Contextuality-by-Default Description of Bell Tests: Contextuality as the Rule and Not as an Exception

Abstract

Contextuality and entanglement are valuable resources for quantum computing and quantum information. Bell inequalities are used to certify entanglement; thus, it is important to understand why and how they are violated. Quantum mechanics and behavioural sciences teach us that random variables ‘measuring’ the same content (the answer to the same Yes or No question) may vary, if ‘measured’ jointly with other random variables. Alice’s and Bob’s raw data confirm Einsteinian non-signaling, but setting dependent experimental protocols are used to create samples of coupled pairs of distant ±1 outcomes and to estimate correlations.Marginal expectations, estimated using these final samples, depend on distant settings. Therefore,a system of random variables ‘measured’ in Bell tests is inconsistently connected and it should be analyzed using a Contextuality-by-Default approach, what is done for the first time in this paper.The violation of Bell inequalities and inconsistent connectedness may be explained using a contextual locally causal probabilistic model in which setting dependent variables describing measuring instruments are correctly incorporated. We prove that this model does not restrict experimenters` freedom of choice which is a prerequisite of science. Contextuality seems to be the rule and not an exception; thus, it should be carefully tested.

Observations of Bell Inequality Violations with Causal Isolation between Source and Detectors

“…As for the physical content, one can argue in scenario 1 that there is no background field; it simply does not exist and something else is responsible for the Bell effect. This is the view espoused in the contextuality approach [ 14 , 15 ]: neither travelling nor standing background waves are needed in order to cause BIV. In this scenario, all we have done here is to reduce luminosity.…”

“…In the view of contextuality, Bell inequalities may be derived using probabilistic models describing four random experiments performed in incompatible experimental contexts [ 14 ]. In this view, all speculations about a Bell “effect” are based on an incorrect causal interpretation of conditional probabilities [ 15 ]. Others argue the physical fact that Bell-type correlations emerge from classical electromagnetism [ 16 ].…”

Quantifying and Interpreting Connection Strength in Macro- and Microscopic Systems: Lessons from Bell’s Approach

“…Interpreting the meaning of a quantum state, and the question of whether it expresses the objective underlying physical state of a system or rather the possible measurement outcomes and information, is still a matter of debate [19,21,23]. Contextuality becomes an important concept [25,28,[78][79][80][81][82][83] and it can be formalized to some degree, for example, by requiring predictive completeness, which means that the quantum state has to be completed by linking it with a measurement operator as well [29].…”

“…John Bell's seminal work [1][2][3][4][5][6] has triggered a rich tradition of experimental studies [7][8][9][10][11][12][13] as well as theoretical and interpretational work [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. To derive his famous inequalities, he has taken a realist worldview, making the additional assumption of free choice and locality, as formally defined by precise equations in a hidden variable model.…”

Assumption-Free Derivation of the Bell-Type Criteria of Contextuality/Nonlocality

“…The term "nonlocality" has been criticized as misleading, unnecessary, or even outright contradicting the tenets of quantum physics in several recent publications [4][5][6]. In this paper, however, the term is used to simply designate a special case of contextuality, for systems where contexts are formed by spacelike separated components.…”