## 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

689 |
Quantum Theory: Concepts and Methods
- Peres
- 1993
(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 ... |

551 | Speakable and Unspeakable in Quantum Mechanics - Bell - 1987 |

446 | Mathematical Foundations of Quantum Mechanics - Neumann - 1932 |

432 |
Mathematische Grundlagen der Quantummechanik
- Neumann
- 1932
(Show Context)
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... |

98 |
Finite-Dimensional Vector spaces
- Halmos
- 1974
(Show Context)
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... |

78 | Quantum Logic
- Svozil
- 1998
(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 ... |

40 | The logico-algebraic approach to quantum mechanics - Hooker |

30 |
The Unitary and Rotation Group (Spartan Books
- Murnaghan
- 1962
(Show Context)
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
- Redhead
- 1987
(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
- Mair
(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... |

7 |
Contextuality for preparations, transformations, and unsharp measurements
- Spekkens
- 2005
(Show Context)
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
- Vaziri, Weihs
(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 |
Deyanova Y
- Torres
(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
- Reck
(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
- Reck
- 1994
(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... |