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arXiv:2509.01290

Counterfactual Local Friendliness: An epsilon-Bounded Interaction-Free Paradox and a Disturbance-Robust Three-Box Inequality

Maximilian Ralph Peter von Liechtenstein

Published Sep 1, 2025• 0 citations
arXivHTMLPDF

Abstract

We introduce a new paradox, which we call Counterfactual Local Friendliness (CLF): a Wigner's-friend-type logical collision in which every decisive inference is obtained by interaction-free flags whose disturbance on the probed object is bounded by a tunable parameter $ε$. Under (Q) universal unitarity for outside observers, (S) single-outcome facts, (C) cross-agent consistency, and (IF-$ε$) $ε$-counterfactuality of the friends' internal modules, quantum theory predicts a nonzero post-selected event that forces mutually incompatible certainties about a single upstream variable -- without appealing to absorptive or projective in-lab measurements. We also derive an $ε$-IF three-box noncontextual bound: any single-world, noncontextual model satisfying exclusivity and epsilon-stability must obey $P(A) + P(B) \le 1 + K_ε$, while quantum theory yields $P(A) = P(B) = 1$, violating the bound for arbitrarily small $ε$. Together these results isolate what is paradoxical about counterfactual phenomena: not energy exchange with the probed system, but the incompatibility of agent-level facts in single-world narratives.

DOI
10.48550/arxiv.2509.01290

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We introduce a new paradox, which we call Counterfactual Local Friendliness (CLF): a Wigner's-friend-type logical collision in which every decisive inference is obtained by interaction-free flags whose disturbance on the probed object is bounded by a tunable parameter εεε. Under (Q) universal unitarity for outside observers, (S) single-outcome facts, (C) cross-agent consistency, and (IF-εεε) εεε-counterfactuality of the friends' internal modules, quantum theory predicts a nonzero post-selected event that forces mutually incompatible certainties about a single upstream variable -- without appealing to absorptive or projective in-lab measurements. We also derive an εεε-IF three-box noncontextual bound: any single-world, noncontextual model satisfying exclusivity and epsilon-stability must obey P(A)+P(B)≤1+KεP(A) + P(B) \le 1 + K_εP(A)+P(B)≤1+Kε​, while quantum theory yields P(A)=P(B)=1P(A) = P(B) = 1P(A)=P(B)=1, violating the bound for arbitrarily small εεε. Together these results isolate what is paradoxical about counterfactual phenomena: not energy exchange with the probed system, but the incompatibility of agent-level facts in single-world narratives.
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.
Wigner's Friend-type paradoxes challenge the assumption that events are absolute—that when we measure a system, we obtain a single result, which is not relative to anything or anyone else. These paradoxes highlight the tension between quantum theory and our intuitions about reality being observer independent. Building on a recent result that developed these paradoxes into a no-go theorem, namely, the , we introduce the , a time-ordered analog of it. In this framework, we replace the usual locality assumption with and show that, when combined with the assumptions of (AOE), , and , we obtain a Causal Time-Symmetric Friendliness inequality. We then show that quantum mechanics violates this inequality and is therefore incompatible with at least one of these assumptions. To probe which assumption might be incompatible, we then examine whether AOE in its entirety is essential for this no-go result. We propose a weaker, operational form of AOE that still leads to inequalities that quantum mechanics violates. This result shows that even under relaxed assumptions, quantum theory resists reconciliation with classical notions of absolute events, reinforcing the foundational significance of Wigner's Friend-type paradoxes in timelike scenarios.
The Wigner's friend thought experiment raises the question of whether quantum theory can be applied consistently to systems that include observers. Extended Wigner's Friend Scenarios develop this question by considering several observers who may assign different descriptions to the same experiment. In the Local Friendliness (LF) framework, these scenarios lead to experimentally testable inequalities derived from assumptions such as Absoluteness of Observed Events and Local Agency. Motivated by the “Thoughtful” version of the Local Friendliness no-go theorem, which points towards future LF tests with human-level artificial agents implemented on quantum computers, this thesis implements the “friend” with explicit agent-like functionality within a reversible quantum circuit. Several such agents are constructed and embedded into a one-friend Extended Wigner's Friend Scenario, following recent work that uses quantum computers as a platform for LF violations with more sophisticated “friend” systems. These agents store measurement outcomes, condition later operations on stored information, and, in the most structured case, use Born-rule probabilities to bet on the outcomes of their own future observations. The circuits are implemented in Qiskit, simulated ideally and with IBM-device noise models, and executed on ibm_marrakesh. In ideal simulations, all agent implementations reproduce the maximal quantum violation of a Local Friendliness inequality up to finite-shot fluctuations. Hardware runs show positive Local Friendliness violations for all implemented agents, with decreasing violation strength consistent with greater noise accumulation. The observed violations also remain above an estimated bound obtained by considering relaxations of a Local Friendliness assumption. These results provide a first step towards more structured agent-like friend models in LF experiments on quantum computers.
The Wigner's friend thought experiment raises the question of whether quantum theory can be applied consistently to systems that include observers. Extended Wigner's Friend Scenarios develop this question by considering several observers who may assign different descriptions to the same experiment. In the Local Friendliness (LF) framework, these scenarios lead to experimentally testable inequalities derived from assumptions such as Absoluteness of Observed Events and Local Agency. Motivated by the "Thoughtful" version of the Local Friendliness no-go theorem, which points towards future LF tests with human-level artificial agents implemented on quantum computers, this work implements the "friend" with explicit agent-like functionality within a reversible quantum circuit. Drawing from the literature on Artificial Intelligence, we construct rudimentary agent-like systems and embed them into a one-friend Extended Wigner's Friend Scenario. These agents store measurement outcomes, condition later operations on stored information, and, in the most structured case, use Born-rule probabilities to bet on the outcomes of their own future observations based on past observations. The circuits are simulated ideally and with an IBM-device noise model and executed on ibm_marrakesh. Ideal simulations reproduce the maximal quantum violation of a Local Friendliness inequality up to finite-shot fluctuations, while hardware runs show positive LF violations for all implemented agents. These results provide a first step towards more structured agent-like friend models in LF experiments on quantum computers.
Local Friendliness (LF) inequalities follow from seemingly reasonable assumptions about reality: (i) ``absoluteness of observed events'' (e.g., every observed event happens for all observers) and (ii) ``local agency'' (e.g., free choices can be made uncorrelated with other events outside their future light cone). Extended Wigner's Friend Scenario (EWFS) thought experiments show that textbook quantum mechanics violates these inequalities. Thus, experimental evidence of these violations would make these two assumptions incompatible. In [Nature Physics 16, 1199 (2020)], the authors experimentally implemented an EWFS, using a photonic qubit to play the role of each of the ``friends'' and measured violations of LF. One may question whether a photonic qubit is a physical system that counts as an ``observer'' and thereby question whether the experiment's outcome is significant. Intending to measure increasingly meaningful violations, we propose using a statistical measure called the ``branch factor'' to quantify the ``observerness'' of the system. We then encode the EWFS as a quantum circuit such that the components of the circuit that define the friend are quantum systems of increasing branch factor. We run this circuit on quantum simulators and hardware devices, observing LF violations as the system sizes scale. As errors in quantum computers reduce the significance of the violations, better quantum computers can produce better violations. Our results extend the state of the art in proof-of-concept experimental violations from branch factor 0.0 to branch factor 16.0. This is an initial result in an experimental program for measuring LF violations at increasingly meaningful branch factors using increasingly more powerful quantum processors and networks. We introduce this program as a fundamental science application for near-term and developing quantum technology.
The renowned Local Friendliness no-go theorem demonstrates the incompatibility of quantum theory with the combined assumptions of Absoluteness of Observed Events - the idea that observed outcomes are singular and objective - and Local Agency - the requirement that the only events correlated with a setting choice are in its future light cone. Granted that the Local Friendliness scenario can be realized, this result is stronger than Bell's theorem because the assumptions of Local Friendliness are weaker than those of Bell's theorem: Local Agency is less restrictive than local causality, and Absoluteness of Observed Events is encompassed within the notion of realism assumed in Bell's theorem. Drawing inspiration from the correspondence between nonlocality proofs in Bell scenarios and generalized contextuality proofs in prepare-and-measure scenarios, we present the Noncontextual Friendliness no-go theorem. This theorem demonstrates the inconsistency of quantum theory with the joint assumptions of Absoluteness of Observed Events and Noncontextual Agency, the latter being a weaker version of noncontextuality, in the same way that Local Agency is a weaker version of local causality. Our result generalizes the Local Friendliness no-go theorem and, granted that the scenario can be realized, is stronger than no-go theorems based on generalized noncontextuality.