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.
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.
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 is Paper 142 in the Anaxiomatic Mechanics / pq-Spacetime stack. It develops a finite mechanical account of quantum entanglement within pq-spacetime. Entanglement is identified with the persistence of a non-factorable family of admissible future histories. Two measurement regions can therefore appear as separate local systems in emergent spacetime while still remaining projections of one joint finite closure problem. Bell inequality violation follows because the joint outcomes are not generated by two independent local completion families. No-signalling is nevertheless preserved because complete changes to a distant measurement boundary do not alter the local marginal outcome weights. The paper establishes the Entanglement Closure Theorem and distinguishes microscopic non-factorability from observable entanglement after coarse-graining into stable measurement records. It also gives an explicit minimal singlet construction using two opposed history fibers carrying the relevant four-phase weights. The resulting finite ledger is antisymmetric, nonseparable, and exactly balanced at each local wing. Complete changes of basis on the distant side preserve those local marginals. Using the previously derived Hilbert-space and beta-Dirac bridges of pq-spacetime, the paper recovers the familiar spinor overlap law, the quantum singlet correlation, the maximal Bell-CHSH value, monogamy of maximal entanglement, and decoherence through environmental boundary enlargement. The analysis also explains why no preferred measurement ordering is required and why entanglement remains compatible with relativistic causality. The resulting picture is direct. Entangled systems do not exchange superluminal messages, carry classical answer sheets, or require a force acting across space. Their local outcomes arise from one shared finite admissibility structure whose joint correlations are nonlocal while its controllable local statistics remain causal. Entanglement is therefore physically real, nonclassical, and nonlocal in correlation, but not a signalling mechanism.
Quantum mechanics has been a paradigm shift and a revolutionary framework in our understanding of the physical world. The theory has been able to describe a wide variety of phenomena and has been experimentally verified with great precision. Despite that, to this day, the seemingly ad hoc formulation of quantum theory and several of its features still elude an intuitive understanding. At the same time, the applications of quantum mechanics in information theory have emerged as a promising avenue. Namely, its potential advantages in computation, in the so-called nascent field of quantum computation and in communication and information processing tasks such as quantum teleportation and super-dense coding. In all these endeavours, a significant effort has been made in understanding the maximum extent to which quantum mechanics can provide an advantage. This thesis explores an intersection of these two research lines, i.e. to have a physical explanation of some of the features of quantum mechanics and at the same time, study the outer limits of quantum mechanics. The combining insight rests on a newer foundational idea: that information itself is physical rather than an abstract entity and thus, is subject to physical laws. In this thesis, we explore the principle of information causality, which states that in any communication scenario, the amount of information carried is bounded by the degrees of freedom of the carrier. Information causality was initially proposed as a physical principle aimed at deriving the predictions of quantum mechanics on the type of correlations observed in a Bell scenario, which is a communication scenario involving multiple parties with access to a shared randomness resource. This principle has been proposed to recover some of the well-known features of quantum mechanics, specifically Tsirelson’s bound of the Clauser-Horne-Shimony-Holt inequality. Earlier results found limited generalisations due to the difficulty of deducing implications of the information causality principle. In this thesis, we greatly expand the scope of applicability of the principle. We develop a general-purpose algorithm to derive constraints on the set of quantum correlations. We extend the principle to be applicable to a wider variety of Bell scenarios, derive new families of quantum Bell inequalities and prove new bounds on the success probabilities of Entanglement Assisted Random Access Codes. We introduce an extension of the principle which applies to any distributed computing scenario. Using this extension, we improve on several previously known results in the field, and in certain cases, we even recover part of the quantum set as well. This extension provides rich insights into the communication complexity of distributed functions, using which we prove theory-independent randomised communication complexity bounds for several well-known functions and provide another general-purpose algorithm to bound the randomised quantum communication complexity of any function. As a consequence of the extension, we also establish that the extension supersedes the principle of non-trivial communication complexity.
Papers I and II derived gravitational geometry and second-order dynamics from finite accessibility without invoking measurement, observation protocols, or collapse as primitive notions. This paper extends the operational program to the measurement sector, deriving the structure of record formation and probabilistic weights from the same finite accessibility and compositional constraints. Finite accessibility restricts admissible operations on a subsystem to a proper operator subalgebra. Because bounded certification excludes operators requiring nonlocal coordination or arbitrarily fine phase resolution, the accessible algebra is strictly smaller than the full operator algebra. When a system becomes correlated with orthogonal environment sectors, off-diagonal operators between those sectors fall outside the accessible algebra. The reduced state is therefore indistinguishable, under all admissible operations, from its diagonal ensemble. Definiteness emerges as an algebraic consequence of sector restriction, not as a collapse postulate. The weights of these sectors are fixed uniquely by compositional consistency. Phase invariance, multiplicativity under independent refinement, and stability under record coarse-graining constrain any admissible assignment of sector weights to satisfy a functional equation whose only continuous, non-contextual solution is quadratic in amplitude. The Born rule therefore arises as the unique invariant measure compatible with finite accessibility. Irreversibility follows from action scaling: reversal requires operators outside the admissible tensor algebra and incurs action cost proportional to the number of correlated subsystems. Since admissible operations are bounded by the action gap, macroscopic record reversal is excluded. Measurement introduces no new physical primitives beyond finite accessibility, locality, and compositional stability. Record formation, classical definiteness, and Born probabilities are structural consequences of algebraic restriction under finite accessibility. **This paper is part of the Finite Accessibility series, which reconstructs gravitational geometry, quantum dynamics, gauge structure, cosmological perturbation theory, and the dark sector from a single operational primitive: a finite certification ceiling ω* governing the maximum rate at which physical relations can be maintained across extended domains.** **Introductory papers** - Geometric Limits to Coherent Timekeeping in Extended Reference Frames — https://doi.org/10.5281/zenodo.18824556 - Accessibility Selection Law (ASL) — https://doi.org/10.5281/zenodo.18824649 - Phase Boundary Gravity — https://doi.org/10.5281/zenodo.18824707 **Pillars (numbered I–IV)** - Paper I: Deriving Gravitational Geometry and Schrödinger Dynamics from Finite Accessibility — https://doi.org/10.5281/zenodo.18601600 - Paper II: Deriving Inertia, Motion, and Wave Propagation from Finite Accessibility — https://doi.org/10.5281/zenodo.18625174 - Paper III: Accessible State Spaces, Record Stability, and the Emergence of Quantum Statistics — https://doi.org/10.5281/zenodo.18625192 - Paper IV: Frame Dissolution, the Certification Ceiling, and Observable Deformations — https://doi.org/10.5281/zenodo.18654458 **Extension papers** - Dark Matter from Finite Accessibility — https://doi.org/10.5281/zenodo.18654433 - Dark Energy from Finite Accessibility — https://doi.org/10.5281/zenodo.18654523 - No-Go Theorems and the Admissibility Corridor — https://doi.org/10.5281/zenodo.18654493 - Gauge Structure from Finite Accessibility — https://doi.org/10.5281/zenodo.18928152 - Perturbation Theory from Finite Accessibility — https://doi.org/10.5281/zenodo.18928213 **Experimental paper** - Experimental Probes of Finite Accessibility: GW Dispersion and Vacuum Path Independence — https://doi.org/10.5281/zenodo.18931126 **Keywords:** Born rule derivation, measurement problem, quantum statistics, finite accessibility, operator subalgebra, record formation, definiteness emergence, wave function collapse, compositional consistency, accessible state spaces, action gap, irreversibility, sector restriction, quantum foundations, algebraic quantum mechanics, decoherence
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.