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arxiv: 2605.07090 · v1 · submitted 2026-05-08 · 🪐 quant-ph · physics.hist-ph

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· Lean Theorem

Decoherence without the state: A causal quantum Darwinist approach

Nick Ormrod , Tein van der Lugt , Y\`il\`e Y\=ing , Jaros{\l}aw K. Korbicz
Authors on Pith no claims yet

Pith reviewed 2026-05-11 01:13 UTC · model grok-4.3

classification 🪐 quant-ph physics.hist-ph
keywords decoherenceconsistent historiesquantum Darwinismunitary evolutioncausal influencesemergence of statespointer basistime asymmetry
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The pith

Decoherence defined solely by causal influences in unitary dynamics, together with its dual, selects a privileged consistent history set from which states and outcomes emerge.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper seeks to unify environmentally induced decoherence with the consistent histories approach by redefining decoherence without assuming a quantum state exists beforehand. It treats decoherence as arising from the causal structure of unitary dynamics that allows information about certain observables to spread. The time-reversed version of this process causes the state to appear, and together they pick out one special set of consistent histories for any given unitary circuit. Examples illustrate how outcomes come from decoherence and states from the dual process. If correct, this shows that the emergence of states from decoherence is what was missing to connect these two descriptions of the classical world.

Core claim

Decoherence is characterized purely as a feature of the unitary dynamics: the causal influences needed for information about observables to proliferate to other systems. Its dual, defined by reversing time in the dynamics, causes the quantum state to emerge. For arbitrary unitary circuits on multiple systems, these two processes together identify a unique consistent history set. In this set, decoherence produces the outcomes while dual decoherence produces the states. This dynamics-first perspective accounts for the suppression of off-diagonal elements in the density matrix, the direction of time in decoherence, and the stability of the pointer basis.

What carries the argument

Causal decoherence, defined via the unitary dynamics' information-proliferating causal influences on observables, along with its time-reversed dual that generates the state.

If this is right

  • Any unitary circuit has a dynamically selected consistent history set without extra postulates.
  • The quantum state is not fundamental but emerges from the dual decoherence process.
  • Outcomes of measurements arise as a direct result of the decoherence mechanism.
  • The pointer basis gains robustness from the causal proliferation of information.
  • Time asymmetry appears naturally from distinguishing decoherence from its dual.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This view supports a causal interpretation of quantum mechanics where dynamics alone determine the classical realm.
  • It could lead to new ways to compute consistent histories in complex circuits by tracing causal influences.
  • The framework might extend to explain why certain observables become classical in open quantum systems without invoking environments explicitly.
  • Testable predictions could arise in quantum information experiments tracking information flow in small circuits.

Load-bearing premise

That a definition of decoherence based only on causal influences required for information proliferation in the unitary dynamics is sufficient, without presupposing a quantum state or any additional selection rules.

What would settle it

Identification of a unitary circuit where decoherence and dual decoherence do not yield a single privileged consistent history set, or where the emerging state from dual decoherence contradicts standard quantum mechanical predictions for that circuit.

Figures

Figures reproduced from arXiv: 2605.07090 by Jaros{\l}aw K. Korbicz, Nick Ormrod, Tein van der Lugt, Y\`il\`e Y\=ing.

Figure 1
Figure 1. Figure 1: illustrates the competition to achieve decoherence through some simple examples. In Example 3.6, all observables survive, and thus no nontrivial observables reproduce. Hence no nontrivial observables succeed in doing both; the decoherent algebra is trivial. In Example 3.7, all observables reproduce, and thus no nontrivial observables survive. Again, the decoherent algebra is trivial. But in Example 3.8, a … view at source ↗
Figure 2
Figure 2. Figure 2: Model of a single measurement. Systems of interest are labelled in black. Decohered and dual decohered algebras, associated emergent events, and their interpretations are labelled in blue. Each decohered algebra is depicted above the corresponding dual decohered algebra because the former arises from the interaction between the system and its future while the latter arises from its interaction with its pas… view at source ↗
Figure 3
Figure 3. Figure 3: Model of two incompatible measurements decorated as before with decohered and dual decohered algebras, associated events, and their interpretation. OT denotes the operator that is transformed to the Z-operator of the (unlabelled) output system of W = W(·)W † . We assume that [OT , ZT ] ̸= 0. event at S corresponding to the outcome of the first measurement thus fails to emerge not only with respect to B, bu… view at source ↗
Figure 4
Figure 4. Figure 4: Model of the Wigner’s friend scenario decorated as before with decohered and dual decohered algebras, associated events, and their interpretation. 33 [PITH_FULL_IMAGE:figures/full_fig_p033_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: In [24], the first step to obtaining the preferred decompositions is to break the wires corresponding to all systems of interest, thus obtaining a unitary channel V : AoutBoutC outP → AinBinC inF , where P (for “past”) is the bottom-right input to the circuit and F (for “future”) is the top-right output. The labels P and F are omitted from the diagram because they are not being considered as systems of int… view at source ↗
read the original abstract

The consistent histories formalism can be used to describe histories comprised of events across many systems, times, and places, plausibly rich enough to describe our experiences of the classical world; however, many consistent history sets are nonclassical and thus not obviously relevant to our experiences. Meanwhile, the program of environmentally induced decoherence identifies dynamically privileged classical degrees of freedom, but provides no general account of when or how many such degrees of freedom consistently combine to form histories. This work shows that the strengths of these two approaches can be combined by adopting a dynamics-first perspective on decoherence. Inspired by quantum causal models and quantum Darwinism, we define the process of decoherence in terms of the causal influences through unitary dynamics required for the proliferation of information about observables. We characterise decoherence as a property of the unitary dynamics, without presupposing the existence of any quantum state. Instead, we show that the state emerges from dual decoherence, related to decoherence by time-reversal of the unitary dynamics. Indeed, for any set of systems in an arbitrary unitary circuit, decoherence and its dual single out a privileged consistent history set -- and we demonstrate through examples that states emerge from dual decoherence while outcomes emerge from decoherence. Hence the idea that quantum states emerge from the process of decoherence turns out to be the key missing ingredient for unifying environmentally induced decoherence and consistent histories. Taking this idea ontologically seriously leads to a recently proposed causal interpretation of quantum theory or a dynamics-first version of the Everett interpretation. The causal approach also sheds light on the suppression of off-diagonal terms, time asymmetry, and robustness of the pointer basis.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes a dynamics-first definition of decoherence based on causal influences in unitary circuits enabling information proliferation about observables, without presupposing quantum states. It introduces dual decoherence via time-reversal of the dynamics, claiming that decoherence and its dual together select a privileged consistent history set for arbitrary unitary circuits. States are said to emerge from dual decoherence, while outcomes emerge from decoherence, as demonstrated in examples. This approach aims to unify environmentally induced decoherence with the consistent histories formalism and leads to a causal interpretation of quantum theory.

Significance. If the central construction holds without implicit selection rules, the work would be significant for providing a state-independent mechanism to select privileged classical histories from unitary dynamics, addressing a key gap between decoherence and consistent histories. It merits credit for grounding the emergence of both states and outcomes in causal processes and for offering perspectives on time asymmetry and pointer-basis robustness. The approach builds on quantum causal models and Darwinism ideas in a coherent way.

major comments (3)
  1. [Abstract and § on decoherence definition] Abstract and definition of decoherence: the claim that decoherence is defined solely via causal influences in the unitary dynamics (without presupposing states or additional selection rules) requires an explicit, basis-independent construction of 'information proliferation about observables' and 'causal influences'; without it, the selection of the privileged consistent history set may not be unique or may tacitly reintroduce the consistency conditions the framework aims to avoid.
  2. [Examples section] Examples demonstrating emergence: the demonstrations that states emerge from dual decoherence and outcomes from decoherence must include full derivations showing that identification of proliferating observables does not rely on any pre-chosen partitioning or state; otherwise the central claim that decoherence and dual select the history set for arbitrary circuits is not fully supported.
  3. [Unification and consistent histories discussion] Unification claim: the paper should explicitly compare the selected history set to standard consistent-histories consistency conditions (e.g., via the decoherence functional) to confirm it is not circular with prior literature on which the causal framework builds.
minor comments (2)
  1. [Notation and figures] Notation for dual decoherence and causal influences could be clarified with additional diagrams or explicit equations relating the time-reversed unitary to the emergence of states.
  2. [Introduction] A few sentences in the introduction repeat material from the abstract; tightening would improve readability.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thorough review and constructive feedback on our manuscript. We address each of the major comments in detail below, providing clarifications and indicating the revisions we will make to improve the manuscript.

read point-by-point responses

  1. Referee: Abstract and § on decoherence definition: the claim that decoherence is defined solely via causal influences in the unitary dynamics (without presupposing states or additional selection rules) requires an explicit, basis-independent construction of 'information proliferation about observables' and 'causal influences'; without it, the selection of the privileged consistent history set may not be unique or may tacitly reintroduce the consistency conditions the framework aims to avoid.

    Authors: We appreciate this point, as it touches on the core of our dynamics-first approach. The manuscript defines information proliferation via the causal influences in the unitary circuit, specifically through the ability of an observable to become correlated with multiple independent systems via the evolution, as formalized in the quantum causal model framework. This construction is basis-independent because it derives from the unitary operator's action on the circuit's causal graph, without reference to any Hilbert space basis or initial state. Regarding uniqueness, the set of such observables is determined uniquely by the circuit's structure for a given dynamics. We do not reintroduce consistency conditions; rather, the selected histories are shown to be consistent as a consequence. To strengthen this, we will include a more formal, explicit definition and a proof of uniqueness in the revised section on the decoherence definition. revision: partial

  2. Referee: Examples section: the demonstrations that states emerge from dual decoherence and outcomes from decoherence must include full derivations showing that identification of proliferating observables does not rely on any pre-chosen partitioning or state; otherwise the central claim that decoherence and dual select the history set for arbitrary circuits is not fully supported.

    Authors: We agree that the examples section would be strengthened by more detailed derivations. Currently, the examples demonstrate the emergence conceptually, but we acknowledge the need for explicit calculations. In the revised manuscript, we will provide full derivations for the key examples, explicitly tracing how the proliferating observables are identified solely from the causal structure of the unitary dynamics, without any pre-chosen partitioning or assumption of a quantum state. This will better support the generality of our claim for arbitrary circuits. revision: yes

  3. Referee: Unification claim: the paper should explicitly compare the selected history set to standard consistent-histories consistency conditions (e.g., via the decoherence functional) to confirm it is not circular with prior literature on which the causal framework builds.

    Authors: This suggestion is helpful for clarifying the relationship to existing literature. Our approach is not circular; the causal selection mechanism operates independently and yields histories that satisfy the consistency conditions. To make this explicit, we will add a comparison in the discussion section, including an analysis of the decoherence functional for the selected history sets in our examples. This will show how the vanishing of interference terms arises from the causal proliferation process, providing a dynamical basis for consistency without presupposing it. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected; derivation remains self-contained

full rationale

The paper defines decoherence as a property of unitary dynamics via causal influences enabling information proliferation about observables, explicitly without presupposing any quantum state, and derives the emergence of states from the time-reversed dual process. This is used to select a privileged consistent-history set for arbitrary circuits. No equations or definitions in the abstract or described framework reduce the output (privileged histories, emergent states/outcomes) to the inputs by construction, nor do they rename known results or smuggle ansatzes via self-citation. References to prior causal interpretations and consistent-histories literature provide context but do not bear the load of the central unification claim, which is demonstrated through examples as having independent content. The approach is presented as dynamics-first and falsifiable in principle against standard decoherence and histories formalisms.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claim rests on the assumption that unitary dynamics alone can be used to define causal influences and information proliferation without states, plus the existence of a time-reversal operation that yields dual decoherence.

axioms (2)
  • standard math The evolution is given by unitary dynamics on a circuit of systems.
    Invoked throughout the abstract as the sole dynamical input.
  • domain assumption Causal influences can be identified from the unitary circuit structure without reference to a state.
    Core to the new definition of decoherence.
invented entities (1)
  • dual decoherence no independent evidence
    purpose: Time-reversed counterpart that allows states to emerge
    Introduced to complement forward decoherence and select histories

pith-pipeline@v0.9.0 · 5614 in / 1369 out tokens · 33843 ms · 2026-05-11T01:13:27.238458+00:00 · methodology

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Reference graph

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