This paper presents a formal framework framing quantum decoherence as an information-theoretic phase transition at the quantum-to-classical boundary. We demonstrate that environment-induced superselection (einselection) can be characterized as a true dynamical phase transition where the system-environment coupling strength acts as a thermodynamic control parameter, and the suppression of off-diagonal density matrix elements functions as an order parameter analogous to magnetization in the Ising model. Using quantum mutual information, von Neumann entropy, and entanglement entropy, we track the operational flow of information from a quantum system into environmental degrees of freedom, demonstrating how a singular classical reality emerges via the redundant copying of pointer states into environmental fragments—a process governed by Quantum Darwinism. We analyze a simulated spin-boson model and random unitary circuits with tunable dissipation, extracting clear signatures of criticality including power-law scaling and diverging correlation times at a critical threshold . Crucially, we connect this behavior to recent advancements (2023–2025) in mixed-state topological order, establishing that decoherence-induced transitions map onto anyon condensation transitions within an errorfield double formulation. Finally, we explore the foundational implications of this framework: it sharpens the measurement problem via informational symmetry breaking, reframes observation as a high-decoherence thermodynamic limit, and introduces a Gödelian perspective by demonstrating that determining the critical threshold for arbitrary many-body environments is formally undecidable due to the non-computability of the spectral gap in the thermodynamic limit.
This paper presents a formal framework framing quantum decoherence as an information-theoretic phase transition at the quantum-to-classical boundary. We demonstrate that environment-induced superselection (einselection) can be characterized as a true dynamical phase transition where the system-environment coupling strength acts as a thermodynamic control parameter, and the suppression of off-diagonal density matrix elements functions as an order parameter analogous to magnetization in the Ising model. Using quantum mutual information, von Neumann entropy, and entanglement entropy, we track the operational flow of information from a quantum system into environmental degrees of freedom, demonstrating how a singular classical reality emerges via the redundant copying of pointer states into environmental fragments—a process governed by Quantum Darwinism. We analyze a simulated spin-boson model and random unitary circuits with tunable dissipation, extracting clear signatures of criticality including power-law scaling and diverging correlation times at a critical threshold . Crucially, we connect this behavior to recent advancements (2023–2025) in mixed-state topological order, establishing that decoherence-induced transitions map onto anyon condensation transitions within an errorfield double formulation. Finally, we explore the foundational implications of this framework: it sharpens the measurement problem via informational symmetry breaking, reframes observation as a high-decoherence thermodynamic limit, and introduces a Gödelian perspective by demonstrating that determining the critical threshold for arbitrary many-body environments is formally undecidable due to the non-computability of the spectral gap in the thermodynamic limit.
The transition from a unitary quantum superposition to a single, localized classical outcome — the measurement problem — is reframed as a deterministic thermodynamic phase transition driven by informational density gradients. Building on Wheeler’s “it from bit” and Landauer’s principle, we treat the vacuum as a high‑density computational lattice. We introduce the Principle of Fundamental Binary Duality, asserting that every physical state is intrinsically coupled to a conjugate partner, and we derive a Critical Instantiation Threshold (HcritHcrit) — the exact environmental entropy required to break this coupling and force classical localization. Applying the threshold across the Standard Model reveals a mass‑decoherence scaling law: lighter particles resist instantiation far more strongly than heavy ones. For macroscopic objects, the ambient entropy of the cosmic background overwhelms the threshold by eighteen orders of magnitude, permanently enforcing classical determinism without observers or branching worlds. The framework provides a strictly mechanical, parameter‑free resolution of the measurement problem.
Quantum Darwinism is a leading framework for explaining how classical reality emerges from a quantum universe—the environment redundantly encodes the pointer state information of quantum systems, enabling multiple independent observers to reach consensus about reality. However, a fundamental question has remained unanswered: Why does the environment possess this capacity for redundant recording? This paper proposes, within the information-potential conversion framework, that the redundant recording mechanism of quantum Darwinism is the physical realization of the information-potential conversion consensus protocol—the environment, acting as the physical medium for information-potential conversion, redundantly encodes system information, providing consistent conversion records for independent information processing units, from which classical reality emerges. Based on this interpretation, three testable quantitative predictions are proposed: (1) In superconducting quantum circuits, when system complexity exceeds a critical threshold, the efficiency of redundant recording should exhibit an abrupt transition—a signal of the information-potential conversion phase transition of the consensus protocol from “quantum critical” to “classically locked”; (2) There should exist a precise linear relationship between functional information and information-potential conversion energy consumption: each additional bit of functional information doubles the minimum heat dissipation required for record stabilization; (3) Consensus strength—the stability of classical reality—should be positively correlated with the number of information processing units participating in the consensus protocol, and a critical number exists at which the consensus phase transition occurs. quantum Darwinism, information-potential conversion, consensus protocol, classical emergence, redundant recording, functional information
Quantum Darwinism extends the traditional formalism of decoherence to explain the emergence of classicality in a quantum universe. A classical description emerges when the environment tends to redundantly acquire information about the pointer states of an open system. In light of recent interest, we apply the theoretical tools of the framework to a qubit coupled with many bosonic subenvironments. We examine the degree to which the same classical information is encoded across collections of (i) complete subenvironments and (ii) residual ``pseudomode'' components of each subenvironment, the conception of which provides a dynamic representation of the reservoir memory. Overall, significant redundancy of information is found as a typical result of the decoherence process. However, by examining its decomposition in terms of classical and quantum correlations, we discover classical information to be nonredundant in both cases i and ii. Moreover, with the full collection of pseudomodes, certain dynamical regimes realize opposite effects, where either the total classical or quantum correlations predominantly decay over time. Finally, when the dynamics are non-Markovian, we find that redundant information is suppressed in line with information backflow to the qubit. By quantifying redundancy, we concretely show it to act as a witness to non-Markovianity in the same way as the trace distance does for nondivisible dynamical maps.
The emergence of the classical world from the quantum substrate of our Universe is a long-standing conundrum. In this paper, I describe three insights into the transition from quantum to classical that are based on the recognition of the role of the environment. I begin with the derivation of preferred sets of states that help to define what exists—our everyday classical reality. They emerge as a result of the breaking of the unitary symmetry of the Hilbert space which happens when the unitarity of quantum evolutions encounters nonlinearities inherent in the process of amplification—of replicating information. This derivation is accomplished without the usual tools of decoherence, and accounts for the appearance of quantum jumps and the emergence of preferred pointer states consistent with those obtained via environment-induced superselection, or einselection . The pointer states obtained in this way determine what can happen—define events—without appealing to Born’s Rule for probabilities. Therefore, p k =| ψ k | 2 can now be deduced from the entanglement-assisted invariance, or envariance —a symmetry of entangled quantum states. With probabilities at hand, one also gains new insights into the foundations of quantum statistical physics. Moreover, one can now analyse the information flows responsible for decoherence. These information flows explain how the perception of objective classical reality arises from the quantum substrate: the effective amplification that they represent accounts for the objective existence of the einselected states of macroscopic quantum systems through the redundancy of pointer state records in their environment—through quantum Darwinism . This article is part of a discussion meeting issue ‘Foundations of quantum mechanics and their impact on contemporary society’.
The quantum-to-classical transition—the precise physical mechanism by which stochastic wave functions resolve into definite classical observables—remains a foundational open question in physics. In this paper, we introduce the State Resolution Model (SRM), a non-axiomatic framework that formulates state reduction as an emergent thermodynamic throughput limit. Synthesizing the Margolus-Levitin quantum processing bound, the Bekenstein-Hawking holographic capacity, and the information-thermodynamics of Szilard and Landauer, we demonstrate that the threshold for classical state instantiation is governed by a derived dimensionless identity, the Szilard-Resolution Ratio: Φ_SZ = [N · C · (ħ ν)] / [H_SL · R_s]. Unobserved quantum systems undergoing unitary evolution operate non-locally in Hilbert space with zero Szilard-Landauer tax (H_SL = 0). Classical geometric instantiation occurs exclusively when environmental interaction drives local state complexity to the holographic capacity limit (Φ_SZ ≥ 1), forcing a non-unitary projection that dissipates entropy across the local apparent horizon. We show that the resulting decay of Hilbert space mutual information weaves an emergent Lorentzian metric g_μν. Finally, we derive two parameter-free asymptotic bounds—a qubit-density limit (ρ_Q^crit) and a critical mass-superposition limit (m_crit)—demonstrating the model’s theoretical consistency and providing principled fundamental constraints on physical information density.
Quantum critical phases are extended regions of phase space characterized by a diverging correlation length. By analogy, we define an \emph{information critical phase} as an extended region of a mixed state phase diagram where the Markov length, the characteristic length scale governing the decay of the conditional mutual information (CMI), diverges.
We demonstrate that such a phase arises in decohered ZN toric codes by assessing both the CMI and the coherent information, the latter quantifying the robustness of the encoded logical qudits. For N>4, we find that the system hosts an information critical phase intervening between the decodable and non-decodable phases where the coherent information saturates to a fractional value in the thermodynamic limit, indicating that a finite fraction of logical information is still preserved. We show that the density matrix in this phase can be decomposed into a convex sum of Coulombic pure states, where gapped anyons reorganize into gapless photons. We further consider the ungauged ZN toric code and interpret its mixed state phase diagram in the language of strong-to-weak spontaneous symmetry breaking. We argue that in the dual model, the information critical phase arises because the spontaneously broken off-diagonal ZN symmetry gets enhanced to a U(1) symmetry, resulting in a novel superfluid phase whose gapless modes involve coherent excitations of both the system and the environment. Finally, we propose an optimal decoding protocol for the corrupted ZN toric code and show that its logical error rate saturates to a fractional value in the information critical phase. Our findings identify a gapless analog for mixed-state phases that still acts as a fractional topological quantum memory, thereby extending the conventional paradigm of quantum memory phases.