical Computer Science C 358: 3-14, 2006",
"title": "On the power of non-local boxes",
"url": "https://arxiv.org/abs/quant-ph/0504136"
},
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