2017
DOI: 10.26421/qic17.13-14-5
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Topological proofs of contextuality in quantum mechanics

Abstract: We provide a cohomological framework for contextuality of quantum mechanics that is suited to describing contextuality as a resource in measurement-based quantum computation. This framework applies to the parity proofs first discussed by Mermin, as well as a different type of contextuality proofs based on symmetry transformations. The topological arguments presented can be used in the state-dependent and the state-independent case.

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Cited by 31 publications
(85 citation statements)
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“…Note that the phase point operators of the form eq. ( 19) only exist when the local Hilbert space dimension d is odd since noncontextual value assignments on E exist only when d is odd [41]. The proof of this statement requires the following lemma.…”
Section: Partial Characterization Of Vertices Of λmentioning
confidence: 96%
See 1 more Smart Citation
“…Note that the phase point operators of the form eq. ( 19) only exist when the local Hilbert space dimension d is odd since noncontextual value assignments on E exist only when d is odd [41]. The proof of this statement requires the following lemma.…”
Section: Partial Characterization Of Vertices Of λmentioning
confidence: 96%
“…The functions Φ and β have a cohomological interpretation elucidated in Ref. [41] (also see Ref. [42]).…”
Section: Introductionmentioning
confidence: 99%
“…Part (1) follows from the definition of the chain complex; see also Ref. 6. Part (2) follows from the observation that γG is the image of the identity map in…”
Section: Ifmentioning
confidence: 99%
“…More recently Okay et al described an obstruction for contextuality in measurement based quantum computation (MBQC) that is based on group cohomology [15]. While the Čech cohomology obstruction is well defined for any set of quantum measurements, their obstruction exploits the algebraic structure of the Pauli measurements used in MBQC.…”
Section: Introductionmentioning
confidence: 99%