Hi all,

Next Monday Ghislain Fourny will talk about his work on “Quantum theory as a game between observers and nature: a local-realist extension model with a revisited form of free choice”, see below for the abstract. The talk will take place in HIT F 12 at 16:00.

Best, Ladina

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Title: Quantum theory as a game between observers and nature: a local-realist extension model with a revisited form of free choice

Abstract: In the field of quantum foundations, it is common to abstract away quantum physics experiments in terms of choosing settings and then reading outcomes on measurement devices. Multiple experiments can then be connected together in a generic fashion with frameworks such as process matrices. Then, the frequency distribution of the outcomes conditioned on the settings can be obtained both theoretically (via the generalized Born rule based on the process matrix and on the local instruments corresponding to the chosen settings and the considered outcomes) and practically (e.g., by actually carrying out the experiment with spin measurements). The consequences of assumptions such as measurement independence (aka free choice) and of local realism can then be investigated in terms of the conditional probabilities being constrained to convex polytopes, the faces of which correspond to Bell inequalities.

Our contribution is that, in the particular case of fixed causal order, we showed that it is possible to view quantum processes as games between the observers (who pick the settings) and the universe (which picks the outcomes)—in other words, we reformulated quantum theory as a decision theory rather than as a probabilistic theory. The game framework, called “spacetime games," is generic enough to account for space-like separation between the labs, time-like separation between the labs but also including adaptive measurements (i.e., a setting may not be fully exogenous, but may instead depend on causally-preceding outcomes). While spacetime games can be seen as a generalization of nonlocal games to general processes (including the derivation of Bell inequalities and the corresponding polytopes), they differ from nonlocal games in that the universe agents do not try to maximally break Bell inequalities, but instead aim at minimizing their action, which is modeled as rewards in the game.

We showed that the Nash-equilibrium approach to game theory checks all the boxes of the assumptions behind Bell inequalities: (i) unilateral deviations of strategies correspond to measurement independence and an exogenous choice of settings, (ii) imperfect information corresponds to locality (finite speed of light) but also more broadly to noncontextuality, and (iii) (Nashian) mixed strategies of the universe to realism and to deterministic hidden variable models. The direct consequence is that Nashian game theory is constrained by Bell inequalities, is formally equivalent to deterministic hidden variable models, and thus inadequate for an extension theory of quantum theory.

However, there exist alternate approaches to game theory that we formalized in the past 20 years, and which we call "Non-Nashian game theory.” Non-Nashian game theory differs from Nash-based game theory in that deviations are not unilateral—thus, it does not fulfill one of the assumptions behind Bell inequalities and many other impossibility theorems of quantum foundations—but it preserves local-realism. More specifically, the prediction of a decision (setting or outcome) depends counterfactually on the decision. In particular, we have in our toolbox a solution concept and algorithm called “Perfect Prediction Equilibrium” that is able to pinpoint either 0 or 1 solutions (a fixpoint), but not more, for any spacetime game in general position. This means that the algorithm predicts individual runs, making it a local-realist (but not measurement-independent) extension model.

The model’s open parameters (which must be specified to make it a full-fledged extension theory) are the reward formulas (depending on the settings, outcomes, and global hidden variable) in the leaves of the game structure. We are currently using a machine-learning approach based on Physics-Inspired Models (PIN) that aims at discovering the reward formulas that recover the frequencies predicted by the Born rule, i.e., in a way that is consistent with actual Bell-inequality-breaking experiments.

In this talk, I will give a general introduction to the spacetime framework and to the non-Nashian resolution algorithm. I will also give a few recent insights regarding the reward formulas in the case of the EPR (2 players/2 settings/2 outcomes) experiment, and show that the non-Nashian algorithm is able, in the EPR case, to produce a frequency distribution that is obtained through the random selection of the value of a hidden variable, and that breaks the CHSH inequality.

I will also briefly explain how spacetime games seen from the Nash perspective recover causal contextuality scenarios (Abramsky et al, 2024) and by transitivity several other frameworks (contextuality and nonlocal games in the flat case, the Gogioso-Pinzani framework in the case of fixed causal order, classical causal networks, etc). This considerably simplifies several constructs and proofs by exploiting well-known, decade-old (1950 and later) game theory results.

[ High-level explanations and references to published papers on http://www.non-nashian-game-theory.org http://www.non-nashian-game-theory.org/ http://www.non-nashian-game-theory.org/ ]