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Counterfactuals in Macroscopic Quantum Physics: Irreversibility, Measurement and Locality

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Pith's one-line read A quantum homogenizer shows that exact irreversibility can coexist with time-reversal-symmetric quantum dynamics.

desk verdict A worthwhile compilation thesis: the clean no-go argument in Chapter 4 and the homogenizer toy model are real contributions, but the central asymptotic irreversibility claim is conditional on an approximation that deserves a more rigorous treatment. read the letter →

arxiv 2505.22834 v1 pith:IWBXMNUN submitted 2025-05-28 quant-ph

Maria Violaris This is my paper
classification quant-ph
keywords counterfactualsconstructortheoryquantumhomogenizerirreversibilityLandauererasureHardy'sparadoxlocalityvonNeumannentropy
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This work argues that apparent macroscopic puzzles—irreversibility, measurement, and locality—can be consistently described by universal quantum theory when stated as counterfactuals about which transformations are possible or impossible in a cycle. Its central result is that a quantum homogenizer, a machine of reservoir qubits interacting via partial swaps, can in a cycle transform a pure qubit into a mixed one but cannot transform a mixed qubit into a pure one, even though every interaction is unitary and time-reversal-symmetric. This constructor-based irreversibility implies an additional cost to information erasure beyond the usual Landauer entropy bound. The same counterfactual method is then applied to measurement: apparent Bell-type non-locality is given a local account, and the locally inaccessible information in entanglement is shown to be quantified by von Neumann entropy.

What carries the argument

The central object is the quantum homogenizer, in which a system qubit interacts one by one with $N$ reservoir qubits through the partial-swap unitary $U = \cos\eta\,\mathbf{1} + i\sin\eta\,S$. The load-bearing quantity is the relative deterioration $R_n^N = \epsilon_n^N / \delta_n^N$, the ratio of the error in homogenizing a system qubit to the robustness of the reservoir after $n$ uses. The criterion is that a task is possible for the homogenizer when $R_n^N \to 0$ in the limit of a large reservoir followed by many cycles, and impossible when it diverges. For the measurement part, the machinery is the Heisenberg-picture local account and the sharpest observable, which connects locally accessible and inaccessible information to the reduced density matrix.

What would settle it

Compute the exact relative deterioration for a mixed-to-pure homogenizer with $N$ reservoir qubits and $n$ cycles without the product-state approximation, keeping all reservoir-reservoir correlations, for weak but nonzero coupling. If $R_n^N$ fails to diverge in the limit $N\to\infty$ followed by $n\to\infty$, the claimed impossibility of erasure in a cycle is refuted; the current exact check reaches only a 3-by-3 homogenizer, so this large-$N$ calculation is the decisive open test.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that exact, scale-independent irreversibility is compatible with unitary quantum dynamics. The proof-model is the quantum homogenizer: the pure-to-mixed task has relative deterioration tending to zero in the double limit of many reservoir qubits and many cycles, so a constructor exists, while the mixed-to-pure erasure task has relative deterioration diverging, so no constructor exists. Because the asymmetry concerns the possibility of performing a task in a cycle rather than the reversibility of a single trajectory, it is not removed by time-reversal-symmetric dynamics. The work infers an additional, non-entropic cost to erasure relevant to Szilard engines, and extends the counterfactual method to measurement, showing that classical reasoning about non-commuting measurements produces apparent contradictions that disappear when the full quantum state of the measurement devices is included.

Load-bearing premise

The asymptotic asymmetry between pure-to-mixed and mixed-to-pure tasks assumes the reservoir can be treated as a product state when computing robustness (Sections 5.3.3 and 5.4.3), neglecting reservoir-reservoir entanglement; exact checks are limited to a 3-by-3 homogenizer, so the large-$N$ divergence is not directly verified.

Editorial extensions

If this is right

  • Pure-to-mixed homogenization can be repeated indefinitely with enough reservoir qubits and weak coupling, while mixed-to-pure erasure cannot; this gives a concrete, exact form of irreversibility in quantum thermodynamics.
  • Because the asymmetry is about performing a task in a cycle rather than about entropy changes, it predicts an additional cost to erasure beyond Landauer's bound, relevant to Szilard engines and programmable nanomachines.
  • The same irreversibility appears in an incoherent controlled-swap homogenizer, so the effect does not depend on coherence between system and reservoir.
  • No universal deterministic work extractor can draw different amounts of work from non-orthogonal coherent inputs; the coherent catalyst in the work-from-coherence protocol must depend on the input state.
  • Apparent Bell non-locality in Hardy-type experiments is locally accounted for, and the locally inaccessible part of entanglement is measured by von Neumann entropy.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper, the relative-deterioration criterion could be applied to other repeated thermal machines, giving a quantitative test for when a finite reservoir can be treated as a constructor.
  • If the mixed-to-pure impossibility is a general information-theoretic constraint rather than a feature of the homogenizer, it would supply a scale-independent second law that constrains successor theories of quantum mechanics as well.
  • The von Neumann-entropy measure of locally inaccessible information suggests that the entropy of a single reduced density matrix in a partially entangled pair could serve as a direct quantitative proxy for the degree of Bell-inequality violation.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. This DPhil thesis uses constructor-theoretic counterfactuals to address irreversibility, measurement, and locality in quantum theory. Part I develops a quantum model of constructors, then analyzes the quantum homogenizer as an example of constructor-based irreversibility: the claim is that the homogenizer can be used in a cycle for the pure-to-mixed task but not for the mixed-to-pure task, yielding an additional cost to erasure beyond Landauer's principle. It also proposes an incoherent cswap homogenizer, reports an NMR implementation, and proves that a known coherent work-extraction protocol cannot be made universal. Part II studies quantum measurement paradoxes, giving a local account of Hardy's paradox and a von Neumann entropy-based measure of locally inaccessible information. The thesis is broad, and several chapters rely on earlier publications.

Significance. The cleanest contribution is Chapter 4, where the unitary, time-reversal-symmetric model of a constructor and the argument that constructor-based irreversibility is compatible with unitary dynamics are presented carefully and soundly. If the Chapter 5 asymmetry between pure-to-mixed and mixed-to-pure transformations could be established rigorously, it would be a notable result: exact, scale-independent irreversibility coexisting with reversible microscopic dynamics, plus a genuine additional cost to erasure. Chapter 8 also contains a clean and explicit demonstration, based on unitary invariance of fidelity, that the preprocessing step of the [15] coherent work-extraction protocol cannot be universal. The experimental and theoretical comparisons in Chapters 6 and 7 are useful supporting material. However, the headline claim of Chapter 5 depends on an uncontrolled product-state approximation, and the general impossibility claims in Chapter 8 depend on an imported theorem and a conjecture, so the manuscript as it stands does not fully establish its most ambitious conclusions.

major comments (2)
  1. [§5.3.3 and §5.4.3, Eqs. (5.4)–(5.6)] The central asymmetry claim—mixed-to-pure is impossible while pure-to-mixed is possible—is based on the limits of relative deterioration in Eq. (5.4), with the robustness denominator computed using the product-state approximation in Eqs. (5.5)–(5.6). This approximation neglects reservoir-reservoir entanglement and is load-bearing for the claimed large-N behavior. Because the reservoir qubits interact with a common sequence of system qubits, their errors are correlated; in the extreme case of fully correlated errors, the joint fidelity with the original product state can decay linearly in N rather than exponentially. If the exact robustness decays only polynomially for the mixed-to-pure task, the relative deterioration need not diverge and the claimed impossibility is not established. The exact checks in §5.4.3 are limited to a 3×3 homogenizer, which cannot distinguish exponential from polynomial scaling, and the von Neumann entropy argument in Fig. 5.6 bounds only the sum of local entropies, not the joint fidelity appearing in Eq. (5.2). The thesis itself notes in §5.4.1 that strong-coupling results are unreliable due to neglected entanglement. The manuscript therefore needs either a rigorous bound or a substantially larger exact or tensor-network computation showing the required exponential decay of the robustness, or the conclusion should be explicitly qualified as conditional on the product-state approximation.
  2. [§8.4, §8.2, and §5.5] The general impossibility of a universal deterministic work extractor from coherence is presented as a consequence of Theorem 1 imported from constructor-theoretic distinguishability, and the explicit quantum demonstration for the [15] protocol is then tied to the conjecture that the mixed-to-pure task is constructor-theoretically impossible. The manuscript states in §8.4 that a universal work extractor using this protocol is possible if and only if the task {mixed state → pure state} is possible, and that this is 'ruled out by the conjecture.' Since the mixed-to-pure impossibility is only demonstrated for the quantum homogenizer and is conjectured to hold generally, the broad claim 'there cannot be a universal work extractor' is not established beyond the homogenizer-based argument. The unitary-invariance argument in §8.3.2 is sound and proves non-universality of the particular protocol, but the chapter should clearly separate that established quantum-mechanical result from the stronger, conjecture-dependent constructor-theoretic claim.
minor comments (5)
  1. [Chapter 1, p. 2] The introduction says the reconciliation of macroscopic irreversibility with unitary dynamics is done 'without the need for approximations,' but §5.3.3 introduces the product-state approximation in Eq. (5.5). Please qualify the claim so it does not contradict the later analysis.
  2. [§2.3 and §3.4] The name Yngvason is misspelled as 'Yvnangson' in §2.2 and as 'Yvnangon' in §3.4; the references should be corrected.
  3. [§2.3] There is a typo: 'seeimingly paradoxical' should be 'seemingly paradoxical.'
  4. [§5.5] The word 'resed' in the first paragraph of §5.5 should be 'reused.'
  5. [§6.1.1] The notation 'CSW AP' is used in the chapter title and headings before being defined; please introduce the abbreviation explicitly as 'controlled-SWAP (cswap)' and use it consistently.

Circularity Check

1 steps flagged · score 4.0 of 10

Core homogenizer asymmetry is self-contained, but the general impossibility of universal work extraction in Chapter 8 reduces to an unproved mixed-to-pure conjecture drawn from the authors' own earlier work.

  1. self citation load bearing [Section 8.4, paragraph beginning 'As discussed in Chapter 5...' (PhD thesis, arXiv:2505.22834, pages 89-90)]
    "There it was shown that the task of transforming a qubit from a maximally mixed to a pure state via the quantum homogenizer is constructor-theoretically impossible, meaning that it deteriorates too rapidly with repeated use to be a constructor for the task [1, 2]. ... Therefore universal work extraction from coherence cannot be reliably implemented with any known constructor, and is ruled out by the conjecture that the mixed-to-pure task is constructor-theoretically impossible."

    The general impossibility of universal work extraction is here reduced to the mixed-to-pure impossibility established in the author's own papers [1,2] and Chapter 5, and the text explicitly labels that premise a 'conjecture'. The thesis does not provide an independent derivation of the general mixed-to-pure impossibility; it imports the unproved homogenizer-based result as the load-bearing premise of the constructor-theoretic claim. The specific non-universality of the [15] protocol is independently argued via unitary invariance of fidelity, so this is a partial reduction rather than a complete collapse of the chapter's contribution.

full rationale

The main homogenizer analysis in Chapter 5 is not circular: the error, robustness, and relative deterioration are computed from recurrence relations derived from the partial-swap unitary, and no parameter is fitted to the target conclusion. The pure-to-mixed versus mixed-to-pure asymmetry follows from the different fidelity expressions (Eqs. 5.32-5.40) and from the defined limit criterion on R_N^n, not from an assumed answer. The product-state approximation in Eq. 5.6 is an unproven large-N assumption and is the main correctness risk, as Section 5.4.1 also concedes that strong-coupling results are unreliable due to neglected entanglement; however, this is a technical limitation rather than a circularity, since the approximation is applied symmetrically to both tasks and checked exactly for a 3x3 homogenizer. The only step that approaches a self-citation chain is in Chapter 8, where the general impossibility of universal work extraction is made to rest on the mixed-to-pure impossibility established in the authors' own earlier work [1,2], which the thesis itself labels a conjecture. That is a partial reduction of the general claim to an unverified prior result. Theorem 1 from [16] is cited as an external constructor-theory result and is not shown to be by the present authors; it raises verification concerns but not a demonstrated circularity. Overall, the central homogenizer derivation is self-contained, so the circularity score is moderate rather than high.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The free parameters and axioms are modest: one tunable coupling strength, the constructor-theory framework, standard unitary dynamics, a product-state approximation, and an explicit conjecture used in Chapter 8. No new physical entities are postulated. The count reflects that the thesis extends an established program rather than deriving everything from scratch.

free parameters (1)
  • coupling strength eta = 0.01, 0.1, 0.5 (chosen, not fitted)
    The convergence and reusability claims are studied in the weak-coupling regime; the relative-deterioration limits depend on this tunable model parameter.
assumptions (4)
  • domain assumption Constructor theory principle of task possibility in a cycle
    The entire thesis evaluates tasks using constructor-theoretic possibility; this is a postulate of the framework, not derived from quantum dynamics.
  • domain assumption Time-reversal symmetric unitary dynamics
    Used in Chapter 4's proof and in the homogenizer model; standard quantum assumption.
  • ad hoc to paper Conjecture that mixed-to-pure transformation is constructor-theoretically impossible in general
    Invoked in Section 8.4 to rule out universal work extractors; only demonstrated for the homogenizer, so it is a load-bearing unproven assumption.
  • ad hoc to paper Product-state approximation for reservoir fidelity
    Equation (5.6) neglects reservoir entanglement; central to the limit analysis but only partially validated.

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Pith. "Pith review of Counterfactuals in Macroscopic Quantum Physics: Irreversibility, Measurement and Locality." pith.science (2026). https://pith.science/paper/IWBXMNUN

@misc{pith2026250522834,
  author       = {Pith},
  title        = {Pith review of: Counterfactuals in Macroscopic Quantum Physics: Irreversibility, Measurement and Locality},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IWBXMNUN}},
  note         = {Machine review of arXiv:2505.22834}
}
read the original abstract

Can quantum theory be applied on all scales? While there are many arguments for the universality of quantum theory, this question remains a subject of debate. It is unknown how far the existence of macroscopic irreversibility can be derived from or reconciled with time-reversal symmetric quantum dynamics. Furthermore, reasoning about quantum measurements can appear to produce surprising and even paradoxical outcomes. The classical outcomes of quantum measurements are in some contexts deemed to violate the fundamental principle of locality, in particular when considering entanglement and Bell non-locality. Therefore measurement, irreversibility and locality can all appear to challenge the universality of quantum theory. In this thesis we approach these problems using counterfactuals -- statements about the possibility and impossibility of transformations. Using the principles of constructor theory and quantum information theory, we find novel features of quantum thermodynamics relating to irreversibility, information erasure and coherence. We also develop tools to quantify the full implications of non-commutativity of quantum operators in settings where quantum theory is applied universally to measurement devices. This reveals new ways of characterising the quantum information stored in entanglement and quantum branching structure. Our results reinforce the ability of universal quantum theory to consistently describe both microscopic and macroscopic observers and thermodynamic systems.

Figures

Figures reproduced from arXiv: 2505.22834 by the authors.

Figure 2.1
Figure 2.1. Visualisation of the Szilard engine cycle. [PITH_FULL_IMAGE:figures/full_fig_p029_2_1.png] view at source ↗
Figure 2.2
Figure 2.2. a) Quantum circuit diagram schematic of the work extraction protocol [PITH_FULL_IMAGE:figures/full_fig_p035_2_2.png] view at source ↗
Figure 2.3
Figure 2.3. Depiction of the quantum homogenizer, which consists of [PITH_FULL_IMAGE:figures/full_fig_p037_2_3.png] view at source ↗
Figures from the paper (32 more)
Figure 2.4
Figure 2.4. Figure 2.4: The Bloch sphere and a Bloch vector of size [PITH_FULL_IMAGE:figures/full_fig_p038_2_4.png]
Figure 4.1
Figure 4.1. Figure 4.1: Every time a machine in the set Σ(i) T is evolved using unitary U to transform a system from ρx to ρy, it is left in a state in the set Σ(i−1) T . The lines between each ρy and Σ(i) T indicate that they may be entangled. Therefore the convex combination PN i=1 λiρCi …
Figure 4
Figure 4. Figure 4: figure 4.1 to convert [PITH_FULL_IMAGE:figures/full_fig_p048_4.png]
Figure 5.2
Figure 5.2. Figure 5.2: Surfaces of relative deteri￾oration for a reservoir of size N used n times, with η = 0.01 for weak coupling and η = 0.1 for strong coupling. and 5.12, with careful attention to the indices, and using the initial condition that the Bloch vector sizes sum to 1 since on…
Figure 5.1
Figure 5.1. Figure 5.1: figure 5.1. Error decreases with increasing reservoir size, and increases with number [PITH_FULL_IMAGE:figures/full_fig_p062_5_1.png]
Figure 5.3
Figure 5.3. Figure 5.3: Approximate relative dete￾rioration for a pure-to-mixed homoge￾nizer used N = n times, with coupling strength η = 0.1 [PITH_FULL_IMAGE:figures/full_fig_p063_5_3.png]
Figure 5.6
Figure 5.6. Figure 5.6: Total von Neumann entropy of the reservoir qubits and system qubits in the pure-to-mixed transformation, with η = 0.01 for weak coupling (flat, meshed surface) and η = 0.1 for strong coupling (curved, solid surface). N is the number of qubits in each reservoir, and n…
Figure 6.1
Figure 6.1. Figure 6.1: The cswap homogenizer. Control qubits are labelled c. The j th reservoir qubit after interaction with the i th system is in the state ξ i j , and the i th system after interaction with the j th reservoir qubit is in the state ρ i j . 62 [PITH_FULL_IMAGE:figures/full…
Figure 6.2
Figure 6.2. Figure 6.2: State fidelity F against number of system-reservoir interactions N for transforming |0⟩ to |+⟩. 6.2.4 Trace Distance Another way of demonstrating an equivalence between the homogenizers is calculat￾ing the minimum number of system-reservoir interactions required so t…
Figure 6.3
Figure 6.3. Figure 6.3: System Bloch vector evolution for the coherent homogenizer with initial [PITH_FULL_IMAGE:figures/full_fig_p081_6_3.png]
Figure 6.4
Figure 6.4. Figure 6.4: System Bloch vector evolution for the incoherent homogenizer with initial [PITH_FULL_IMAGE:figures/full_fig_p081_6_4.png]
Figure 6.5
Figure 6.5. Figure 6.5: Von Neumann entropy S as a function of the number of system￾environment interactions N with coupling strengths η = π 8 and η = 3π 8 . This can be understood in terms of the system being homogenized quicker in the strong coupling case (leading to a plateau in joint sy…
Figure 7.1
Figure 7.1. Figure 7.1: A quantum homogenizer with two system qubits and two reservoir qubits [PITH_FULL_IMAGE:figures/full_fig_p088_7_1.png]
Figure 7
Figure 7. Figure 7: plots the von Neumann entropy [PITH_FULL_IMAGE:figures/full_fig_p089_7.png]
Figure 7.2
Figure 7.2. Figure 7.2: Experimental results and theoretical predictions for the quantum homog [PITH_FULL_IMAGE:figures/full_fig_p090_7_2.png]
Figure 7.3
Figure 7.3. Figure 7.3: Von Neumann entropies of qubits B and C against coupling strength, cal [PITH_FULL_IMAGE:figures/full_fig_p091_7_3.png]
Figure 7.4
Figure 7.4. Figure 7.4: Total von Neumann entropies of the four individual qubits, calculated [PITH_FULL_IMAGE:figures/full_fig_p092_7_4.png]
Figure 8.1
Figure 8.1. Figure 8.1: Consider deterministic work extraction from non-orthogonal coherent [PITH_FULL_IMAGE:figures/full_fig_p096_8_1.png]
Figure 8.2
Figure 8.2. Figure 8.2: a) Quantum circuit diagram schematic of the work extraction protocol [PITH_FULL_IMAGE:figures/full_fig_p100_8_2.png]
Figure 9.1
Figure 9.1. Figure 9.1: Quantum circuit for measuring correlations of an entangled pair of qubits. [PITH_FULL_IMAGE:figures/full_fig_p111_9_1.png]
Figure 9.2
Figure 9.2. Figure 9.2: Alice and Bob are treated as quantum systems, so all measurement oper [PITH_FULL_IMAGE:figures/full_fig_p114_9_2.png]
Figure 10.1
Figure 10.1. Figure 10.1: Quantum circuit which demonstrates the impossibility of using classical [PITH_FULL_IMAGE:figures/full_fig_p120_10_1.png]
Figure 10.2
Figure 10.2. Figure 10.2: Illustration of the individually consistent but incompatible deductions [PITH_FULL_IMAGE:figures/full_fig_p123_10_2.png]
Figure 10.3
Figure 10.3. Figure 10.3: A Penrose triangle. Each corner is consistent as the corner of a triangle. [PITH_FULL_IMAGE:figures/full_fig_p124_10_3.png]
Figure 10.4
Figure 10.4. Figure 10.4: Unitary implementation of the Frauchiger-Renner paradox quantum [PITH_FULL_IMAGE:figures/full_fig_p125_10_4.png]
Figure 10.5
Figure 10.5. Figure 10.5: Modification of the Frauchiger-Renner paradox quantum circuit to [PITH_FULL_IMAGE:figures/full_fig_p126_10_5.png]
Figure 10.6
Figure 10.6. Figure 10.6: figure 10.6 [PITH_FULL_IMAGE:figures/full_fig_p129_10_6.png]
Figure 10.6
Figure 10.6. Figure 10.6: A depiction of Hardy’s paradox as a quantum circuit. [PITH_FULL_IMAGE:figures/full_fig_p130_10_6.png]
Figure 10.7
Figure 10.7. Figure 10.7: The pigeonhole paradox as a quantum circuit. [PITH_FULL_IMAGE:figures/full_fig_p132_10_7.png]
Figure 11.1
Figure 11.1. Figure 11.1: For the state |ψ⟩ = a |00⟩+b |01⟩+b |10⟩: Sum of von Neumann entropy of reduced states; probability of post-selecting on states required to formulate a Hardy￾type paradox; and incompatibility of relevant pairs of observables, as functions of a. general expression fo…
Figure 11.2
Figure 11.2. Figure 11.2: Quantum circuit to prepare a Hardy-type state parameterised by [PITH_FULL_IMAGE:figures/full_fig_p145_11_2.png]
Figure 11.3
Figure 11.3. Figure 11.3: Quantum circuit which stores the value θ in a partially locally inaccessible way. Finally the third statement for formulating Hardy’s paradox, 11.3, states that: ⟨Π−1(ˆqaz(2))Π−1(ˆqbz(2))⟩ = 0 (11.28) with the corresponding sharp observable enabling us to retrieve l…

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.