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arxiv: 2604.10562 · v1 · submitted 2026-04-12 · 🪐 quant-ph

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The spontaneous disentanglement hypothesis and causality

Eyal Buks
Authors on Pith no claims yet

Pith reviewed 2026-05-10 16:05 UTC · model grok-4.3

classification 🪐 quant-ph
keywords spontaneous disentanglementcausalitymaximum entropy principleLagrange multipliersquantum foundationsfinite-dimensional Hilbert spacequantum mechanics
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The pith

A maximum-entropy formulation of spontaneous disentanglement respects causality in any finite-dimensional quantum system.

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

The spontaneous disentanglement hypothesis posits that entangled quantum states can lose their correlations spontaneously, motivated by longstanding puzzles in the foundations of quantum mechanics. In some cases this process risks violating causality by allowing influences to propagate faster than light. The paper develops a version of the hypothesis that incorporates the maximum entropy principle and uses Lagrange multipliers to enforce causality as a constraint. This construction works for every quantum system whose Hilbert space has finite dimension. A sympathetic reader would care because it supplies a concrete way to keep the hypothesis from contradicting relativistic causality while preserving its potential to address measurement and entanglement issues.

Core claim

The proposed formulation for the spontaneous disentanglement hypothesis, which is based on the maximum entropy principle, is applicable for any quantum system having a Hilbert space of finite dimensionality and ensures consistency with causality via the method of Lagrange multipliers.

What carries the argument

The maximum entropy principle applied to spontaneous disentanglement dynamics, with causality enforced through Lagrange multipliers.

If this is right

  • Spontaneous disentanglement becomes compatible with causality for every finite-dimensional quantum system.
  • The hypothesis can now be studied without immediate contradiction to relativistic principles.
  • The formulation supplies a well-defined dynamical rule that can be applied to any finite Hilbert space.
  • Causality is maintained by treating it as an explicit constraint rather than an emergent feature.

Where Pith is reading between the lines

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

  • The same maximum-entropy-plus-Lagrange approach might be used to derive consistent disentanglement rates in small systems such as trapped ions or superconducting qubits.
  • If the formulation holds, it could be compared with standard decoherence models to see whether spontaneous disentanglement produces distinguishable predictions.
  • The method might be adapted to approximate infinite-dimensional cases by taking controlled limits of finite-dimensional truncations.

Load-bearing premise

The maximum entropy principle can be imposed directly on the spontaneous disentanglement process without creating inconsistencies in the time evolution or measurement rules.

What would settle it

An explicit calculation for a two-qubit entangled state showing that the Lagrange-multiplier constraints still permit a superluminal signaling channel.

Figures

Figures reproduced from arXiv: 2604.10562 by Eyal Buks.

Figure 1
Figure 1. Figure 1: FIG. 1: Two spin 1/2 system. Plots generated without (with) a [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Dipolar coupling. Time evolution of the single spin n [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
read the original abstract

The hypothesis that disentanglement spontaneously occurs in quantum systems is motivated by some outstanding issues in the foundations of quantum mechanics. However, for some cases, spontaneous disentanglement enables the violation of the causality principle. To mitigate the conflict with causality, a formulation for the hypothesis, which is based on the maximum entropy principle, is proposed. The method of Lagrange multipliers is implemented to ensure consistency with causality. The proposed formulation is applicable for any quantum system having a Hilbert space of finite dimensionality.

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

2 major / 2 minor

Summary. The paper proposes a formulation of the spontaneous disentanglement hypothesis motivated by foundational issues in quantum mechanics. It applies the maximum entropy principle with the method of Lagrange multipliers as a constraint to ensure consistency with causality. The formulation is claimed to be applicable to any quantum system with a finite-dimensional Hilbert space.

Significance. If the Lagrange multiplier constraint produces a valid causal dynamics, the work would offer a parameter-free way to incorporate spontaneous disentanglement while respecting no-signaling, using only standard tools from statistical mechanics and constrained optimization. This is a strength, as the approach avoids new free parameters or ad-hoc entities. However, the significance is currently limited because the central consistency claim is not yet supported by an explicit dynamical map or proof.

major comments (2)
  1. [Abstract and main formulation] Abstract and formulation section: the claim that the maximum entropy principle with Lagrange multipliers 'ensures consistency with causality' is stated without deriving the resulting time evolution (e.g., a master equation or quantum channel) or verifying that the reduced dynamics on subsystems preserve the no-signaling condition for arbitrary initial states and bipartitions. This is load-bearing for the central claim, as the skeptic note correctly identifies that the max-ent procedure must yield a completely positive trace-preserving map whose generator commutes appropriately with local observables.
  2. [Implementation of Lagrange multipliers] The applicability statement for finite-dimensional Hilbert spaces is not accompanied by an explicit check that the constrained optimization produces a valid quantum dynamical map; without this step the consistency with causality remains an unexamined assumption rather than a demonstrated result.
minor comments (2)
  1. [Abstract] The abstract would be clearer if it briefly indicated the form of the causality constraint (e.g., which local observables are held fixed by the multipliers).
  2. Notation for the entropy functional and the constraint equations could be introduced earlier to improve readability for readers outside the immediate subfield.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review. The comments correctly identify that the central claim of causal consistency requires explicit verification through derivation of the dynamics. We will revise the manuscript to include these derivations and checks while preserving the original formulation.

read point-by-point responses

  1. Referee: [Abstract and main formulation] Abstract and formulation section: the claim that the maximum entropy principle with Lagrange multipliers 'ensures consistency with causality' is stated without deriving the resulting time evolution (e.g., a master equation or quantum channel) or verifying that the reduced dynamics on subsystems preserve the no-signaling condition for arbitrary initial states and bipartitions. This is load-bearing for the central claim, as the skeptic note correctly identifies that the max-ent procedure must yield a completely positive trace-preserving map whose generator commutes appropriately with local observables.

    Authors: We agree that the original manuscript states the consistency claim via the constrained maximum-entropy procedure but does not derive the explicit time evolution or perform the no-signaling verification. The Lagrange-multiplier term is introduced precisely to enforce the causality constraint on the entropy maximization; however, to demonstrate that this yields a valid CPTP generator commuting with local observables, we will add in the revision a general derivation of the resulting master equation for finite-dimensional systems and an explicit check that the reduced dynamics on any subsystem satisfy the no-signaling condition for arbitrary initial states and bipartitions. revision: yes

  2. Referee: [Implementation of Lagrange multipliers] The applicability statement for finite-dimensional Hilbert spaces is not accompanied by an explicit check that the constrained optimization produces a valid quantum dynamical map; without this step the consistency with causality remains an unexamined assumption rather than a demonstrated result.

    Authors: We acknowledge that the manuscript asserts applicability to any finite-dimensional Hilbert space without supplying the explicit verification that the constrained optimization produces a CPTP map. In the revised version we will provide a general argument showing that the Lagrange-multiplier constraint, when solved within the space of density operators, yields a completely positive trace-preserving evolution whose generator respects the required commutation relations with local observables, thereby confirming the causal consistency for the stated class of systems. revision: yes

Circularity Check

0 steps flagged

No circularity: constructive proposal of max-ent formulation with Lagrange constraint

full rationale

The paper advances a hypothesis formulation by directly applying the maximum entropy principle subject to a causality constraint implemented via Lagrange multipliers. This is presented as a constructive method applicable to any finite-dimensional Hilbert space, without any equations that reduce by construction to fitted parameters, self-citations, or prior results from the same authors. No uniqueness theorems, ansatzes smuggled via citation, or renamings of known results are invoked. The central claim of causality consistency is asserted as a property of the proposed method rather than derived from a self-referential loop or statistically forced prediction, leaving the derivation chain self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on applying the maximum entropy principle as a selection rule for disentanglement dynamics and on the validity of Lagrange multipliers for enforcing causality constraints. No free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption The maximum entropy principle can be used to select the form of spontaneous disentanglement consistent with causality.
    Invoked as the basis for the proposed formulation in the abstract.

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Reference graph

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