Sequential Detection of Non-Classical Coordination in the Limited Communication Regime: Orthogonal Divergence and the Internal Observer Detection Problem
Paper 3 in the Limited Communication series. The first two papers asked what an outside observer sees when quantum coordination affects their environment. This paper asks the opposite question: what does the coordinating party themselves see? If a physical mechanism exists that shifts the measurement statistics of an entangled partner — even slightly — the partner can detect that shift over time using sequential statistical testing, without any classical communication channel. This paper develops the complete detection architecture: how to detect the shift, how long it takes, how confident you can be, and how to verify pre-agreed signals using a codebook established before separation. The paper does not claim this capability exists today. It derives what follows if it becomes possible, using the mathematical framework established in Papers 1 and 2. The theory is built before the technology, so the formal tools are ready if the physics arrives. Technically: derives the detection-theoretic consequences when a coordinating party observes their own marginal statistics under a hypothesized non-linear bias mechanism. Develops sequential hypothesis testing (SPRT) architecture for detecting orthogonal divergence — environmental divergence at the entangled partner's location — without any classical communication channel. Proves the detection protocol saturates the Shannon capacity bound. Positions the conditional within a trilemma relative to Gisin's (1990) theorem on non-linear signaling. Extends the LCT framework inward, from the excluded observer to the coordinating party.
Paper 3 in the Limited Communication series. The first two papers asked what an outside observer sees when quantum coordination affects their environment. This paper asks the opposite question: what does the coordinating party themselves see? If a physical mechanism exists that shifts the measurement statistics of an entangled partner — even slightly — the partner can detect that shift over time using sequential statistical testing, without any classical communication channel. This paper develops the complete detection architecture: how to detect the shift, how long it takes, how confident you can be, and how to verify pre-agreed signals using a codebook established before separation. The paper does not claim this capability exists today. It derives what follows if it becomes possible, using the mathematical framework established in Papers 1 and 2. The theory is built before the technology, so the formal tools are ready if the physics arrives. Technically: derives the detection-theoretic consequences when a coordinating party observes their own marginal statistics under a hypothesized non-linear bias mechanism. Develops sequential hypothesis testing (SPRT) architecture for detecting orthogonal divergence — environmental divergence at the entangled partner's location — without any classical communication channel. Proves the detection protocol saturates the Shannon capacity bound. Positions the conditional within a trilemma relative to Gisin's (1990) theorem on non-linear signaling. Extends the LCT framework inward, from the excluded observer to the coordinating party.
This paper asks a question the quantum information literature has not addressed: what happens to the rest of the world when quantum coordination activates? When two parties coordinate using shared entanglement, the standard analysis stops at their joint measurement outcomes. This paper goes further — it formalizes what a third-party observer, one completely excluded from the quantum state, experiences in the downstream environment. The answer: environmental consequences that no classical physics can explain, and in the strongest case, consequences that are identical to what the observer would experience if the parties had secretly communicated. The paper introduces the excluded observer interface model, defines environmental divergence as an operational measure, and proves a leakage-performance separation theorem: quantum coordination simultaneously exceeds the classical performance ceiling while leaking zero information about local conditions to the excluded observer — breaking the classical Pareto frontier between coordination performance and operational security. Demonstrated across the CHSH game (Δ_TV = 0.104, distinguishable from communication) and the Mermin-Peres Magic Square game (Δ_TV = 0.111, indistinguishable from communication, ε = 0). This is Paper 1 in a four-paper series: Paper 1 (this paper) — Existence. Proves the excluded observer's environment diverges from classical baselines. Paper 2 — Structure. Extends the framework into complex-valued information geometry, demonstrating that the excluded observer's information space acquires a CP¹ structure and that complex phase tracking becomes operationally necessary for predictive consistency in multi-outcome environments. Zenodo DOI 10.5281/zenodo.18944106. Paper 3 — Detection. Shifts the observer partition inward, deriving a sequential detection architecture for the coordinating party to detect marginal bias using only local statistics. Proves the protocol is information-theoretically optimal (saturates the Shannon capacity bound). Zenodo DOI 10.5281/zenodo.19056735. Paper 4 — Action. Derives the organizational decision-theoretic consequences: optimal hierarchy depth as a computable function of adversary coordination quality, decision window, and stakes magnitude. The result generalizes beyond quantum coordination to any scenario with external time pressure, communication friction, and unforeseen disruption. Zenodo DOI 10.5281/zenodo.19057065.
When two quantum-entangled agents coordinate their actions, a third-party observer — one with no access to the quantum system — can experience environmental effects indistinguishable from classical communication, even though no information was transmitted. The Limited Communication Theorem (Ericksen 2026) proved this formally. This paper asks the next question: does that phenomenon have deeper mathematical structure that standard real-valued measures miss? We propose a complex-valued extension of environmental divergence: Δ_C = Δ_TV × e^{iφ}, where the phase encodes the quantum fill fraction — how far quantum coordination has closed the gap between classical local behavior and full classical communication. Four computational tests show that this construction traces structured, physics-determined curves in the complex plane, organizes coordination scenarios by physically meaningful fill fraction, produces interpretable real-time trajectories under noise and resource switching, and reveals that three independent construction pathways converge on the same geometric object: the square-root embedding of the probability simplex into CP¹, the complex projective line, equipped with the Fisher-Rao metric. We prove that the real-valued divergence and its complex magnitude are formal LOSR monotones — they can only decrease under local degradation, never increase. The phase angle and imaginary component behave as diagnostic indicators that are non-increasing under local degradation, isolating the portion of the observer's experience that is structurally indistinguishable from communication. The central result: two quantum strategies can produce identical outcome statistics under every classical measurement while being fully orthogonal in the complex Fubini-Study metric. When the environment evolves, this hidden separation becomes a measurable 13.1% total variation divergence — a predictive failure that no real-valued model can anticipate or resolve. The complex-projective representation is not an arbitrary formalism — it is the geometry required for predictive consistency when quantum coordination enters multi-outcome environments. This paper is a companion to "The Limited Communication Theorem" (Ericksen 2026, Zenodo DOI: 10.5281/zenodo.18868863). The core results of that paper are independent of this extension. If the results here hold under further scrutiny, the limited communication phenomenon is not merely a statistical anomaly — it carries its own irreducible geometric structure in the macroscopic world.
The before-before experiment (Stefanov, Zbinden, Gisin and Suarez, 2002) showed that the coordination of two spacelike-separated measurements on an entangled pair carries no device-relative time order: each analyzer can be made to measure ``first'' in its own rest frame, and the correlations do not disappear, as multisimultaneity had predicted. The reading that survived, ``coordination from outside space-time,'' names an absence rather than a location. We ask where a carrier of that coordination — any physical structure providing the two wings with a shared outcome space at measurement time — could be located if the metric arena is a discrete substrate with a finite budget per node. Four constructions exhaust the metric options, and each is closed separately: a carrier the quantum pays for from its own energy (58 to 129 orders of magnitude short of the reference weight), one propagating at finite speed (strict light cone, spacelike antibunching, and the result of Bancal et al.), one statically wired into the lattice (clique, star and chain each unphysical), and one carried along with the quanta from the source — excluded not by counting but by Bell's theorem with the spacelike Bell tests. What survives is a carrier that is pre-existing, at graph distance zero from both wings, and non-metric. Two further results follow with separately stated assumptions. A device-relative time order would itself need a carrier of the excluded class; a universal order would not, and the substrate model used here has one. And a carrier compatible with no-signaling may be read out only through functions of the local reduced state, which excludes a shared table of outcome values but not the coherent amplitude that Bell correlations require. The result gives Suarez's Principle Q a restricted, computed form for one class of carriers. It claims neither the existence of a carrier, nor the immateriality of what lies outside, nor any deviation from quantum mechanics in the accessible regime.
Historically, quantum mechanics has relied on the assumption of non-communicating parties, enforced via space-like separation, to witness the gap between classical and quantum descriptions. This thesis explores the boundaries of the standard Bell non-local scenario, investigating how to preserve this gap when communication is allowed. In particular, this work focuses on restricted communication, multipartite settings, and operator-algebraic formulations. Key contributions of this work include: • Dimensional Constraints: Establishing mathematical maps from standard Bell scenarios to prepare-and-measure scenarios with dimensionally bounded channels, proving that quantum bounds and self-testing properties are preserved. • Cryptographic Constraints: Analyzing compiled non-local games using quantum homomorphic encryption. The research proves asymptotic quantum soundness for all multipartite compiled games and introduces a quantitative hierarchy, similar to the NPA hierarchy, to characterize sequential correlations. • Operational Equivalences: Demonstrating that correlations arising from arbitrary compositions of non-signalling assemblages in multipartite communication schemes always reduce to standard spatial quantum Bell correlations. • Operator-Algebraic Tools: Introducing a novel chain rule for the Radon-Nikodym derivative to dilate chains of completely-positive maps, alongside the construction of a universal C*-algebra for sequential measurements. Overall, the manuscript unifies concepts from quantum foundations, complexity theory, and operator algebras to provide a rigorous mathematical framework for characterizing and certifying multipartite sequential quantum correlations.
In the past century, experimental discoveries have witnessed phenomena in Nature which challenge our everyday classical intuition. In order to explain these facts, quantum theory was developed, which so far has been able to reproduce the observed results. However, I believe that our understanding of quantum mechanics can be significantly improved by the search for an operational meaning behind its mathematical formulation, which would help to identify the limitations and possibilities of the theory for information processing. An intriguing property of quantum theory is its intrinsic randomness. Indeed, Einstein, Podolsky and Rosen in 1935 questioned the completeness of quantum theory. They argued the possibility of the existence of a complete theory where variables to which we have not access determine the behaviour of physical systems, and the randomness observed in quantum mechanics is then due to our ignorance of these variables. These hidden variables theories, however, were proved not to be enough for explaining the predictions of quantum theory, as shown in the no-go theorems by Bell on quantum-nonlocality and by Kochen and Specker on quantum-contextuality. In the past decades, many experiments have corroborated the nonlocal and contextual character of Nature. However, no intuition behind these phenomena has been found, in particular about what limits their strength. In fact, special relativity alone would allow for phenomena which are more nonlocal than what quantum theory allows. Hence, much effort has been devoted to find the physical properties of quantum theory that restricts these phenomena. In this thesis, we study the constraints that arise on nonlocal and contextual phenomena when a certain exclusiveness structure compatible with quantum theory is imposed in the space of events. Here, an event denotes the situation where an outcome is obtained given that a measurement is performed on the physical system. Regarding nonlocality, we introduce a notion of orthogonality that states that events involving different outcomes of the same local measurement are exclusive, and construct constraints that the correlations among observers should satisfy. We denote this by Local Orthogonality principle (LO), which is the first intrinsically multipartite principle for bounding quantum correlations. We prove that LO identifies the supra-quantum character of some bipartite and multipartite correlations, and gets close to the quantum boundary. When studying contextuality, the same abstract event may correspond to outcomes of different measurements, which introduces a non-trivial structure in the space of events. For its study, we develop a general formalism for contextuality scenarios in the spirit of the recent approach by Cabello, Severini and Winter. In our framework, nonlocality arises as a particular case of contextuality, which allows us to study a generalization of LO. Both in nonlocality and contextuality, we find close connections to problems in combinatorics and hence use graph-theoretical tools for studying correlations. Finally, this thesis also studies the detection of nonlocal correlations. Most results on quantum nonlocality focus on few particles' experiments, while less is known about the detection of quantum nonlocality in many-body systems. Standard many-body observables involve correlations among few particles, while there is still no multipartite Bell inequality to test nonlocality merely from these data. In this thesis, we provide the first proposal for nonlocality detection in many-body systems using two-body correlations. We construct families of Bell inequalities from two-body correlators, which can detect nonlocality for systems with large number of constituents. In addition, we prove violations by systems which are relevant in nuclear and atomic physics, and show how to test these inequalities by measuring global spin components, hence opening the problem to experimental realizations.
We explore whether quantum entanglement might be detectable through information-theoretic coordination patterns in measurement outcomes alone, without requiringquantum states, density matrices, or Hilbert space structure. Using Local DivergenceIntensity (LDI), a universal measure of symbolic sequence decorrelation [6], we ana-lyze three types of simulated quantum measurements: (1) Bell states (simulated per-fect correlation), (2) product states (simulated independence), and (3) quantum walks(simulated structured dynamics).In simplified probabilistic simulations that approximate expected quantum mea-surement statistics, we observe 95% separation between correlated and independentbitstrings (∆Φ = 0.953) with 2% added noise. The framework operates on discrete bi-nary sequences and reveals different scale-dependence patterns for different correlationtypes.This conceptual study suggests LDI analysis of measurement sequences could po-tentially complement traditional quantum information measures, but experimental val-idation on real quantum hardware is required before any claims about detecting actualquantum entanglement can be made.