Abstract
In a recent work, it was shown by one of us (EGC) that Bell-Kochen-Specker inequality violations in phenomena satisfying the no-disturbance condition (a generalisation of the no-signalling condition) cannot in general be explained with a faithful classical causal model---that is, a classical causal model that satisfies the assumption of no fine-tuning. The proof of that claim however was restricted to Bell scenarios involving 2 parties or Kochen-Specker-contextuality scenarios involving 2 measurements per context. Here we show that the result holds in the general case of arbitrary numbers of parties or measurements per context; it is not an artefact of the simplest scenarios. This result unifies, in full generality, Bell nonlocality and Kochen-Specker contextuality as violations of a fundamental principle of classical causality. We identify, however, an implicit assumption in the former proof, making it explicit here: that certain operational symmetries of the phenomenon are reflected in the model, rather than requiring fine-tuned choices of model parameters. This clarifies a subtle but important distinction between Bell nonlocality and Kochen-Specker contextuality.
Highlights
Bell nonlocality [1] and Kochen-Specker (KS) contextuality [2] are classically forbidden correlations characteristic of quantum phenomena
Bell nonlocality is a key resource for quantum communication, with applications such as reducing communication complexity [5] and secure communication [6]
Since classical simulation of Bell correlations is possible via the addition of communication channels between the parties in the Bell test [7, 8], quantum over classical advantages provided by Bell nonlocality can be understood as quantum protocols having access to correlations that can only be simulated classically with the aid of extra resources
Summary
Bell nonlocality [1] and Kochen-Specker (KS) contextuality [2] are classically forbidden correlations characteristic of quantum phenomena. Considering a classical causal model to be (essentially) a classical simulation of a quantum phenomenon, this provides a novel approach to understanding the quantum over classical advantage provided by Bell-KS correlations: fine-tuning can be considered an unavoidable resource waste in any classical simulation, relative to the quantum realisation of the same correlations. We generalise the framework of [15] to arbitrary numbers of parties or measurements per context, demonstrating in full generality the need for fine-tuning in classical causal models for Bell-KS inequality violations. That definition did not account for the possibility that the same measurement could have different statistics depending on which random variable in a causal model it is associated with, which would represent a form of contextuality not ruled out by the notion of no fine-tuning used in that work.
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