dorsal/arxiv
View SchemaUnbounded violation of tripartite Bell inequalities
| Authors | D. Perez-Garcia, M. M Wolf, C. Palazuelos, I. Villanueva, M. Junge |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0702189 |
| URL | https://arxiv.org/abs/quant-ph/0702189 |
| DOI | 10.1007/s00220-008-0418-4 |
| Journal | Comm. Math. Phys. 279, 455 (2008) |
Abstract
We prove that there are tripartite quantum states (constructed from random unitaries) that can lead to arbitrarily large violations of Bell inequalities for dichotomic observables. As a consequence these states can withstand an arbitrary amount of white noise before they admit a description within a local hidden variable model. This is in sharp contrast with the bipartite case, where all violations are bounded by Grothendieck's constant. We will discuss the possibility of determining the Hilbert space dimension from the obtained violation and comment on implications for communication complexity theory. Moreover, we show that the violation obtained from generalized GHZ states is always bounded so that, in contrast to many other contexts, GHZ states do in this case not lead to extremal quantum correlations. The results are based on tools from the theories of operator spaces and tensor norms which we exploit to prove the existence of bounded but not completely bounded trilinear forms from commutative C*-algebras.
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"abstract": "We prove that there are tripartite quantum states (constructed from random\nunitaries) that can lead to arbitrarily large violations of Bell inequalities\nfor dichotomic observables. As a consequence these states can withstand an\narbitrary amount of white noise before they admit a description within a local\nhidden variable model. This is in sharp contrast with the bipartite case, where\nall violations are bounded by Grothendieck\u0027s constant. We will discuss the\npossibility of determining the Hilbert space dimension from the obtained\nviolation and comment on implications for communication complexity theory.\nMoreover, we show that the violation obtained from generalized GHZ states is\nalways bounded so that, in contrast to many other contexts, GHZ states do in\nthis case not lead to extremal quantum correlations. The results are based on\ntools from the theories of operator spaces and tensor norms which we exploit to\nprove the existence of bounded but not completely bounded trilinear forms from\ncommutative C*-algebras.",
"arxiv_id": "quant-ph/0702189",
"authors": [
"D. Perez-Garcia",
"M. M Wolf",
"C. Palazuelos",
"I. Villanueva",
"M. Junge"
],
"categories": [
"quant-ph",
"math-ph",
"math.MP"
],
"doi": "10.1007/s00220-008-0418-4",
"journal_ref": "Comm. Math. Phys. 279, 455 (2008)",
"title": "Unbounded violation of tripartite Bell inequalities",
"url": "https://arxiv.org/abs/quant-ph/0702189"
},
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