Contextually in a Peres—Mermin square using arbitrary operators

Emergent Quantum Mechanics 2015

Laversanne-Finot, A.^1 ; Ketterer, A.^1 ; Barros, M.R.^3 ; Walborn, S.P.^3 ; Coudreau, T.^1 ; Keller, A.^2 ; Milman, P.^1

Univ. Paris Diderot, Sorbonne Paris Cité, Laboratoire Matériaux et Phénomènes Quantiques, UMR 7162, CNRS, Paris

F-75205, France^1

Univ. Paris Sud, Institut des Sciences Moléculaires d'Orsay (UMR 8214 CNRS), Orsay

F-91405, France^2

Instituto de Física, Universidade Federal Do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro, RJ

21941-972, Brazil^3

关键词: Arbitrary dimension;    Arbitrary operators;    Contextuality;    Continuous spectrum;    Continuous variables;    Gaussians;    Measurements of;    Non-Gaussian;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/701/1/012026/pdf
DOI  :  10.1088/1742-6596/701/1/012026

来源: IOP

【 摘 要 】

The contextuality of quantum mechanics can be shown by the violation of inequalities based on measurements of well chosen observables. These inequalities have been designed separately for both discrete and continuous variables. Here we unify both strategies by introducing general conditions to demonstrate the contextuality of quantum mechanics from measurements of observables of arbitrary dimensions. Among the consequences of our results is the impossibility of having a maximal violation of contextuality in the Peres-Mermin scenario with discrete observables of odd dimensions. In addition, we show how to construct a large class of observables with a continuous spectrum enabling the realization of contextuality tests both in the Gaussian and non-Gaussian regimes.