## Noncontextuality in multipartite entanglement (2005)

Venue: | J. Phys. A: Math. Gen |

Citations: | 11 - 11 self |

### BibTeX

@ARTICLE{Svozil05noncontextualityin,

author = {Karl Svozil},

title = {Noncontextuality in multipartite entanglement},

journal = {J. Phys. A: Math. Gen},

year = {2005},

pages = {5781--5798}

}

### OpenURL

### Abstract

Abstract. We discuss several multiport interferometric preparation and measurement configurations and show that they are noncontextual. Generalizations to the n particle case are discussed.

### Citations

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Citation Context ...kkens has proposed an operational definition of contextuality which generalizes the standard notion based on the quantum contextuality of sharp measurements [11]. Proofs of the Kochen-Specker theorem =-=[12, 13, 14, 15, 5, 16, 17, 18, 19, 20, 21, 22, 23]-=- utilize properly chosen finite systems of interlinked contexts; every single context corresponding to a system of maximal comeasurable observables. The systems of contexts are chosen for the purpose ... |

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Citation Context ..... but also on the complete disposition of the apparatus.” That is, the outcome of the measurement of an observable A might depend on which other observables from systems of maximal observables (Ref. =-=[9]-=-, p. 173 and Ref. [10], Sec. 84) are measured alongside with A. The simplest such configuration corresponds to an arrangement of five observables A,B,C,D,K with two comeasurable, mutually commuting, s... |

100 |
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Citation Context ...mplete disposition of the apparatus.” That is, the outcome of the measurement of an observable A might depend on which other observables from systems of maximal observables (Ref. [9], p. 173 and Ref. =-=[10]-=-, Sec. 84) are measured alongside with A. The simplest such configuration corresponds to an arrangement of five observables A,B,C,D,K with two comeasurable, mutually commuting, systems of operators {A... |

79 | Automaton logic
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Citation Context ...kkens has proposed an operational definition of contextuality which generalizes the standard notion based on the quantum contextuality of sharp measurements [11]. Proofs of the Kochen-Specker theorem =-=[12, 13, 14, 15, 5, 16, 17, 18, 19, 20, 21, 22, 23]-=- utilize properly chosen finite systems of interlinked contexts; every single context corresponding to a system of maximal comeasurable observables. The systems of contexts are chosen for the purpose ... |

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Citation Context ...algorithmic, constructive and tractable manner. The method is similar to Gaussian elimination and facilitates the parameterization of elements of the unitary group in arbitrary dimensions (e.g., Ref. =-=[28]-=-, Chapter 2). Reck, Zeilinger, Bernstein and Bertani have suggested to implement these group theoretic results by realizing interferometric analogues of any discrete unitary and hermitean operators in... |

20 |
Completeness, Nonlocality and Realism: A Prolegomenon to the Philosophy of Quantum Mechanics
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(Show Context)
Citation Context ...study properties of systems of observables corresponding to interlinked arrangements of tripods in three-dimensional Hilbert space, or interlinked orthogonal bases in higher dimensions. Contextuality =-=[5, 6, 7]-=- has been introduced by Bohr [8] and Bell (Ref. [5], Sec. 5) as the presumption § that the “... result of an observation may reasonably depend not only on the state of the system ... but also on the c... |

7 |
Vaziri A, Weihs G and Zeilinger A 2001 Nature 412
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Citation Context ...tuality in multipartite entanglement 2 1. Contextuality in universal quantum networks In addition to recent techniques to prepare engineered entangled states in any arbitrarydimensional Hilbert space =-=[1, 2, 3, 4]-=-, multiport interferometers could provide feasible quantum channels for physical questions requiring the utilization of higher than twodimensional states. In what follows, multiport interferometry wil... |

7 |
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- 2005
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Citation Context ...ated explicitly in Section 3. Recently, Spekkens has proposed an operational definition of contextuality which generalizes the standard notion based on the quantum contextuality of sharp measurements =-=[11]-=-. Proofs of the Kochen-Specker theorem [12, 13, 14, 15, 5, 16, 17, 18, 19, 20, 21, 22, 23] utilize properly chosen finite systems of interlinked contexts; every single context corresponding to a syste... |

2 |
Zeilinger A 2002
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Citation Context ...tuality in multipartite entanglement 2 1. Contextuality in universal quantum networks In addition to recent techniques to prepare engineered entangled states in any arbitrarydimensional Hilbert space =-=[1, 2, 3, 4]-=-, multiport interferometers could provide feasible quantum channels for physical questions requiring the utilization of higher than twodimensional states. In what follows, multiport interferometry wil... |

2 |
Deyanova Y
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(Show Context)
Citation Context ...tuality in multipartite entanglement 2 1. Contextuality in universal quantum networks In addition to recent techniques to prepare engineered entangled states in any arbitrarydimensional Hilbert space =-=[1, 2, 3, 4]-=-, multiport interferometers could provide feasible quantum channels for physical questions requiring the utilization of higher than twodimensional states. In what follows, multiport interferometry wil... |

2 |
Zeilinger A 1994 Quantum phase tracing of correlated photons in optical multiports
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(Show Context)
Citation Context ...d Bertani have suggested to implement these group theoretic results by realizing interferometric analogues of any discrete unitary and hermitean operators in a unified and experimentally feasible way =-=[26, 29]-=-. Early on, one of the goals was to achieve experimentally realizable multiport analogues of multipartite correlation experiments; in particular for particle states in dimensions higher than two. The ... |

2 |
Unitary operators as multiport interferometers Mathematica Program
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(Show Context)
Citation Context ...tted. Based on the decomposition of an arbitrary unitary transformation in four dimensions into unitary transformations of two-dimensional subspaces [28], Reck et al. [26] have developed an algorithm =-=[31]-=- for the experimental realization of any discrete unitary operator. When applied to the preparation and analyzing stages corresponding to the preparation transformation Up in Eq. (19) and the analizin... |

2 |
Properties of multi-partite dark states 2002
- Kok, Nemoto, et al.
(Show Context)
Citation Context ...depict reflectors. 3. Two particles three-state analogue 3.1. Singlet state preparation A group theoretic argument shows that in the case of two three-state particles, there is just one singlet state =-=[32, 33, 34]-=- |Φ〉 = 1 √ 3 (e1 ⊗ e3 − e2 ⊗ e2 + e3 ⊗ e1) ≡ 1 √ 3 (0,0,1,0,−1,0,1,0,0) T , (21) where again e1 = (1,0,0), e2 = (0,1,0) and e3 = (0,0,1) refer to elements of the standard basis of Hilbert space C 3 of... |

2 |
Svozil K 2005 All the singlet states
- Kasperkovitz
- 2005
(Show Context)
Citation Context ...ate, measured along three particular directions, such that the context structure is x ′′ 3 − x′′ 2 − x′′ 1 = x1 − x2 − x3 = x ′ 3 − x′ 1 − x′ 2 ; as depicted in Fig. 5. Group theoretic considerations =-=[38, 34]-=- show that the only singlet state for three threestate particles is |∆〉 = 1 √ 6 (| − +0〉 − | − 0+〉 + | + 0−〉 − | + −0〉 + |0 − +〉 − |0 + −〉). (32)sNoncontextuality in multipartite entanglement 14 x3 = ... |

1 |
Dialectica 14, 175–182 Reprinted in [44, pp. 175–182]; English translation: The logic of propositions which are not simultaneously decidable, reprinted in [45
- Specker
- 1960
(Show Context)
Citation Context ...kkens has proposed an operational definition of contextuality which generalizes the standard notion based on the quantum contextuality of sharp measurements [11]. Proofs of the Kochen-Specker theorem =-=[12, 13, 14, 15, 5, 16, 17, 18, 19, 20, 21, 22, 23]-=- utilize properly chosen finite systems of interlinked contexts; every single context corresponding to a system of maximal comeasurable observables. The systems of contexts are chosen for the purpose ... |

1 |
A and Zeilinger A
- Greenberger, Horne
- 1993
(Show Context)
Citation Context ...two phase shifters P1 and P2 in the input ports, followed by a beam splitter S, which is followed by a phase shifter P3 in one of the output ports. The device can be quantum mechanically described by =-=[39]-=- P1 : |0〉 → |0〉e i(α+β) , P2 : |1〉 → |1〉e iβ , S : |0〉 → √ T |1 ′ 〉 + i √ R|0 ′ 〉, S : |1〉 → √ T |0 ′ 〉 + i √ R|1 ′ 〉, P3 : |0 ′ 〉 → |0 ′ 〉e iϕ , (A.2) where every reflection by a beam splitter S cont... |