Abstract
This paper proposes a necessary clarification about the problematic of super-quantum correlations, whose mainstream debate relies on an incorrect, statistical interpretation of the no-signaling condition. The no-signaling condition is an informational constraint that limits the strength of non-local correlations to the Tsirelson bound.
Highlights
Open AccessIt has been suggested that non-local correlations stronger than quantum correlations between two sub-systems that cannot exchange any information would be “theoretically possible” [1] [2]
2) The “no-signaling” assumption (NS), which obviously aims to assert that Alice and Bob cannot exchange any signal or any information, has been expressed in the mainstream literature—for example in Popescu’s and Rohrlich’s work [2]—by the following statistical condition according to which the probability that Alice obtains a particular outcome “a” is independent of the choice of Bob’s action, when he decides to push his joystick to the right or to the left -that is, this probability is independent of the value of y, and vice versa [1]: For all possible actions x, x′, y, y′ and for all possible outcomes a,b
Note that another interpretation of the term “super-quantum” has been provided in the literature [10] [11]: “super-quantum” or “post-quantum”, would refer to the impossibility of describing an experimental situation within the framework of quantum theory, by representing observables by operators of a C* algebra, states as vectors of a Hilbert space and by computing the probabilities of outcomes by the Born rule. With this linguistic-like interpretation of “super-quantum”, as quantum describability, the latter conclusion does not hold any more because, as can be shown, quantum “noisy” states, which are partially entangled, can give rise to correlations whose maximal degree is smaller than the Tsirelson bound. This implies that the quantum describability interpretation of “super-quantum” does not coincide with Popescu’s and Rohrlich’s interpretation of “super-quantum” in terms of “stronger than quantum correlations”, interpretation on which we have focused in this article
Summary
It has been suggested that non-local correlations stronger than quantum correlations between two sub-systems that cannot exchange any information would be “theoretically possible” [1] [2]. A “box”, which is the central device of the Bell’s game played by two parties, can be described by an arithmetic relation between couples of “inputs”, which can be regarded as the indexes of the two directions (right or left) each of the two parties (Alice and Bob) push her/his joystick, and “outputs”, which are the possible responses of the box for these actions. This convenient representation of bipartite correlations will be adopted here for discussing the validity of some mainstream ideas about the question of super-quantum correlations
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