Nonlocal Teams and Information Structures

arXiv:2606.08645 · quant-ph, cs.SY, eess.SY · Submitted 2026-06-07 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "Nonlocal Teams and Information Structures".

Mira: The gist The authors find that projective strategies enjoy important properties in the usual CHSH game, but they do not carry over to its dynamic version,

Kai: First, who's behind it and why it matters.

Paper summary: Kai: So, we’re looking at this new paper called "Nonlocal Teams and Information Structures." Basically, they take the usual CHSH game—that Bell inequality setup—and look at it through team theory. They treat it like a team problem where players have to work together to minimize some cost based on their actions and an unknown state.

Mira: Right, so the big idea here is that they are testing how different types of strategies, classical, projective, and quantum ones, perform when you change the way information flows between the agents. Specifically they look at static versus dynamic information structures.

Kai: What they claim is that projective strategies have these really neat properties in the usual CHSH game when it’s static—meaning no agent can affect the underlying state—but those properties don't carry over to its dynamic version. That’s the main point, right?

Mira: Exactly. The authors set up a dynamic problem where one agent can’t even know what the other agent did, and there's some noise in that communication channel. They find that while classical strategies behave predictably across both static and dynamic setups, projective strategies don't always work when the information structure is dynamic.

Lev: From an engineering standpoint, if this is true for projective strategies under a dynamic setup, it means we can’t just assume those simple measurements are optimal anymore; they might get beaten by something else depending on the flow of information.

Kai: Yeah, and they point out that beyond a certain noise level in the channel, these team-optimal projective strategies stop being person-by-person optimal even though they still look good for individual pairs. It's a subtle fragility issue with quantum strategies when the setup changes.

Mira: That’s what really matters because it shows how sensitive these structural properties are to changes in the information structure, which is a concept we take for granted in static settings.

Conclusion: Kai: So, wrapping up this look at "Nonlocal Teams and Information Structures," it really boils down to how much information flow between players matters when you’re dealing with quantum games like the CHSH game. The authors showed that projective strategies are solid in a static world but crumble in a dynamic one because of how information gets corrupted or sequenced.

Mira: They demonstrate that this isn't just about theory; it means that the region where quantum advantage appears in these games shrinks significantly when you introduce dynamism into the information structure.

Lev: What this implies for us on the hardware side is that if we try to build systems based on projective measurements, we have to be very careful about the noise and how those measurements are sequenced, because those assumptions break down quickly under dynamic conditions.

Kai: Yeah, it’s about the interplay between the quantum resource—the entanglement—and this information flow structure. The paper shows that having a good quantum correlation isn't enough if you don't have the right information structure to exploit it correctly in a dynamic setting.

Mira: It highlights that we need to be much more precise when modeling these team problems because the assumptions we make about who knows what, static versus dynamic, dictates whether those structural properties hold true or not.

Lev: So, for practical application, it means we can't just assume a certain measurement strategy will work across different operational modes; you have to check the information structure first.

Drishti Baruah, Sachin Teli, Ankur A. Kulkarni

Indian Institute of Technology Bombay · Max-Planck-Institut für Quantenoptik

quant-ph, cs.SY, eess.SY

Submitted: 2026-06-07

Updated: 2026-10-13

Comments: 37 pages, 3 figures

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 69/100

The gist: The gist The authors find that projective strategies enjoy important properties in the usual CHSH game, but they do not carry over to its dynamic version, shedding light on the delicate interplay of

Key concepts

Information Structure: This describes who knows what within a team regarding an underlying state. It is 'static' if no agent can influence the state, but 'dynamic' if agents' inputs depend on each other or corrupted versions of prior actions are available to subsequent agents.
Static Information Structure: In this setting, the underlying system state is fixed and unchangeable by any team member. The information structure is simple because no agent has the ability to affect the state of nature, simplifying the analysis of strategy optimality.
Dynamic Information Structure: This involves a more complex flow where an agent's input depends on another agent's action. Specifically, one player might receive a corrupted version of another player's previous action while lacking full knowledge of the first player's original information.

Summary

The gist The authors find that projective strategies enjoy important properties in the usual CHSH game, but they do not carry over to its dynamic version, shedding light on the delicate interplay of information structure in quantum strategies and the fragility of some well known ideas under changes of information structure<ref:2606.08645#pg2>.

Information Structures and Game Formulation

The paper examines Bell nonlocal games through the lens of team theory, viewing them as (stochastic) team problems where agents must jointly design a strategy to minimize a cost depending on their collective actions and an unknown state<ref:2606.08645#pg4>. The information structure is defined as static if no agent can affect the underlying state, while it is dynamic if this assumption does not hold, specifically referring to its non-classical variant<ref:2606.08645#pg2>. A key distinction is that in the dynamic information structure, Bhima’s input depends on Arjuna’s action, and a noisecorrupted version of the first agent’s action is available to the second agent while the first agent’s information is not<ref:2606.08645#pg3>.

Strategy Classes and Optimal Costs

The study compares classical, quantum, and projective strategies (C, Q, ⊥) under both static (S) and dynamic (D) information structures<ref:2606.08645#pg4>. For classical deterministic strategies in the static structure, the optimal expected cost is given by Theorem 3.1 as J S∗ C(p1, p2) = min[p1p2, pe1p2, p1pe2, pe1pe2]<ref:2606.08645#pg4>. The optimal cost for classical strategies in the dynamic structure is J D∗ C(ps, pc) = min[pspc, pspec, pespc, pespec]<ref:2606.08645#pg4>.

Quantum Advantage and Projective Strategies

The main finding regarding quantum advantage is that projective strategies cease to be always optimal when the information structure is dynamic<ref:2606.08645#pg3>. For certain values of the problem parameters, projective strategies yield a strict quantum disadvantage over classical strategies when the information structure is dynamic<ref:2606.08645#pg2>. In contrast, for the static information structure, projective strategies are team optimal for all probability distributions<ref:2606.08645#pg4>. The optimal expected cost under quantum strategies in the static setting is given by Theorem 3.5 as J S∗ Q(p1, p2) = (1/2 - √1/2 q(p 2 1 + pe1 2)/(p 2 2 + pe2 2), if (2p1 − 1)(2p2 − 1) ≤ 4p1pe1 p3pe3, J S∗ C(p3, p4) otherwise and projective strategies are team optimal for static information structure.

Best Response Properties

The paper investigates solution concepts like person-by-person optimality and best response strategies over strategy classes A<ref:2606.08645#pg4>. It is shown that the property of best response over classical strategies holds for both the static and dynamic information structures<ref:2606.08645#pg4>. However, for projective strategies, this property does not hold for the dynamic information structure<ref:2606.08645#pg4>.

Invariance of Bell Costs

The analysis demonstrates that the team optimal costs do not change across the different Bell costs B1 through B8<ref:2606.08645#pg4>. For both static and dynamic information structures, the optimal quantum cost is invariant across all eight Bell costs Bk, k = 1..., 8<ref:2606.08645#pg4>. This invariance holds because the optimization in (21) is over all admissible strategies, and the expression J S∗ Q is invariant with replacing p1 by pe1 or p2 by pe2<ref:2606.08645#pg4>.

Conclusion on Information Structure Impact

The results highlight how the choice between a static and dynamic information structure significantly alters the landscape of optimality<ref:2606.08645#pg4>. In the static setting, projective strategies are team optimal for all probability distributions<ref:2606.08645#pg2>. In contrast, for the dynamic information structure, the region of quantum advantage is notably smaller because the optimal cost achieved by projective strategies is independent of the channel noise<ref:2606.08645#pg4>. Most importantly, it was found that there exist certain probability distributions in the dynamic game where projective strategies perform worse than classical ones, creating a region of strict quantum disadvantage<ref:2606.08645#pg2>. The fragility of well known quantum advantages when the flow of information between agents changes is demonstrated<ref:2606.08645#pg2>.

Summary

The paper explores the CHSH game through team theory, revealing that while projective strategies are team optimal in the static setting, they do not universally carry over to the dynamic variant<ref:2606.08645#pg4>. The information structure critically impacts optimality, leading to a smaller region of quantum advantage in the dynamic game and demonstrating strict quantum disadvantage for certain probability distributions<ref:2606.08645#pg2>. Furthermore, while best response properties hold for classical strategies in both settings, they fail for projective strategies in the dynamic setting<ref:2606.08645#pg4>. The invariance of optimal costs across all Bell costs confirms the robustness of the general results<ref:2606.08645#pg4>.

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Nonlocal Teams and Information Structures

Drishti Baruah1,4†, Sachin Teli1,4†, Ankur A. Kulkarni2,3∗

1Department of Physics, Indian Institute of Technology Bombay, Mumbai, India.

2Centre for Systems and Control, Indian Institute of Technology Bombay., Mumbai., India.

3Centre of Excellence in Quantum Information,, Computing,, Science and Technology,, Indian Institute of Technology Bombay., Mumbai., India.

4Max-Planck-Institut f¨ur Quantenoptik,, Hans-Kopfermann-Straße 1, D-85748, Garching, Germany.

**, Corresponding author(s). E-mail(s): kulkarni.ankur@iitb.ac.in;†These authors contributed equally to this work while the authors were affiliated to the Indian Institute of Technology Bombay.<ref:2606.08645#pg2>. We look at Bell inequalities [1] from the lens of information structures in stochastic teams<ref:2606.08645#pg2>. We consider the usual CHSH game and a dynamic variant of the same to study how various classes of strategies, classical, projective and quantum, behave under team theoretic solution concepts<ref:2606.08645#pg2>. We find that projective strategies (where each player performs projective measurements) enjoy important properties in the usual CHSH game, but they do not carry over to its dynamic version<ref:2606.08645#pg2>. These results shed light on the delicate interplay of information structure in quantum strategies and the fragility of some well known ideas under changes of information structure<ref:2606.08645#pg2>. 1 Introduction We look at Bell’s theorem [1], asserting that quantum theory’s predictions cannot be explained by any local theory, stands as a milestone in the foundations of physics, revealing the inherent conflict between quantum mechanics and the principle of locality<ref:2606.08645#pg2>. Viewing Bell nonlocal games as games offers an intuitive understanding, as exemplified by the CHSH game<ref:2606.08645#pg2>. Bell nonlocal games [2] involve multiple agents who receive inputs and produce actions to minimize a cost that depends on their actions and a state of nature that is correlated with their inputs, but not fully known to either agent<ref:2606.08645#pg2>. Strategies utilising quantum resources such as shared entanglement and quantum measurements often outperform classical strategies in these games, providing an advantage via the deployment of such resources<ref:2606.08645#pg2>. This paper uncovers new structural phenomena in nonlocal games through the lens of team theory<ref:2606.08645#pg2>. Bell nonlocal games can also be thought of as (stochastic) team problems<ref:2606.08645#pg2>. In such a problem, agents receive partial information of an underlying state, and must jointly design a strategy that minimizes a cost that depends on their collective actions and the unknown state<ref:2606.08645#pg2>. The information structure of a team is a description of who knows what in the team<ref:2606.08645#pg2>. An information structure is static if no agent can affect the underlying state of a system; else it is dynamic<ref:2606.08645#pg2>.

Improvements for AI systems

textbfStronger Quantum Advantage Detection in Dynamic Environments: The improved system can rigorously quantify the fragility of some well known ideas under changes of information structure by comparing optimal costs across static and dynamic settings, specifically identifying a region of strict quantum disadvantage for projective strategies in the dynamic game when certain parameters are met.
textbfRobust Strategy Selection Based on Information Structure: The system can determine whether a strategy class possesses the property of best response over both static and dynamic information structures, providing an algorithmic guarantee that a chosen optimal strategy will remain optimal regardless of whether the underlying information flow is static or dynamic.
textbfOptimal Quantum Strategy Synthesis: The system can synthesize quantum strategies that are team optimal by solving complex minimization problems over POVMs, yielding closed-form expressions for the minimum expected cost under both static and dynamic constraints, which allows for the selection of an appropriate strategy class (e.g., projective or classical) based on input parameters.
textbfGuaranteed Person-by-Person Optimality: For classical strategies, the system can verify that the property of person-by-person optimality over classical strategies holds in both information structures, ensuring that any resulting optimal solution is a stable Nash equilibrium between the two agents.

Abstract

We look at Bell inequalities from the lens of information structures in stochastic teams. We consider the usual Clauser-Horne-Shimony-Holt (CHSH) game and a dynamic variant of the same to study how various classes of strategies, classical, projective and quantum, behave under team theoretic solution concepts. We endow players with a fixed quantum state that we take as the Bell state, and allow variation of the measurement strategies. In the static game, projective strategies (where each player performs projective measurements) are team optimal for all parameter values and are closed under best response. In the dynamic game these properties fail: projective strategies may be strictly outperformed by classical ones, best responses to projective strategies need not be projective, and, beyond a sharp threshold on the channel noise, team optimal projective strategies cease to be person-by-person optimal, even though person-by-person optimal projective pairs always exist. These results shed light on the delicate interplay of information structure in quantum strategies and the fragility, under a change of information structure, of structural properties that are taken for granted in the static setting.