Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2610.09845

Redundant Records of the Past: Unifying Quantum Darwinism and Decoherent Histories

Philipp Strasberg

quant-phcond-mat.stat-mechgr-qcSubmitted Oct 7, 2026• Announced Oct 8, 2026• 0 citations• Revised Oct 28, 2026 (v2)
v1 · Oct 7, 2026v2 · Oct 28, 2026
arXivHTMLPDF

Abstract

There exist two different paradigms for records in isolated quantum systems: decoherent histories (which determines which past events leave formal records) and quantum Darwinism (which determines which current events get redundantly recorded). Neither one implies the other, and connections between the two are scarcely investigated. We unify quantum Darwinism and decoherent histories based on the insight that only redundant records about past events matter. The resulting framework of past redundancy encompasses quantum Darwinism when applied to events at the current time, and it implies the probability sum rule or decoherence of histories. The Bhattacharyya coefficient (or fidelity) plays an important role to establish this connection. Importantly, various examples show that past redundancy is a more widespread phenomenon than the fine-tuned models necessary for quantum Darwinism suggest. We thus arrive at a richer picture in which redundancy can be caused by mechanisms different from quantum Darwinism (such as macroevents or cascade structures), which emphasizes that redundancy is necessary but not sufficient for objectivity, and which, overall, allows to realistically investigate the question: how generic is redundancy in nature?

Comments
Improved clarity and a new result (redundancy implies classicality). One more page. Comments from v1 still apply

Related papers

Objective past of a quantum universe: Redundant records of consistent histories

C. Jess Riedel, Wojciech Hubert Zurek, Michael P. Zwolak

Motivated by the advances of quantum Darwinism and recognizing the role played by redundancy in identifying the small subset of quantum states with resilience characteristic of objective classical reality, we explore the implications of redundant records for consistent histories. The consistent histories formalism is a tool for describing sequences of events taking place in an evolving closed quantum system. A set of histories is consistent when one can reason about them using Boolean logic, i.e., when probabilities of sequences of events that define histories are additive. However, the vast majority of the sets of histories that are merely consistent are flagrantly nonclassical in other respects. This embarras de richesses (known as the set selection problem) suggests that one must go beyond consistency to identify how the classical past arises in our quantum universe. The key intuition we follow is that the records of events that define the familiar objective past are inscribed in many distinct systems, e.g., subsystems of the environment, and are accessible locally in space and time to observers. We identify histories that are not just consistent but redundantly consistent using the partial-trace condition introduced by Finkelstein as a bridge between histories and decoherence. The existence of redundant records is a sufficient condition for redundant consistency. It selects, from the multitude of the alternative sets of consistent histories, a small subset endowed with redundant records characteristic of the objective classical past. The information about an objective history of the past is then simultaneously within reach of many, who can independently reconstruct it and arrive at compatible conclusions in the present.

arXiv:1312.0331•Physical Review A•Mar 21, 2016•56 citations

Pastness as Redundant Broadcastability: Recoverability, Objective Records, and a No-Go for the Cost of Undoing Facts

Thomas Mayer

Quantum Darwinism, Spectrum Broadcast Structures, and redundant-histories work already explain how objective classical information arises through redundant environmental records. This paper asks a different question: once a quantum alternative has become objective in this record-based sense, what is the operational cost of undoing it, of recohering the alternatives?

•May 31, 2026•0 citations

Before Decoherence: Consequential Registration, Redundant Physical Records, and the Pre-Quantum Origin of Environmental Objectivity: A theorem-backed distinction between Registration Theory and Quantum Darwinism

EUGENE CATRAMBONE

Quantum Darwinism explains effective classical objectivity through the selective proliferation of information about preferred quantum states into multiple environmental fragments. Its mature formulations operate within quantum theory, using a system-environment decomposition, decoherence or einselection, and information-theoretic or broadcast-structure criteria for redundant accessibility.This paper asks an upstream question from Registration Theory (RT): what makes a physical distinction a record before that record is described as information available to an observer? Canonical RT answers that retained registration is persistent organization constraining later evolution, that a distinction becomes a physical record only when it remains consequential, and that persistent physical organization is prior to information extracted from it.The paper assembles a theorem-backed finite-model chain now available in the RT corpus. Canonical ACRF dynamics supplies write-retain-read consequential history. The exact finite-amplitude ACRF-4 quotient identifies a nine-dimensional host-host-boundary state. The certified consequence-minimality theorem (DOI 10.6084/m9.figshare.34063464) shows that the retained relational boundary contributes irreducible future-consequence directions. The spectrum-preserving ACRF-8 redundant-record theorem (DOI 10.6084/m9.figshare.34063500) then proves an explicit local witness in which one quotient-valid source distinction is written into two disjoint retained fragments that are locally recoverable, counterfactually separable, and independently readable, giving \(R_{RT}(q)\ge 2\) under the stated criteria.The resulting distinction from Quantum Darwinism is precise but bounded. RT recordhood is consequence-based, while Darwinian objectivity is an accessibility-and-redundancy criterion formulated within quantum theory. The ACRF witness demonstrates redundant retained record formation without assuming Hilbert space, density operators, mutual information, decoherence, einselection, Born probabilities, or an observer-defined environment. Therefore, multiple persistent records of one distinction are not definitionally identical to Quantum-Darwinian redundancy.The paper does not claim that Quantum Darwinism is false or that RT has derived quantum mechanics, decoherence, Born probabilities, a mutual-information redundancy plateau, or macroscopic objectivity. Instead, it proposes a disciplined hierarchy: consequential distinction → retention → persistent record → branching → redundant retained records → redundant accessibility → environmental objectivity. The final two steps remain open in RT. A future bridge must dynamically select and scale multi-host redundancy and map consequence-bearing RT records into quantum environmental fragments that satisfy decoherence and strong objectivity conditions.

•Oct 3, 2026•0 citations

Redundancy-Limited Emergence of Classical Histories in Quantum Systems: A Covariant Information-Theoretic Bound from Decoherence

David Reardon

Redundancy-Limited Emergence of Classical Histories in Quantum Systems This work investigates how classical reality emerges from underlying quantum dynamics, focusing on the role of environmental information, noise, and fundamental entropy limits. In quantum theory, systems evolve into superpositions of many possible outcomes. However, in practice we observe a world with definite, classical histories. A widely accepted explanation is decoherence, in which interactions with the environment suppress interference between different quantum states. More recent developments, particularly in quantum Darwinism, emphasize that classical information becomes objective when it is redundantly recorded across many independent parts of the environment. This paper addresses a key unresolved question: how many distinct classical histories can physically exist? To answer this, we construct a minimal computational model in which a system’s history is encoded into multiple environmental fragments, each subject to noise. By computing how much information about the system can be recovered from subsets of these fragments, we identify a characteristic scale that determines how many fragments are required to reconstruct the system’s history. Our results reveal a simple and robust relationship: the ability to recover classical information depends on the entropy of the noise affecting environmental records. As noise increases, more fragments are required to reconstruct a history, reflecting a loss of distinguishability. This leads to the definition of a “recoverability factor,” which quantifies how efficiently entropy can be converted into usable, classical information. We then connect this information-theoretic result to fundamental bounds from gravitational physics. In particular, existing entropy bounds limit the total amount of information that can pass through a region of spacetime. We show that only a fraction of this entropy—determined by the recoverability factor—can contribute to distinguishable classical histories. This leads to a new principle: the number of classical histories is not limited only by total entropy, but by the efficiency with which that entropy can be encoded, preserved, and accessed. Applying this framework to cosmological entropy estimates, we derive explicit upper bounds on the number of distinguishable classical histories in the observable universe. While this number is extraordinarily large, it is nonetheless finite and strongly constrained by both entropy and noise. These results refine the standard picture of quantum branching. While quantum theory allows a vast number of possible outcomes, only a subset can become physically meaningful in the sense of being stable, redundantly recorded, and accessible to observers. More broadly, this work provides a quantitative bridge between decoherence theory, information theory, and gravitational entropy bounds. It suggests that classical reality is fundamentally constrained not just by physical laws governing entropy, but by the efficiency of information transfer within those constraints.

•Apr 30, 2026•0 citations

Bridging Quantum Darwinism and Decoherent Histories via Redundant Past Records: Towards an Objective Classical Past in a Quantum Universe

Ijaz Durrani

•Oct 9, 2026•0 citations

Approximate Decoherence, Recoherence and Records in Isolated Quantum Systems

Philipp Strasberg, Joseph Schindler, Jiaozi Wang +1 more

Using the framework of decoherent histories, we study which past events leave detectable records in isolated quantum systems under the realistic assumption that decoherence is approximate and not perfect. In the first part we establish -- asymptotically for a large class of (pseudo-)random histories -- that the number of reliable records can be much smaller than the number of possible events, depending on the degree of decoherence. In the second part we reveal a clear decoherence structure for long histories based on a numerically exact solution of a random matrix model that, as we argue, captures generic aspects of decoherence. We observe recoherence between histories with a small Hamming distance, for localized histories admitting a high purity Petz recovery state, and for maverick histories that are statistical outliers with respect to Born's rule. From the perspective of the Many Worlds Interpretation, the first part -- which views the self-location problem as a coherent version of quantum state discrimination -- reveals a "branch selection problem", and the second part sheds light on the emergence of Born's rule and the theory confirmation problem.

quant-pharXiv:2601.19703•Jan 28, 2026•0 citations
There exist two different paradigms for records in isolated quantum systems: decoherent histories (which determines which past events leave formal records) and quantum Darwinism (which determines which current events get redundantly recorded). Neither one implies the other, and connections between the two are scarcely investigated. We unify quantum Darwinism and decoherent histories based on the insight that only redundant records about past events matter. The resulting framework of past redundancy encompasses quantum Darwinism when applied to events at the current time, and it implies the probability sum rule or decoherence of histories. The Bhattacharyya coefficient (or fidelity) plays an important role to establish this connection. Importantly, various examples show that past redundancy is a more widespread phenomenon than the fine-tuned models necessary for quantum Darwinism suggest. We thus arrive at a richer picture in which redundancy can be caused by mechanisms different from quantum Darwinism (such as macroevents or cascade structures), which emphasizes that redundancy is necessary but not sufficient for objectivity, and which, overall, allows to realistically investigate the question: how generic is redundancy in nature?
Motivated by the advances of quantum Darwinism and recognizing the role played by redundancy in identifying the small subset of quantum states with resilience characteristic of objective classical reality, we explore the implications of redundant records for consistent histories. The consistent histories formalism is a tool for describing sequences of events taking place in an evolving closed quantum system. A set of histories is consistent when one can reason about them using Boolean logic, i.e., when probabilities of sequences of events that define histories are additive. However, the vast majority of the sets of histories that are merely consistent are flagrantly nonclassical in other respects. This embarras de richesses (known as the set selection problem) suggests that one must go beyond consistency to identify how the classical past arises in our quantum universe. The key intuition we follow is that the records of events that define the familiar objective past are inscribed in many distinct systems, e.g., subsystems of the environment, and are accessible locally in space and time to observers. We identify histories that are not just consistent but redundantly consistent using the partial-trace condition introduced by Finkelstein as a bridge between histories and decoherence. The existence of redundant records is a sufficient condition for redundant consistency. It selects, from the multitude of the alternative sets of consistent histories, a small subset endowed with redundant records characteristic of the objective classical past. The information about an objective history of the past is then simultaneously within reach of many, who can independently reconstruct it and arrive at compatible conclusions in the present.
Quantum Darwinism explains effective classical objectivity through the selective proliferation of information about preferred quantum states into multiple environmental fragments. Its mature formulations operate within quantum theory, using a system-environment decomposition, decoherence or einselection, and information-theoretic or broadcast-structure criteria for redundant accessibility.This paper asks an upstream question from Registration Theory (RT): what makes a physical distinction a record before that record is described as information available to an observer? Canonical RT answers that retained registration is persistent organization constraining later evolution, that a distinction becomes a physical record only when it remains consequential, and that persistent physical organization is prior to information extracted from it.The paper assembles a theorem-backed finite-model chain now available in the RT corpus. Canonical ACRF dynamics supplies write-retain-read consequential history. The exact finite-amplitude ACRF-4 quotient identifies a nine-dimensional host-host-boundary state. The certified consequence-minimality theorem (DOI 10.6084/m9.figshare.34063464) shows that the retained relational boundary contributes irreducible future-consequence directions. The spectrum-preserving ACRF-8 redundant-record theorem (DOI 10.6084/m9.figshare.34063500) then proves an explicit local witness in which one quotient-valid source distinction is written into two disjoint retained fragments that are locally recoverable, counterfactually separable, and independently readable, giving RRT(q)≥2R_{RT}(q)\ge 2RRT​(q)≥2 under the stated criteria.The resulting distinction from Quantum Darwinism is precise but bounded. RT recordhood is consequence-based, while Darwinian objectivity is an accessibility-and-redundancy criterion formulated within quantum theory. The ACRF witness demonstrates redundant retained record formation without assuming Hilbert space, density operators, mutual information, decoherence, einselection, Born probabilities, or an observer-defined environment. Therefore, multiple persistent records of one distinction are not definitionally identical to Quantum-Darwinian redundancy.The paper does not claim that Quantum Darwinism is false or that RT has derived quantum mechanics, decoherence, Born probabilities, a mutual-information redundancy plateau, or macroscopic objectivity. Instead, it proposes a disciplined hierarchy: consequential distinction → retention → persistent record → branching → redundant retained records → redundant accessibility → environmental objectivity. The final two steps remain open in RT. A future bridge must dynamically select and scale multi-host redundancy and map consequence-bearing RT records into quantum environmental fragments that satisfy decoherence and strong objectivity conditions.
Redundancy-Limited Emergence of Classical Histories in Quantum Systems This work investigates how classical reality emerges from underlying quantum dynamics, focusing on the role of environmental information, noise, and fundamental entropy limits. In quantum theory, systems evolve into superpositions of many possible outcomes. However, in practice we observe a world with definite, classical histories. A widely accepted explanation is decoherence, in which interactions with the environment suppress interference between different quantum states. More recent developments, particularly in quantum Darwinism, emphasize that classical information becomes objective when it is redundantly recorded across many independent parts of the environment. This paper addresses a key unresolved question: how many distinct classical histories can physically exist? To answer this, we construct a minimal computational model in which a system’s history is encoded into multiple environmental fragments, each subject to noise. By computing how much information about the system can be recovered from subsets of these fragments, we identify a characteristic scale that determines how many fragments are required to reconstruct the system’s history. Our results reveal a simple and robust relationship: the ability to recover classical information depends on the entropy of the noise affecting environmental records. As noise increases, more fragments are required to reconstruct a history, reflecting a loss of distinguishability. This leads to the definition of a “recoverability factor,” which quantifies how efficiently entropy can be converted into usable, classical information. We then connect this information-theoretic result to fundamental bounds from gravitational physics. In particular, existing entropy bounds limit the total amount of information that can pass through a region of spacetime. We show that only a fraction of this entropy—determined by the recoverability factor—can contribute to distinguishable classical histories. This leads to a new principle: the number of classical histories is not limited only by total entropy, but by the efficiency with which that entropy can be encoded, preserved, and accessed. Applying this framework to cosmological entropy estimates, we derive explicit upper bounds on the number of distinguishable classical histories in the observable universe. While this number is extraordinarily large, it is nonetheless finite and strongly constrained by both entropy and noise. These results refine the standard picture of quantum branching. While quantum theory allows a vast number of possible outcomes, only a subset can become physically meaningful in the sense of being stable, redundantly recorded, and accessible to observers. More broadly, this work provides a quantitative bridge between decoherence theory, information theory, and gravitational entropy bounds. It suggests that classical reality is fundamentally constrained not just by physical laws governing entropy, but by the efficiency of information transfer within those constraints.
Using the framework of decoherent histories, we study which past events leave detectable records in isolated quantum systems under the realistic assumption that decoherence is approximate and not perfect. In the first part we establish -- asymptotically for a large class of (pseudo-)random histories -- that the number of reliable records can be much smaller than the number of possible events, depending on the degree of decoherence. In the second part we reveal a clear decoherence structure for long histories based on a numerically exact solution of a random matrix model that, as we argue, captures generic aspects of decoherence. We observe recoherence between histories with a small Hamming distance, for localized histories admitting a high purity Petz recovery state, and for maverick histories that are statistical outliers with respect to Born's rule. From the perspective of the Many Worlds Interpretation, the first part -- which views the self-location problem as a coherent version of quantum state discrimination -- reveals a "branch selection problem", and the second part sheds light on the emergence of Born's rule and the theory confirmation problem.