Quantum bounds on Bell inequalities

Research output: Contribution to journalArticle

46 Citations (Scopus)

Abstract

We have determined the maximum quantum violation of 241 tight bipartite Bell inequalities with up to five two-outcome measurement settings per party by constructing the appropriate measurement operators in up to six-dimensional complex and eight-dimensional real-component Hilbert spaces using numerical optimization. Out of these inequalities 129 have been introduced here. In 43 cases higher-dimensional component spaces gave larger violation than qubits, and in three occasions the maximum was achieved with six-dimensional spaces. We have also calculated upper bounds on these Bell inequalities using a method proposed recently. For all but 20 inequalities the best solution found matched the upper bound. Surprisingly, the simplest inequality of the set examined, with only three measurement settings per party, was not among them, despite the high dimensionality of the Hilbert space considered. We also computed detection threshold efficiencies for the maximally entangled qubit pair. These could be lowered in several instances if degenerate measurements were also allowed.

Original languageEnglish
Article number022120
JournalPhysical Review A
Volume79
Issue number2
DOIs
Publication statusPublished - Feb 26 2009

Fingerprint

bells
Hilbert space
operators
optimization
thresholds

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

Quantum bounds on Bell inequalities. / Pál, K.; Vértesi, T.

In: Physical Review A, Vol. 79, No. 2, 022120, 26.02.2009.

Research output: Contribution to journalArticle

@article{a3d07b26aa6c43c8a95a65d844177fe1,
title = "Quantum bounds on Bell inequalities",
abstract = "We have determined the maximum quantum violation of 241 tight bipartite Bell inequalities with up to five two-outcome measurement settings per party by constructing the appropriate measurement operators in up to six-dimensional complex and eight-dimensional real-component Hilbert spaces using numerical optimization. Out of these inequalities 129 have been introduced here. In 43 cases higher-dimensional component spaces gave larger violation than qubits, and in three occasions the maximum was achieved with six-dimensional spaces. We have also calculated upper bounds on these Bell inequalities using a method proposed recently. For all but 20 inequalities the best solution found matched the upper bound. Surprisingly, the simplest inequality of the set examined, with only three measurement settings per party, was not among them, despite the high dimensionality of the Hilbert space considered. We also computed detection threshold efficiencies for the maximally entangled qubit pair. These could be lowered in several instances if degenerate measurements were also allowed.",
author = "K. P{\'a}l and T. V{\'e}rtesi",
year = "2009",
month = "2",
day = "26",
doi = "10.1103/PhysRevA.79.022120",
language = "English",
volume = "79",
journal = "Physical Review A",
issn = "2469-9926",
publisher = "American Physical Society",
number = "2",

}

TY - JOUR

T1 - Quantum bounds on Bell inequalities

AU - Pál, K.

AU - Vértesi, T.

PY - 2009/2/26

Y1 - 2009/2/26

N2 - We have determined the maximum quantum violation of 241 tight bipartite Bell inequalities with up to five two-outcome measurement settings per party by constructing the appropriate measurement operators in up to six-dimensional complex and eight-dimensional real-component Hilbert spaces using numerical optimization. Out of these inequalities 129 have been introduced here. In 43 cases higher-dimensional component spaces gave larger violation than qubits, and in three occasions the maximum was achieved with six-dimensional spaces. We have also calculated upper bounds on these Bell inequalities using a method proposed recently. For all but 20 inequalities the best solution found matched the upper bound. Surprisingly, the simplest inequality of the set examined, with only three measurement settings per party, was not among them, despite the high dimensionality of the Hilbert space considered. We also computed detection threshold efficiencies for the maximally entangled qubit pair. These could be lowered in several instances if degenerate measurements were also allowed.

AB - We have determined the maximum quantum violation of 241 tight bipartite Bell inequalities with up to five two-outcome measurement settings per party by constructing the appropriate measurement operators in up to six-dimensional complex and eight-dimensional real-component Hilbert spaces using numerical optimization. Out of these inequalities 129 have been introduced here. In 43 cases higher-dimensional component spaces gave larger violation than qubits, and in three occasions the maximum was achieved with six-dimensional spaces. We have also calculated upper bounds on these Bell inequalities using a method proposed recently. For all but 20 inequalities the best solution found matched the upper bound. Surprisingly, the simplest inequality of the set examined, with only three measurement settings per party, was not among them, despite the high dimensionality of the Hilbert space considered. We also computed detection threshold efficiencies for the maximally entangled qubit pair. These could be lowered in several instances if degenerate measurements were also allowed.

UR - http://www.scopus.com/inward/record.url?scp=62549090212&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=62549090212&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.79.022120

DO - 10.1103/PhysRevA.79.022120

M3 - Article

AN - SCOPUS:62549090212

VL - 79

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 2

M1 - 022120

ER -