What limits quantum coherence on a causal network: distance, noise, or the act of recording which structure was taken? This two-paper study develops a unified framework for answering that question. The first paper proves a general spacetime law for coherence transport in quantum networks. It separates three physically distinct effects: finite-speed causal propagation, contraction of pre-existing coherence by a quantum channel, and long-range coherence injected by non-local structural changes. The resulting bound reveals two unavoidable regimes: an early-time decay law for coherence prepared across large separations, followed by a spatial coherence envelope once the corresponding causal depth has been reached. The second paper turns to a different regime in which the network structure itself is coherently controlled. It proves that two alternative structures remain perfectly indistinguishable until quantum matter acquires amplitude in the region where they differ. More generally, it derives causal bounds on visibility loss, structure–matter entanglement, and the optimal probability of determining which structure was present. Numerical network-walk experiments illustrate exact causal protection, coherent visibility revivals, and the suppression of those revivals when environmental records are introduced. Together, the papers distinguish structural difference from irreversible decoherence: non-locality or alternative geometry alone need not destroy coherence. The decisive mechanism is whether information distinguishing the alternatives is physically acquired and irreversibly recorded. Included works:A General Causal Coherence Transport Law and Causal Protection of Coherently Superposed Network Structures.
What limits quantum coherence on a causal network: distance, noise, or the act of recording which structure was taken? This two-paper study develops a unified framework for answering that question. The first paper proves a general spacetime law for coherence transport in quantum networks. It separates three physically distinct effects: finite-speed causal propagation, contraction of pre-existing coherence by a quantum channel, and long-range coherence injected by non-local structural changes. The resulting bound reveals two unavoidable regimes: an early-time decay law for coherence prepared across large separations, followed by a spatial coherence envelope once the corresponding causal depth has been reached. The second paper turns to a different regime in which the network structure itself is coherently controlled. It proves that two alternative structures remain perfectly indistinguishable until quantum matter acquires amplitude in the region where they differ. More generally, it derives causal bounds on visibility loss, structure–matter entanglement, and the optimal probability of determining which structure was present. Numerical network-walk experiments illustrate exact causal protection, coherent visibility revivals, and the suppression of those revivals when environmental records are introduced. Together, the papers distinguish structural difference from irreversible decoherence: non-locality or alternative geometry alone need not destroy coherence. The decisive mechanism is whether information distinguishing the alternatives is physically acquired and irreversibly recorded. Included works:A General Causal Coherence Transport Law and Causal Protection of Coherently Superposed Network Structures.
This paper is the thirty-fourth in a sequence developing an interpretive framework that redescribes physical reality as a causally consistent history of information updates rather than as a collection of independently existing objects. It is the capstone (third panel) of the ninth grouping — the quantum-mechanics–gravity interface trilogy (32 Quantum Geometry → 33 Records Backreacting on Geometry → 34 Causal Structure Without a Global Order) — and closes that trilogy. Its core physics is the process-matrix framework (Oreshkov, Costa, & Brukner, 2012), with the quantum switch (Chiribella et al., 2013) as the worked instance and causal (non)separability as the central classification. When the order of operations is quantum-controlled — and, at the interface, when geometry is superposed so different branches carry different causal graphs — the temptation is to posit a hidden definite global total order behind the indefiniteness. The thesis is that there is no Global Causal Sequencer; P1 is a declared architectural commitment, not a theorem, and a rival that posits a deeper definite order underwriting the indefiniteness is acknowledged but declined architecturally. R-A: indefinite operational order is not causal inconsistency or a closed loop — a coherent superposition of order components is causally nonseparable (witness-certifiable; note that witness-based nonseparability and causal-inequality violation are not equivalent, and the quantum switch need not violate a causal inequality) yet a valid, consistent process. R-B (restricted to controlled-order processes such as the quantum switch, or any process with a declared physically recorded order-control observable): recording the order-control does not by itself produce a determinate order — one must distinguish the coherent control, the decohered-but-unconditioned causally separable mixture, and the conditioned record-relative effective order — only the last is determinate, and only relative to a recorded value and the declared parameter chi, whose order-control basis is an admissible decoherence-stable pointer basis/algebra (not an arbitrary rotation). R-C: causal structure is profile-valued, CausalProf = (d_order, d_interv, d_record, d_valid, d_family, d_arrow), with a process-validity (not graph-acyclicity) component and an independent record-arrow component from Paper 9's arrow package. R-D (the novelty witness): effective order is provenance-gradable — a matched pair of histories with identical audited world-side order records but different provenance yields different warranted standing (OrderStandProf). R-E: a conservative-before-radical discipline works indefinite operational order first, then a minimal superposed-causal-graph bridge on Paper 32's identity fibers, separating an identity disposition from an order disposition; full quantization of the causal relation is flagged, not claimed. This retires the Global Causal Sequencer and closes the interface trilogy; no causal loops, no retrocausal signaling, no revived global order, no quantum-gravity completion. Presents no new physics; results are interpretive (L2) on imported physics (L1).
This paper establishes the structural inevitability of quantum-theoretical description within the framework of Causal Update Cosmology (CUC I–IX). Rather than deriving quantum-mechanical equations or advocating a specific interpretation of quantum theory, the present work adopts an exclusion-based structural approach. Starting from the completed formulation of CUC and the concept of the central regime, it demonstrates that classical deterministic description is structurally impossible in causal update systems that have not yet reached or cannot maintain the central regime. Below the central regime, causal path competition remains immature, history indistinguishability is unsaturated, and self-averaging does not operate. Under these conditions, states cannot be uniquely defined, deterministic temporal evolution cannot be constructed, and observation cannot be treated as a passive readout. These failures are not due to epistemic limitations or insufficient information, but follow directly from the causal update structure itself. The paper shows that while probabilistic description becomes unavoidable once determinism is excluded, classical probability theory is insufficient, because probability in such systems is intrinsically coupled to the update process and competing causal histories are structurally non-independent. As a result, quantum-theoretical description emerges as the minimal and only consistent remaining framework. Observation is reinterpreted as an irreversible causal update rather than a measurement of a pre-existing state. This provides a structural resolution of the measurement problem and explains why quantum systems consistently appear on the initial side of the central regime upon observation: not because they are fundamentally incapable of reaching the central regime, but because observational updates disrupt the conditions required to maintain it in systems with limited causal redundancy. Classical description, determinism, and decoherence are shown to arise only as derived and conditional features once the central regime is reached and stably maintained. In this sense, classical theory is not fundamental but emergent. The conclusions of this paper are structurally symmetric to those obtained in the analysis of relativistic inevitability within CUC. Just as relativistic spacetime structure is unavoidable in central-regime–admitting systems, quantum theory is unavoidable below the central regime. Both are thus positioned as necessary descriptive frameworks selected by causal structure, rather than as exceptional postulates. This work represents a key step in extending Causal Update Cosmology beyond relativistic structure to the foundations of quantum theory, and sets the stage for a unified structural treatment of gravity and spacetime curvature in future studies. Note on AI Use This work also explores the broader question of whether new physical theories can emerge through collaboration with AI systems. ChatGPT (OpenAI) was used extensively in the generation and structuring of theoretical ideas and manuscript text, beyond simple editing or polishing. All numerical experiments and scientific validation were performed by the human author.
Problem What must a physical record preserve to reveal temporal direction, measure duration, and support a calibrated experiment? This two-volume mathematical working paper distinguishes causal order, clock readings, and forward–reverse evidence, and studies their joint realization under one history law. Principal results Relative-entropy disintegration identifies evidence lost through observation. Graph potentials characterize sufficient current sensors by the absence of affinity on unobserved cycles; paired histories extend the criterion to silent events and indistinguishable reaction channels. Anonymous records, finite memory, and stopped decisions are treated explicitly. Compensated currents control clock calibration under shared environmental dynamics. A preparation-and-work identity bounds directional records and terminal organization together. Exact elimination retains hidden memory, while inverse and energy margins control response. A moving-sector comparison bounds the complete quantum apparatus record, including interactions, leakage, and transport; a spectral gap gives an explicit operating-time estimate. Analytical constructions and counterexamples cover graph–matter selection, ring and torus persistence, localized field clocks and receivers, and source-correlated records. A kinetic parent combines a selected ring, an inertial field, and a finite reversible receiver. Preparation frontiers separate information cost from attainable initial laws of a fixed dynamics. Methods, scope, and open questions The proofs use conditioning, path potentials, martingale compensation, generating functions, and stable operator comparison. The project includes editable sources, bibliography, 47 reproducible finite verification programs, provenance, and a separate corrections report. The results concern specified model classes and conditional external inputs. Selected spatial geometry is not a derived Lorentzian spacetime; the joint ring receiver uses supplied capture materials and diffusive transport. A common microscopic derivation of Lorentzian geometry, apparatus formation, two distinct proper-time clocks, constrained gravitational response, and typical directional preparation remains open.
Recent works in foundations of quantum (field) theory and relativistic quantum information try to better grasp the interplay between the structure of quantum correlations and the constraints imposed by causality on physical operations. Chapter 1 is dedicated to the study of the conceptual implications of quantum nonlocality, a concept that subsumes that of entanglement in a certain way. We detail the recent information-theoretic approaches to understanding the structure of nonlocal correlations, and the issues the latter raise concerning the ability of local observers to isolate a system from its environment. Chapter 2 reviews in what sense imposing Poincare invariance affects entanglement detection and quantification procedures. This invariance ultimately forces a description of all quantum systems within the framework of quantum field theory, which leads to the impossibility of localized finite-energy states and to the divergence of all entanglement measures for local observers. We provide a solution to these two problems by showing that there exists a generic equivalence between a finite spatial resolution of the measurement apparatus and the exclusion of high-energy degrees of freedom from the definition of the observed system. This equivalence allows for an epistemic interpretation of the standard quantum formalism describing nonrelativistic localized systems and their correlations, hence a clarification of the origin of the finite measures of entanglement between such systems. Chapter 3 presents a recent theoretical framework that predicts the existence of correlations with indefinite causal order. In analogy to the information-theoretic approaches to nonlocal correlations, we introduce some principles that constrain the structure of such correlations, which is a first step toward a clear understanding of their physical origin.
The title of the present dissertation Decoherence in Quantum Network sounds very general and all-inclusive. Indeed it embraces two topics (decoherence and quantum network) from the area of Quantum Mechanics each of which is described in all respects by a huge literature developed in the last three decades [...]. Quantum decoherence, as the name lets it mean, is the mechanism that makes a quantum system loose its coherence properties, and with them the capability of giving rise to interference phenomena or to other interesting quantum effects [...]. The key idea promoted by decoherence is the insight that realistic quantum systems are never isolated, but are immersed in the surrounding environment and interact continuously with it [...]. As an example one may consider a two-level quantum system (i.e. a quantum bit, usually shortened with a terminology from information science to \\qubit" ) in contact with a wide environment. Hence, quantum systems are open systems, and continuously interact or exchange information with an external environment whose degrees of freedom are too numerous to be monitored. The resulting correlation between the system and the environment spoils quantum coherence and brings about the transition from a pure quantum state to a mixture of quantum state resulting a classical state. To describe decoherence different kind of approaches can be used (for example Master equation, random matrix, etc). A quantum network typically consists of a number of quantum objects (e.g., atoms, ions, quantum dots, cavities, etc.), to be referred to hereafter as the sites or the nodes of the network. They can interact and the interactions (or their correlations) will be usually described by the edges of a graph. Quantum networks can address different information processing tasks. For instance a quantum state can be transferred from qubit to qubit down a chain solely due to the interactions, that is according to the laws of quantum physics [...]. Quantum networks offer us new opportunities and phenomena as compared to classical networks. An extension to large scale of the idea of a quantum network could lead to a futurible quantum internet [...]. The study of networks has traditionally been the territory of graph theory [...], also with the advent of their quantum versions. Within simple quantum network model information processing is usually described by assuming perfect control of the underlying graph. However, this is not much realistic since randomness is often present and it leads to decoherence effects [...]. In contrast, the conservation of coherence is essential for any quantum information process [...], hence there is a persistent interest in decoherence effects in quantum networks, which motivate us to study models for describing such noisy effects. We consider a simple model of quantum network, employing qubits (spin-1/2 particles) attached to the nodes of an underlying graph and we study the simplest task, namely information storage (on a single and two qubits), when the graph randomly changes in time. Actually we randomly add edges to an initially disconnected graph according to the Gilbert model characterized by a weighting parameter ex [...] and in an identically and independent way at each time step. We find that by increasing ex the dynamics of relevant quantities like fidelity, entropy or concurrence, gradually transforms from damped to damped oscillatory and finally to purely oscillatory. That leads to the paper [see, Information dissipation in random quantum networks, by U. Farooq and S. Mancini, OSID 21(3), 1450004, 2014]. We also study a system composed by pairs of qubits attached to each node of a linear chain, a model that stems from quantum dot arrays. Here we use the approach of evolution with a stochastic Hamiltonian to describe the noisy effects. We then evaluate the effect of two most common disorders, namely exchange coupling and hyperfine interaction fluctuations, in adiabatic preparation of ground state in such model. We show that the adiabatic ground state preparation is highly robust against these disorders making the chain a good analog simulator. Moreover, we also study the adiabatic information transfer, using singlet-triplet states, across the chain. In contrast to ground state preparation the transfer mechanism is highly affected by disorders. This suggested that for communication tasks across such chains adiabatic evolution is not as effective and quantum quenches would be preferable. That leads to the paper [see, Adiabatic many-body state preparation and information transfer in quantum dot arrays, by U. Farooq, A. Bayat, S. Mancini and S. Bose Phys. Rev. B 91, 134303, 2015]. The present work is organized as follows. In chapter 1, we shall give a survey of the various types of approach which can be employed to analyse the dynamics of open quantum systems that leads to decoherence effects. In chapter 2, we shall give a general description about quantum network and its possible applications. In chapter 3, we shall discuss the problem of quantum state transfer in qubit network and shall give a brief overview of some scheme that enable nearly prefect state transfer. In chapter 4, we shall discuss singlet-triplet networks, that is networks having on each site a pair of (generally entangled) qubit. Then within this framework we propose a model stemming from quantum dot array. There we shall address the problem of ground state preparation and state transfer. Finally we shall describe the inherent entanglement of the ground state of strongly correlated systems can be exploited for both classical and quantum communications. In chapter 5, we shall propose a decoherence model for qubit networks based on edges representing XY interactions randomly added to a disconnected graph accordingly to a suitable probability distribution. In this way we shall describe dissipation of information initially localize in single or two qubits all over the network. In chapter 6 we shall model the noisy effects in the quantum dot array introduced in chapter 4 and investigate their consequences on the preparation of ground state and quantum state transfer mechanism. Finally we shall draw conclusions.
This note presents the unified structure behind a series of exact results on quantum reference frames, superselection sectors, gravitational information, and the emergence of time. The central result is that these apparently different phenomena are governed by one mathematical object: the probability distribution of a conserved quantity and its characteristic function. The theory shows that different properties of this distribution correspond to different physical laws. Entropy determines the information deficit caused by the absence of a reference frame; representation support determines matching conditions; the mean generates entangling phases; the variance determines the fundamental resolution–decoherence price; cumulant structure explains limits on improving clocks and networks; the magnitude of the characteristic function gives the relation between records and decoherence; periodicity explains revival phenomena; heavy tails determine protection effects; and products of record overlaps govern the emergence of relational time. The framework unifies exact results previously obtained for charge superselection, quantum clocks, position reference frames, quantum geometry, gravitationally induced entanglement, mediator dynamics, spacetime classicality, and timeless quantum models. The note also derives a new thermal-revival universality law: at revival times, entanglement generated by a quantum mediator is independent of the mediator state, including thermal, squeezed, and displaced states. Thermal noise affects intermediate visibility but does not remove the revival entanglement. All results are based on pre-registered predictions, symbolic derivations, and machine verification. Reproducibility materials are included. The results are established within exactly solvable finite quantum models. No claim is made for a complete theory of quantum gravity or full dynamical Einstein spacetime.