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arXiv:2407.20346 · Physical Review A

Local friendliness polytopes in multipartite scenarios

Marwan Haddara, Eric G. Cavalcanti

Published Jan 9, 2025• 3 citations
arXivHTMLPDF

Abstract

Recently, the local friendliness (LF) no-go theorem has attracted considerable interest due to its deep foundational implications. This no-go theorem applies to scenarios which combine Bell experiments with Wigner's friend-type setups, containing spacelike separated superobservers assumed to be capable of performing quantum operations on a local observer, also known as their ``friend.'' The theorem shows that a set of assumptions termed ``local friendliness''---weaker than the set of assumptions required for proving Bell's theorem---constrains the space of probabilistic behaviors in extended Wigner's friend scenarios to the ``local friendliness (LF) polytope,'' and that quantum correlations can, in principle, violate those constraints. In this work, we extend the study of local friendliness to multipartite scenarios---with arbitrary but finite numbers of superobservers, friends, measurements, and outcomes---and fully characterize the corresponding LF polytopes, their relationships with each other, with the Bell polytope, the no-signaling polytope, and the quantum set of correlations. In particular, we identify, via constructive proofs, all the canonical LF scenarios where the LF polytope coincides with the Bell polytope---hence identifying all the scenarios where ``genuine LF inequalities'' may arise. Among other results, we also show that whenever the LF polytope is distinct from the Bell and the no-signaling polytope, it also is neither contained in nor contains the quantum set of correlations. Apart from the foundational motivation of better understanding the constraints from local friendliness, our results may also find use in a priori unrelated contexts of device-independent information processing, where the LF polytopes have also been shown to arise, under the name of ``partially deterministic polytopes.''

DOI
10.1103/physreva.111.012206

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Recently, the local friendliness (LF) no-go theorem has attracted considerable interest due to its deep foundational implications. This no-go theorem applies to scenarios which combine Bell experiments with Wigner's friend-type setups, containing spacelike separated superobservers assumed to be capable of performing quantum operations on a local observer, also known as their friend.'' The theorem shows that a set of assumptions termed local friendliness''---weaker than the set of assumptions required for proving Bell's theorem---constrains the space of probabilistic behaviors in extended Wigner's friend scenarios to the local friendliness (LF) polytope,'' and that quantum correlations can, in principle, violate those constraints. In this work, we extend the study of local friendliness to multipartite scenarios---with arbitrary but finite numbers of superobservers, friends, measurements, and outcomes---and fully characterize the corresponding LF polytopes, their relationships with each other, with the Bell polytope, the no-signaling polytope, and the quantum set of correlations. In particular, we identify, via constructive proofs, all the canonical LF scenarios where the LF polytope coincides with the Bell polytope---hence identifying all the scenarios where genuine LF inequalities'' may arise. Among other results, we also show that whenever the LF polytope is distinct from the Bell and the no-signaling polytope, it also is neither contained in nor contains the quantum set of correlations. Apart from the foundational motivation of better understanding the constraints from local friendliness, our results may also find use in a priori unrelated contexts of device-independent information processing, where the LF polytopes have also been shown to arise, under the name of ``partially deterministic polytopes.''
The Local Friendliness argument is an extended Wigner's friend no-go theorem that provides strong constraints on the nature of reality – stronger even than those imposed by Bell's theorem or by noncontextuality arguments. In this work, we prove a variety of connections between Local Friendliness scenarios and Kochen-Specker noncontextuality. Specifically, we first show how one can derive new Local Friendliness inequalities using known tools and results from the literature on Kochen-Specker noncontextuality. In doing so, we provide a new derivation for some of the facets of the Local Friendliness polytope, and we prove that this polytope is equal to the Bell polytope in a wide range of extended Wigner's friend scenarios with multipartite agents and sequential measurements. We then show how any possibilistic Kochen-Specker argument can be mathematically translated into a related proof of the Local Friendliness no-go theorem. In particular, we construct a novel kind of Local Friendliness scenario where a friend implements several compatible measurements (or joint measurements of these) in between the superobserver's operations on them. We illustrate this with the well-known 5-cycle and Peres-Mermin contextuality arguments.
A recent paper by two of us and co-workers \cite{CQD20}, based on an extended Wigner's friend scenario, demonstrated that certain empirical correlations predicted by quantum theory (QT) violate inequalities derived from a set of metaphysical assumptions we called "Local Friendliness" (LF). These assumptions are strictly weaker than those used for deriving Bell inequalities. Crucial to the theorem was the premise that a quantum system with reversible evolution could be an observer (colloquially, a "friend"). However, that paper was noncommittal on what would constitute an observer for the purpose of an experiment. Here, we present a new LF no-go theorem which takes seriously the idea that a system's having thoughts is a sufficient condition for it to be an observer. Our new derivation of the LF inequalities uses four metaphysical assumptions, three of which are thought-related, including one that is explicitly called "Friendliness". These four assumptions, in conjunction, allow one to derive LF inequalities for experiments involving the type of system that "Friendliness" refers to. In addition to these four metaphysical assumptions, this new no-go theorem requires two assumptions about what is technologically feasible: Human-Level Artificial Intelligence, and Universal Quantum Computing which is fast and large scale. The latter is often motivated by the belief that QT is universal, but this is not an assumption of the theorem. The intent of the new theorem is to give a clear goal for future experimentalists, and a clear motivation for trying to achieve that goal. We review various approaches to QT in light of our theorem. The popular stance that "quantum theory needs no interpretation" does not question any of our assumptions and so is ruled out. Finally, we quantitatively discuss how difficult the experiment we envisage would be, and briefly discuss milestones on the paths towards it.
The Wigner’s friend thought experiment has gained a resurgence of interest in recent years thanks to no-go theorems that extend it to Bell-like scenarios. One of these, by us and co-workers, showcased the contradiction that arises between quantum theory and a set of assumptions, weaker than those in Bell’s theorem, which we named ‘Local Friendliness’. Using these assumptions, it is possible to arrive at a set of inequalities for a given scenario, and, in general, some of these inequalities will be harder to violate than the Bell inequalities for the same scenario. A crucial feature of the extended Wigner’s friend scenario in our aforementioned work was the ability of a superobserver to reverse the unitary evolution that gives rise to their friend’s measurement. Here, we present a new scenario where the superobserver can interact with the friend repeatedly in a single experimental instance, either by asking them directly for their result, thus ending that instance, or by reversing their measurement and instructing them to perform a new one. We show that, in these scenarios, the Local Friendliness inequalities will always be the same as Bell inequalities.
Abstract The famous ‘Wigner’s friend’ paradox highlights the difficulty of modelling the evolution of quantum systems under measurement in situations where observers themselves are considered to be subject to the laws of quantum mechanics. In recent years, variations of the original Wigner’s friend paradox have been recognized as fruitful arenas for probing the foundations of quantum theory. In particular (Bong et al 2020 Nat. Phys. 16 1199) demonstrated a contradiction between a set of intuitive assumptions called ‘Local Friendliness’ (LF) and certain quantum phenomena on an extended version of the Wigner’s friend paradox. The LF assumptions can be understood as the conjunction of two independent assumptions: Absoluteness of Observed Events requires that any event observed by any observer has an absolute, rather than relative, value; Local Agency is the assumption that an intervention cannot be correlated with relevant events outside its future light cone. These assumptions are weaker than the assumptions that lead to Bell’s theorem, and thus while the LF result may be considered to be conceptually comparable to Bell’s result, its implications are even deeper. The proof of the LF no-go theorem, however, relies on probability theory, and a fundamental question remained whether or not LF is an inherently statistical concept. Here we present a probability-free version of the LF theorem, building upon Hardy’s no-go theorem for local hidden variables. The argument is phrased in the language of possibilities, which we make formal by using a modal logical approach. It relies on a weaker version of Local Agency, which we call ‘Possibilistic Local Agency’: the assumption that an intervention cannot affect the possibilities of events outside its future light cone.
We provide a new formulation of the Local Friendliness no-go theorem of Bong et al. [Nat. Phys. 16, 1199 (2020)] from fundamental causal principles, providing another perspective on how it puts strictly stronger bounds on quantum reality than Bell's theorem. In particular, quantum causal models have been proposed as a way to maintain a peaceful coexistence between quantum mechanics and relativistic causality while respecting Leibniz's methodological principle. This works for Bell's theorem but does not work for the Local Friendliness no-go theorem, which considers an extended Wigner's Friend scenario. More radical conceptual renewal is required; we suggest that cleaving to Leibniz's principle requires extending relativity to events themselves.
Recent no-go theorems based on extended Wigner's Friend scenarios (EWFS) reveal a deep tension between the universal validity of quantum theory and local friendliness (LF), the conjunction of three natural assumptions: the absoluteness of observed events, locality, and no-superdeterminism. In a recent work, Adlam argues that this tension can be dissolved by appealing to quantum reference frames (QRFs). We present and critically assess her proposal. We show that her proposed resolution does not arise from QRFs, but instead relies on three independent modifications: certain degrees of freedom are always definite, observers can flip upon measuring spins, and the outcomes the superobservers record and use to test the inequalities are not their friends' observed results. The proposal and the arguments for the plausibility of these modifications rest on several misconceptions about QRFs and EWFS, which we rectify. We conclude that, within standard quantum theory, quantum reference frames do not evade the EWFS no-go theorems.