AIP Advances

Record-based onset of irreversibility in continuously monitored open quantum systems

David Werner

Published Jun 1, 2026• 0 citations

Abstract

We develop a calibration-based framework for effective irreversibility in continuously monitored open quantum systems. The central quantity is Irec(t)=DKL(P1(t)‖P0(t)), the Kullback–Leibler divergence between calibrated measurement-record laws under two controlled branches. Within the equal-covariance Gaussian class, Irec(t) is deterministic for fixed record laws, is computable from Kalman-filter innovations, and obeys an exact master curve for minimum branch-discrimination error. The trajectory-level log-likelihood ratio Λ(t) is stochastic: a candidate onset location t× begins a sustained evidence interval, whereas a causal declaration is available only at tdec, after the interval has been verified. Thus, Idec = Irec(tdec) is distributed across trajectories, although Irec(t) is deterministic at a fixed time. A calibrated reference-register construction assigns a one-nat excess-free-energy reference to the stored record. The primary new protocol result is that, in information time u = Irec(t), a hold interval specified in accumulated-information units yields a rate-invariant declaration distribution within the Gaussian benchmark, whereas a fixed physical-time hold interval generally does not. As a model-specific physical corollary, for pure coherent output pointers and a complete matched homodyne record, residual branch coherence obeys Cdet(t) = exp[−Irec(t)/4]; selecting Cdet = 1/2 gives the illustrative marker Irec = 4 ln 2 nats. For incomplete detected records, the mapping acquires an effective-efficiency correction. In practical terms, the framework tells an experimenter when a continuously recorded signal has acquired stable evidence and how that declaration changes as measurement quality varies. We also derive the deterministic reference-time correction for time-dependent information rates and state experimentally testable failure criteria.

DOI: 10.1063/5.0340108

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AIP Advances

Record-based onset of irreversibility in continuously monitored open quantum systems

David Werner

Published Jun 1, 2026• 0 citations

Publisher

Abstract

DOI: 10.1063/5.0340108

Related papers

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We construct a finite quantum measurement model using a quantum-nondemolition (QND) qubit coupled to a two-photon-driven Kerr parametric oscillator (KPO) with continuously monitored homodyne output. A unitary dilation of the qubit, pointer, and field accounts for decoherence, output noise, and conditioning; the stochastic master equation is a filter for the observed record, not an objective-collapse law. Exact QND commutation makes the conditioned source-sector weight a bounded martingale. Under asymptotic output identifiability, it becomes extremal almost surely, with terminal hitting probabilities equal to the initial Born sector weights. This establishes instrument-level Born consistency, not a derivation of the Hilbert-space probability rule from dynamics alone. The nonlinear KPO amplifies sector-dependent biases and registers information in metastable pointer basins. Pointer separation scales as $\sqrt{N}$ and the effective semiclassical noise scale as $N^{-1/2}$ . Full quantum trajectories show synchronization of conditional extremalization and pointer locking. Over the simulated finite-size range, wrong registration and later record corruption decrease approximately exponentially with distinct rates. Reduced first-passage, Liouvillian-metastability, and Freidlin-Wentzell minimum-action calculations independently support the corruption exponent to within a few percent. Thus conditional extremalization, single-basin registration, and metastable storage coexist within standard unitary-background quantum mechanics, without deleting unconditioned global components or adding a fundamental stochastic selector. Classical actuality remains a separate record-level ontological claim. The stored KPO record is a local building block for the companion Framework, whose broader claims require persistent co-recordable records in one commutative record algebra.We construct a finite quantum measurement model using a quantum-nondemolition (QND) qubit coupled to a two-photon-driven Kerr parametric oscillator (KPO) with continuously monitored homodyne output. A unitary dilation of the qubit, pointer, and field accounts for decoherence, output noise, and conditioning; the stochastic master equation is a filter for the observed record, not an objective-collapse law. Exact QND commutation makes the conditioned source-sector weight a bounded martingale. Under asymptotic output identifiability, it becomes extremal almost surely, with terminal hitting probabilities equal to the initial Born sector weights. This establishes instrument-level Born consistency, not a derivation of the Hilbert-space probability rule from dynamics alone. The nonlinear KPO amplifies sector-dependent biases and registers information in metastable pointer basins. Pointer separation scales as $\sqrt{N}$ and the effective semiclassical noise scale as $N^{-1/2}$. Full quantum trajectories show synchronization of conditional extremalization and pointer locking. Over the simulated finite-size range, wrong registration and later record corruption decrease approximately exponentially with distinct rates. Reduced first-passage, Liouvillian-metastability, and Freidlin-Wentzell minimum-action calculations independently support the corruption exponent to within a few percent. Thus conditional extremalization, single-basin registration, and metastable storage coexist within standard unitary-background quantum mechanics, without deleting unconditioned global components or adding a fundamental stochastic selector. Classical actuality remains a separate record-level ontological claim. The stored KPO record is a local building block for the companion Framework, whose broader claims require persistent co-recordable records in one commutative record algebra.

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Admissible Record Construction in Physically Non-Selective Quantum Regimes

Amos Maley

A Kernel-Role Determinacy Theorem for Record Fixation, Fixed-Domain Quotients, and Boundary-Trace Normal Form This paper specializes the AASC kernel to the construction and use of quantum measurement records. Its central question is not initially how outcomes are produced, whether a wavefunction collapses, or which interpretation of quantum theory is correct. It asks what must be fixed for a measurement record to function as the same determinate physical and evidential object across retention, prospective use, deliberation, comparison, and report. For any non-degenerate determinate physical object, state, carrier, transformation, record, comparison, or endpoint, the paper takes the governing kernel to be: NDObj(x) ⇒ K(x) = (Adm, Stand, Ref, Irr). Admissibility, standing, reference, and irreversibility are therefore treated as necessary role conditions of determinate record use, not as an optional interpretive overlay added to an otherwise complete physical description. Measurement-record determinacy The manuscript constructs a fixed-domain measurement-record target in which a record must preserve: reference to the same construction token; standing-bearing evidential eligibility; admissible reuse; original act-time qualification; lawful redescription; retained and prospective record use; deliberative and comparative use; reportability and downstream inheritance. The resulting assignment space is quotiented by equivalence of standing-bearing measurement-record content. A rival quotient claiming exactly the same content collapses to the canonical measurement-record quotient. Representational differences that preserve the complete role content are treated as skin; differences affecting record identity, evidential ordering, admissibility, continuation, or downstream use remain physically relevant. 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The paper shows that non-selective structures may agree on branch weights, density content, decoherence, correlations, instrument sums, channel closure, effect weights, projector orthogonality, and repeatability without selecting one fine record as the standing evidential record. Fixed-domain quotient and fixation commutation The theorem ladder establishes: fixed-domain assignment-space forcing; exact quotient construction for standing-bearing record content; same-scope equivalence collapse; fixation commutation under admissible transformation; inheritance of the original qualification requirement; persistence-bearing reuse; asymmetry exhaustion; anti-weakening; selector exhaustion. If evidential ordering varies across admissible assignments while the target requires one fixed-domain ordering, the ordering is not defined on that scope merely because numerical values or branch-local reports happen to coincide. The paper therefore treats measurement-record fixation as prior to the theory-level evidential reuse that depends on it. Boundary-trace normal form After internal and provenance/indexical routes have been exhausted, the residual same-domain route is a singleton stable boundary trace. Such a trace is not collapse dynamics, hidden-variable selection, or a new physical mechanism. It is an admissibility-preserving role anchor that can fix a record-bearing assignment only when its channel, incidence, transport law, original authority, and singleton-positive condition are independently warranted. The result distinguishes: sound partial selection from complete role fixation; unique trace value from unique original occupant; class-valued record fixation from raw-token fixation; later discovery of an original qualification from retroactive repair; physical record occurrence from standing evidential identity. 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Instrumentalist and QBist strategies instead reduce or redirect the target explanatory burden. Role in the AASC programme This paper provides the record-fixation layer of the AASC Quantum Determinacy Pair. Its companion Bell-scope work addresses the compatibility and no-signaling side of quantum witness determinacy. Together, the pair treats quantum records and witnesses as kernel-governed standing structures rather than as automatically determinate physical occurrences. The paper’s principal contribution is to identify the first failure point in a physically non-selective measurement regime: The initial problem is not necessarily the production of branch-local outcomes. It is the admissible fixation of the record role through which outcomes are retained, reported, remembered, compared, and used as evidence. The public Lean 4 formalization is synchronized with the finite measurement-boundary release v0.9.1 and provides the finite artifact for the declared effect, projector, compatibility, closed-stack, boundary-certificate, and audit layers. Keywords AASC; measurement problem; quantum measurement; measurement-record fixation; physically non-selective regimes; Everettian non-selection; record-role determinacy; fixed-domain quotient; standing equivalence; boundary-trace fixation; selector exhaustion; decoherence; branch-local records; admissibility and irreversibility; Lean 4 formalizationA Kernel-Role Determinacy Theorem for Record Fixation, Fixed-Domain Quotients, and Boundary-Trace Normal Form This paper specializes the AASC kernel to the construction and use of quantum measurement records. Its central question is not initially how outcomes are produced, whether a wavefunction collapses, or which interpretation of quantum theory is correct. It asks what must be fixed for a measurement record to function as the same determinate physical and evidential object across retention, prospective use, deliberation, comparison, and report. For any non-degenerate determinate physical object, state, carrier, transformation, record, comparison, or endpoint, the paper takes the governing kernel to be: NDObj(x) ⇒ K(x) = (Adm, Stand, Ref, Irr). Admissibility, standing, reference, and irreversibility are therefore treated as necessary role conditions of determinate record use, not as an optional interpretive overlay added to an otherwise complete physical description. 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Physically non-selective quantum regimes The paper then studies a physically non-selective quantum regime containing unitary branching, entanglement, decoherence, branch-local records, and stable local reports. The central result is conditional and target-specific: The bare unitary-entangling-decohering package can support multiple stable branch-local records without supplying a unique standing evidential record for the fixed construction-relative target. This is not a claim that branch-local records are unreal, unstable, or physically useless. It is a distinction between: physical occurrence of branch-local record structures; local branch-relative reportability; evidential role fixation for a record reused as the same standing object across the measurement practice. The paper shows that non-selective structures may agree on branch weights, density content, decoherence, correlations, instrument sums, channel closure, effect weights, projector orthogonality, and repeatability without selecting one fine record as the standing evidential record. Fixed-domain quotient and fixation commutation The theorem ladder establishes: fixed-domain assignment-space forcing; exact quotient construction for standing-bearing record content; same-scope equivalence collapse; fixation commutation under admissible transformation; inheritance of the original qualification requirement; persistence-bearing reuse; asymmetry exhaustion; anti-weakening; selector exhaustion. If evidential ordering varies across admissible assignments while the target requires one fixed-domain ordering, the ordering is not defined on that scope merely because numerical values or branch-local reports happen to coincide. The paper therefore treats measurement-record fixation as prior to the theory-level evidential reuse that depends on it. Boundary-trace normal form After internal and provenance/indexical routes have been exhausted, the residual same-domain route is a singleton stable boundary trace. Such a trace is not collapse dynamics, hidden-variable selection, or a new physical mechanism. It is an admissibility-preserving role anchor that can fix a record-bearing assignment only when its channel, incidence, transport law, original authority, and singleton-positive condition are independently warranted. The result distinguishes: sound partial selection from complete role fixation; unique trace value from unique original occupant; class-valued record fixation from raw-token fixation; later discovery of an original qualification from retroactive repair; physical record occurrence from standing evidential identity. Finite quantum specialization The paper occupies the abstract structure with an explicit finite two-branch quantum measurement domain containing: two outcomes; two fine records and one merged record; denominator-two branch weights; a balanced integer-amplitude state; density-table realization; selective and non-selective instrument maps; environment-record maps; projective branch maps; complementary effects; zero-product projectors; repeatability operations. On the declared balanced witness, amplitude weights, density weights, branch-map traces, effect weights, pointer records, instrument records, environment records, and channel records agree on the same branch architecture. Selective surfaces preserve the fine-record distinction. Non-selective surfaces agree only on the merged record. The fine records therefore remain separated, while the declared non-selective surfaces supply no singleton fine-record selector. The finite selector-boundary theorem eliminates the disjunction of candidate hidden selectors across the state, instrument, environment, channel, effect, and repeatability surfaces. The resulting diagnosis is precise: the missing structure is admissible fine-record role fixation, not further branch production, weighting, decoherence, stabilization, or repeatability. Scope and non-claims The manuscript establishes a finite, conditional, manuscript-facing theorem. It does not claim: to derive Hilbert-space quantum mechanics; to derive general POVM theory; to derive full projection-valued-measure theory; to reconstruct the full operator algebra; to provide a general Kraus representation theorem; to reconstruct complete positivity; to derive the continuum Born rule; to derive universal physical decoherence theory; to introduce a new collapse dynamics; to prove that no physical collapse process occurs in nature; to prove physical branch selection; to establish interpretive truth; to classify every possible physical measurement mechanism. The absence of a hidden selector on the declared finite non-selective surfaces is therefore not a theorem that no physical collapse or selection process can occur elsewhere. It is the finite theorem that those declared surfaces do not themselves supply the required fine-record selector. Relation to quantum interpretations The result does not deny the practical success of quantum theory, decoherence, branch-relative reporting, instrumental updates, or decision-theoretic methods. A practice aimed only at prediction, branch-local reporting, or instrumental updating may be a different target from the construction-relative record use studied here. If a theory claims to underwrite retained, prospective, deliberative, and evidential reuse of the same record-bearing construction token, it must preserve the relevant kernel roles and admit a standing-bearing fixation regime. Bare Everettian dynamics, without additional dynamics, ontological privileging, or admissible restriction to one constructional class, supplies no fine-record selector on the declared target. A strategy that preserves non-selective physics while restricting admissible record-fixation assignments belongs to a restriction-to-one-constructional-class route. Instrumentalist and QBist strategies instead reduce or redirect the target explanatory burden. Role in the AASC programme This paper provides the record-fixation layer of the AASC Quantum Determinacy Pair. Its companion Bell-scope work addresses the compatibility and no-signaling side of quantum witness determinacy. Together, the pair treats quantum records and witnesses as kernel-governed standing structures rather than as automatically determinate physical occurrences. The paper’s principal contribution is to identify the first failure point in a physically non-selective measurement regime: The initial problem is not necessarily the production of branch-local outcomes. It is the admissible fixation of the record role through which outcomes are retained, reported, remembered, compared, and used as evidence. The public Lean 4 formalization is synchronized with the finite measurement-boundary release v0.9.1 and provides the finite artifact for the declared effect, projector, compatibility, closed-stack, boundary-certificate, and audit layers. Keywords AASC; measurement problem; quantum measurement; measurement-record fixation; physically non-selective regimes; Everettian non-selection; record-role determinacy; fixed-domain quotient; standing equivalence; boundary-trace fixation; selector exhaustion; decoherence; branch-local records; admissibility and irreversibility; Lean 4 formalization

Feb 7, 20260 citations

\sqrt{N}

and the effective semiclassical noise scale as

N^{-1/2}

. Full quantum trajectories show synchronization of conditional extremalization and pointer locking. Over the simulated finite-size range, wrong registration and later record corruption decrease approximately exponentially with distinct rates. Reduced first-passage, Liouvillian-metastability, and Freidlin-Wentzell minimum-action calculations independently support the corruption exponent to within a few percent. Thus conditional extremalization, single-basin registration, and metastable storage coexist within standard unitary-background quantum mechanics, without deleting unconditioned global components or adding a fundamental stochastic selector. Classical actuality remains a separate record-level ontological claim. The stored KPO record is a local building block for the companion Framework, whose broader claims require persistent co-recordable records in one commutative record algebra.