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REVIEW 3 major objections 5 minor 57 references

Wavefunction branches demand a definition!

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The paper argues that wavefunction branches—the orthogonal, tree-structured components into which a macroscopic quantum state evolves—still have no first-principles definition, and that neither of the two recent complexity-based proposals…

desk verdict A useful and honest perspective comparing two complexity-based branch definitions, whose title overpromises but whose content is a solid mapping of open problems. read the letter →

arxiv 2506.15663 v1 pith:I5NQEBBC submitted 2025-06-18 quant-ph

C. Jess Riedel This is my paper
classification quant-ph
keywords wavefunctionbranchesquantumcomplexitydecoherencemeasurementproblemmany-bodysystemsconsistenthistorieseffectivecollapseclassicalsimulationof
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

The paper's central claim is that wavefunction branching—a macroscopic quantum state decomposing into orthogonal, tree-structured components that look like classical outcomes—is real and central to quantum mechanics, but still lacks a precise, first-principles definition. It compares the two leading complexity-based proposals, Taylor-McCulloch and Weingarten, and argues that neither is satisfactory: one produces non-unique 'good' decompositions, the other imposes a unique but possibly artificial sharp threshold with a free scale parameter. A correct definition would extend decoherence theory beyond system-environment splits, could replace the subjective collapse postulate, and would enable efficient classical simulation by sampling branches with bounded entanglement. The paper concludes that the problem remains open and that solving it is a pressing task for quantum foundations.

What carries the argument

The central machine is quantum unitary complexity $C(U)$, roughly the length of the shortest decomposition of a unitary into elementary local operations; it supplies a distance between states. Taylor & McCulloch's branch criterion is the branchiness gap $C_I - C_D$: the large difference between the complexity of the least-complex unitary that can interfere two branch states and the one that can distinguish them. Weingarten instead minimizes $Q = \sum_i |\psi_i|^2[C(\psi_i,\Omega)^2 - b\ln |\psi_i|^2]$ over decompositions, a weighted trade-off between expected squared complexity and branch norm entropy. Both definitions lean on the 'second law of quantum complexity'—that state complexity grows almost linearly under generic local Hamiltonian evolution—to conclude that branches, once formed, persist on long timescales.

What would settle it

Compute the state complexity of a finite spin lattice evolving under a generic local Hamiltonian from a product state; if the complexity does not grow approximately linearly for exponentially long times—or if an explicit initial state returns to near-zero complexity without fine-tuning—the shared persistence argument behind both branch definitions is refuted.

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Extended reading notes

Core claim

The paper's thesis, stated on its own terms, is that wavefunction branches are not an optional interpretive add-on but a structural feature of typical macroscopic unitary evolution, and that the absence of a definition is a genuine gap in quantum theory. Neither current proposal closes the gap: Taylor & McCulloch's criterion—that branches are components which are easy to distinguish but hard to interfere, quantified by $C_I - C_D$—fails to pick out a unique decomposition; Weingarten's unique minimization of $Q = \sum_i |\psi_i|^2[C(\psi_i,\Omega)^2 - b\ln |\psi_i|^2]$ is exact but may force a sharp, scale-dependent threshold inconsistent with smoothly decaying coherences. The paper therefore leaves the question open and identifies testable subquestions: whether either decomposition can unbranch, whether they reproduce hydrodynamic decoherence, and whether the two definitions ever disagree dramatically.

Load-bearing premise

The load-bearing premise is that unitary state complexity is a well-defined physical quantity that generically grows almost linearly with time; if that fails, neither complexity-based proposal will produce branches that persist.

Editorial extensions

If this is right

  • A valid branch definition would let decoherence theory operate without a fixed system-environment split, recovering preferred variables and coarse-graining from the wavefunction itself.
  • Branch sampling would make correlated observables of closed many-body systems classically computable when branches have bounded entanglement, avoiding the exponential simulation cost.
  • The Taylor-McCulloch criteria imply a code-theoretic picture: branch bases protect classical information against unitary noise below complexity $C_I$ while destroying conjugate phase information; exploring this picture is a natural next step.
  • Weingarten's variational parameter $b$ behaves like a length scale, so his branches may enforce area-law entanglement at the price of tension with long-baseline interferometry.
  • Neither proposal yet provides a relativistic, continuum, unique, and physically motivated definition; those are the open criteria any successor must meet.

Reading between the lines

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

  • A testable extension the paper leaves implicit: on small spin lattices, one can numerically compute the branchiness gap for candidate decompositions and check whether multiple incompatible 'good' decompositions persist as system size grows.
  • If $C_I - C_D$ is UV-finite in the continuum limit, Taylor-McCulloch's lattice dependence might disappear without Weingarten's vacuum reference or scale parameter.
  • The shared reliance on complexity growth suggests that a low-complexity recurrence—a local Hamiltonian evolution that returns to low complexity without fine-tuning—would be a sharper falsifier than any dispute about branch definitions themselves.
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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

3 major / 5 minor

Summary. This paper argues that the problem of providing a first-principles definition of wavefunction branches in many-body quantum mechanics remains open. It reviews two recent complexity-based proposals: Weingarten's definition, which chooses the decomposition minimizing a weighted sum of expected squared state complexity and Shannon entropy (Eq. 2), and Taylor and McCulloch's definition, which characterizes branches by a large gap between the unitary complexity needed to interfere two components and that needed to distinguish them (Eqs. 3 and 4). The paper discusses strengths and weaknesses of each, identifies open questions, and concludes that both proposals require further development before a fundamental definition can be claimed.

Significance. If the conclusions are accepted, the paper would refocus research on an important foundational problem and could stimulate improved branch definitions with implications for decoherence theory, classical simulation of quantum systems, and the measurement problem. The paper provides a careful and largely accurate exposition of the two proposals and makes explicit several useful open questions. However, the central negative claims—that Weingarten's minimization yields an implausibly sharp threshold and that Taylor-McCulloch non-uniqueness is a genuine defect—rest on heuristic arguments rather than demonstrated counterexamples, which limits the current significance.

major comments (3)
  1. [III, Eq. (2)] The objection to Weingarten's definition is explicitly speculative: 'I worry that minimization is a way to force a precise decomposition, and that a sharp threshold may be incongruous with most models of decoherence' (Section III). Because the conclusion that branches still demand a definition depends on Weingarten's proposal being unsatisfactory, this worry needs to be substantiated with a concrete demonstration. I suggest computing the Q-minimizing decomposition in a standard decoherence model (e.g., a central spin coupled to a bath with exponential decay of off-diagonals) for a range of b, and showing that the minimizer has a sharp threshold that does not track the smooth branch structure. Without such an example, the claim that Weingarten's definition is incorrect is not established.
  2. [III, Eqs. (3)-(4)] The non-uniqueness of Taylor-McCulloch good decompositions is presented as a defect, but the paper does not sufficiently engage with the consistent-histories precedent it cites, in which multiple decoherent realms are acceptable. To make the objection load-bearing, the author should argue why a fundamental branch definition must be unique, and why the existence of multiple incompatible good decompositions cannot be understood as a plurality of valid codes or coarse-grainings. The appeal to 'objective' macroscopic facts in Section I is a useful starting point but does not directly connect to the tree-structure and effective-collapse requirements; this gap should be addressed.
  3. [III and IV] The paper's title and conclusion state that wavefunction branches 'demand a definition,' implying that no satisfactory definition exists. Yet Weingarten's construction is an exact, unique definition up to the free parameter b. The paper does not demonstrate that this definition fails in the relevant regime; it only raises a worry. The author should either present a concrete failure of Weingarten's definition or explicitly frame the paper as a discussion of open issues rather than an assertion of the non-existence of a first-principles definition.
minor comments (5)
  1. [Throughout] There is inconsistent hyphenation of 'Taylor-McCulloch' vs 'Taylor–McCulloch'; please use one style throughout.
  2. [Abstract] The citation appears as '[ Quantum 9, 1670 (2025)]' with an extra space after the bracket; fix formatting.
  3. [Fig. 1(b)] The caption does not explain the meaning of the green and yellow trajectories; add a sentence to the caption.
  4. [Eq. (2)] Equation (2) uses Ω for the vacuum, but the notation is not defined until a sentence later; define it at first use.
  5. [Reference [36]] Reference [36] is cited as a PhD thesis 'to appear 2025'; update the reference if it has been published.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: this is a review/position piece whose verdicts are qualitative comparisons of two external proposals, not reductions to the paper's own inputs.

full rationale

The paper makes no fitted-parameter predictions and does not derive branch structure from its own definitions. Its central claim is normative: neither Taylor-McCulloch nor Weingarten yet supplies a satisfactory first-principles branch definition, supported by comparing the proposals' explicit criteria (Eqs. (2)-(4)) and the properties reported by those authors. The only self-citations, e.g. Ref. [35] for a uniqueness result about objective observables and Refs. [10,11] for decoherence bounds, are background motivation or stated complements; the comparison of the two complexity proposals does not presuppose those results. The objection that Weingarten's minimization may impose a sharp threshold is explicitly flagged as a worry ('I worry...') in Section III rather than derived, and the Taylor-McCulloch non-uniqueness critique cites their published demonstration; neither step is circular. A weak objection can be a legitimate correctness concern, but it is not a self-referential reduction. The paper is self-contained against external benchmarks, so the circularity score is 0.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new free parameters or invented entities; the parameters listed belong to the proposals under review and are essential to their definitions. The axioms capture the background physics and the unproven complexity assumptions on which the discussion depends.

free parameters (2)
  • Weingarten's branch scale b = not fitted here; free parameter with units of volume
    Appears in Eq. (2) as the coefficient of the entropy term in Q({ψ_i}). It controls the trade-off between branch number and mean complexity and is central to Weingarten's proposal under review.
  • Taylor-McCulloch error parameter epsilon = small error threshold, not fixed
    Defines 'good' branches through Eqs. (3) and (4). The paper notes that little is known about how branch structure varies with epsilon, and the error choice is a free input of the proposal under review.
assumptions (5)
  • domain assumption Quantum unitary complexity C(U) is a well-defined, physically meaningful measure, with state complexity C(ψ, φ) as a distance on Hilbert space.
    Both proposals and the branching-persistence arguments rest on this measure. Invoked in Section III: 'Both proposals are fundamentally based on quantum unitary complexity'.
  • domain assumption Second law of quantum complexity: state complexity grows nearly linearly and maximally under generic local Hamiltonian evolution.
    Invoked in Section III to infer that branches persist once created. This is an unproven generic behavior, cited to Refs. [42-45], not established by the present paper.
  • domain assumption Macroscopic facts should be objective: many independent local observers can deduce them through local measurements, making spatial correlations a valid foundation for branch structure.
    Section I argues that objectivity can be formalized via correlations across disjoint spatial regions, citing Ref. [35]. This motivates the entire branch-definition project but involves a length-scale choice that the paper acknowledges is unresolved.
  • standard math Standard quantum mechanics with unitary evolution and the Born rule for branch weights.
    Background throughout, for example Eq. (1) which decomposes ψ(t) into orthogonal components, and the claim that expectation values are the Born-weighted mean of branch expectation values.
  • domain assumption Branches, if defined, have bounded entanglement and can be identified numerically, enabling efficient classical simulation by sampling.
    Section II item 2 promises efficient classical simulation 'when such branches have bounded entanglement and can be effectively identified numerically'. The paper itself notes that complexity is generally infeasible to compute, so this remains an assumption rather than a demonstrated capability.

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Cite this review

Pith. "Pith review of Wavefunction branches demand a definition!." pith.science (2026). https://pith.science/paper/I5NQEBBC

@misc{pith2026250615663,
  author       = {Pith},
  title        = {Pith review of: Wavefunction branches demand a definition!},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/I5NQEBBC}},
  note         = {Machine review of arXiv:2506.15663}
}
read the original abstract

Under unitary evolution, a typical macroscopic quantum system is thought to develop wavefunction branches: a time-dependent decomposition into orthogonal components that (1) form a tree structure forward in time, (2) are approximate eigenstates of quasiclassical macroscopic observables, and (3) exhibit effective collapse of feasibly measurable observables. If they could be defined precisely, wavefunction branches would extend the theory of decoherence beyond the system-environment paradigm and could supplant anthropocentric measurement in the quantum axioms. Furthermore, when such branches have bounded entanglement and can be effectively identified numerically, sampling them would allow asymptotically efficient classical simulation of quantum systems. I consider a promising recent approach to formalizing branches on the lattice by Taylor & McCulloch [Quantum 9, 1670 (2025), arXiv:2308.04494], and compare it to prior work from Weingarten [Found. Phys. 52, 45 (2022), arXiv:2105.04545]. Both proposals are based on quantum complexity and argue that, once created, branches persist for long times due to the generic linear growth of state complexity. Taylor & McCulloch characterize branches by a large difference in the unitary complexity necessary to interfere vs. distinguish them. Weingarten takes branches as the components of the decomposition that minimizes a weighted sum of expected squared complexity and the Shannon entropy of squared norms. I discuss strengths and weaknesses of these approaches, and identify tractable open questions.

Figures

Figures reproduced from arXiv: 2506.15663 by the authors.

Figure 1
Figure 1. FIG. 1. (a) A schematic Wigner function of diverging chaotic [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) The Bloch sphere for the span of [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

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Works this paper leans on

57 extracted references · 42 canonical work pages

  1. [1]

    Decoherence theory has proven insightful and prac- tically useful; it’s worth generalizing to cases where the preferred variables vary or are unknown

    work page

  2. [2]

    This would natu- rally extend the efficient classical simulability of de- cohering variables [10, 38] beyond the open-system paradigm

    Bounded-order correlation functions could be clas- sically computed by sampling branches [35, 36], potentially reducing or even (if they have area- law entanglement [37]) eliminating the exponential growth rate of simulation cost. This would natu- rally extend the efficient classical simulability of de- cohering variables [10, 38] beyond the open-system paradigm

    work page

  3. [3]

    xtPa5Ia2mLM5M3qE2LQAZMl0p5s=

    The branches ψi and probabilities |ψi|2 would give a unified description of what happens in closed sys- tems like the universe, recovering the traditional collapse postulate in the special case of lab mea- surements. Think of the stakes! A principle that picks out a wavefunction’s distinct outcomes – of cosmic inflation, of last week’s storm, and of the p...

    work page

  4. [4]

    Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics,

    John von Neumann, “Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics,” The European Physical Journal H 35, 201–237 (2010), arXiv:1003.2133

    arXiv 2010

  5. [5]

    Long-Time Behavior of Macroscopic Quantum Systems: Commentary Accompanying the En- glish Translation of John von Neumann’s 1929 Article on the Quantum Ergodic Theorem,

    Sheldon Goldstein, Joel L. Lebowitz, Roderich Tumulka, and Nino Zanghi, “Long-Time Behavior of Macroscopic Quantum Systems: Commentary Accompanying the En- glish Translation of John von Neumann’s 1929 Article on the Quantum Ergodic Theorem,” The European Physical Journal H 35, 173–200 (2010), arXiv:1003.2129

    arXiv 2010

  6. [6]

    Macroscopic Superposition States in Isolated Quantum Systems

    Roman V. Buniy and Stephen D. H. Hsu, “Macroscopic Superposition States in Isolated Quantum Systems,” Foundations of Physics 51, 85 (2021), arXiv:2011.11661

    work page Pith review arXiv 2021

  7. [7]

    Quantum chaos: Localization vs. ergodicity,

    B.V. Chirikov, F.M. Izrailev, and D.L. Shepelyansky, “Quantum chaos: Localization vs. ergodicity,” Physica D: Nonlinear Phenomena 33, 77–88 (1988)

    work page 1988

  8. [8]

    Decoherence, chaos, quantum- classical correspondence, and the algorithmic arrow of time,

    Wojciech H. Zurek, “Decoherence, chaos, quantum- classical correspondence, and the algorithmic arrow of time,” Physica Scripta T76, 186 (1998), arXiv:quant- ph/9802054

    work page arXiv 1998

Show all 57 references
  1. [9]

    Decoherence, einselection, and the quantum origins of the classical,

    Wojciech H. Zurek, “Decoherence, einselection, and the quantum origins of the classical,” Reviews of Modern Physics 75, 715–775 (2003), arXiv:quant-ph/0105127

    2003 arXiv

  2. [10]

    E. Joos, H. D. Zeh, C. Kiefer, D. Giulini, J. Kupsch, and I.-O. Stamatescu, Decoherence and the Appearance of a Classical World in Quantum Theory, 2nd ed. (Springer- Verlag, Berlin, 2003)

    2003

  3. [11]

    Schlosshauer, Decoherence and the Quantum-to- Classical Transition(Springer-Verlag, Berlin, 2008)

    M. Schlosshauer, Decoherence and the Quantum-to- Classical Transition(Springer-Verlag, Berlin, 2008)

    2008

  4. [12]

    Zurek, Decoherence and Quantum Darwin- ism (Cambridge University Press, New York, 2025)

    Wojciech H. Zurek, Decoherence and Quantum Darwin- ism (Cambridge University Press, New York, 2025)

    2025

  5. [13]

    Ehrenfest’s theorem beyond the Ehrenfest time,

    Felipe Hern´ andez, Daniel Ranard, and C. Jess Riedel, “Ehrenfest’s theorem beyond the Ehrenfest time,” (2023), arXiv:2306.13717

    2023 arXiv

  6. [14]

    Classical correspondence beyond the Ehrenfest time for open quantum systems with general Lindbladians,

    Felipe Hern´ andez, Daniel Ranard, and C. Jess Riedel, “Classical correspondence beyond the Ehrenfest time for open quantum systems with general Lindbladians,” Communications in Mathematical Physics 406, 4 (2024), arXiv:2307.05326

    2024 arXiv

  7. [15]

    continuous branches, different fla- vors of consistent histories, rare re-interference, small non-orthogonalities, and the grounding or modification of the Born rule

    For brevity I will elide many important details through- out, like discrete vs. continuous branches, different fla- vors of consistent histories, rare re-interference, small non-orthogonalities, and the grounding or modification of the Born rule

  8. [16]

    Quasiclassical coarse graining and thermodynamic entropy,

    Murray Gell-Mann and James B. Hartle, “Quasiclassical coarse graining and thermodynamic entropy,” Physical Review A 76, 022104 (2007), arXiv:quant-ph/0609190

    2007 arXiv

  9. [17]

    Slowest local operators in quantum spin chains,

    Hyungwon Kim, Mari Carmen Ba˜ nuls, J. Ignacio Cirac, Matthew B. Hastings, and David A. Huse, “Slowest local operators in quantum spin chains,” Physical Review E 92, 012128 (2015), arXiv:1410.4186

    2015 arXiv

  10. [18]

    Decoherence of histories and hydrody- namic equations for a linear oscillator chain,

    J. J. Halliwell, “Decoherence of histories and hydrody- namic equations for a linear oscillator chain,” Physical Review D 68, 025018 (2003), arXiv:quant-ph/0305084

    2003 arXiv

  11. [19]

    Classical equa- tions for quantum systems,

    Murray Gell-Mann and James B. Hartle, “Classical equa- tions for quantum systems,” Physical Review D 47, 3345– 3382 (1993), arXiv:gr-qc/9210010

    1993 arXiv

  12. [20]

    Quantum me- chanics in the light of quantum cosmology,

    Murray Gell-Mann and James B. Hartle, “Quantum me- chanics in the light of quantum cosmology,” in Com- plexity, Entropy, and the Physics of Information, Vol. VIII, edited by Wojciech Zurek (Addison Wesley, Read- ing, MA, 1990) pp. 425–458

    1990

  13. [21]

    Adaptive coarse graining, environment, strong decoherence, and quasiclassical realms,

    Murray Gell-Mann and James B. Hartle, “Adaptive coarse graining, environment, strong decoherence, and quasiclassical realms,” Physical Review A 89, 052125 (2014), arXiv:1312.7454

    2014 arXiv

  14. [22]

    More Is Different,

    P.W. Anderson, “More Is Different,” Science 177, 393 (1972)

    1972

  15. [23]

    The Theory of Every- thing,

    R. B. Laughlin and David Pines, “The Theory of Every- thing,” Proceedings of the National Academy of Sciences 97, 28–31 (2000)

    2000

  16. [24]

    The New Quantum Logic,

    Robert B. Griffiths, “The New Quantum Logic,” Foun- dations of Physics 44, 610–640 (2014), arXiv:1311.2619

    2014 arXiv

  17. [25]

    Everett and structure,

    David Wallace, “Everett and structure,” Studies In His- tory and Philosophy of Science Part B: Studies In History and Philosophy of Modern Physics 34, 87–105 (2003)

    2003

  18. [26]

    On the consistent histo- ries approach to quantum mechanics,

    Fay Dowker and Adrian Kent, “On the consistent histo- ries approach to quantum mechanics,” Journal of Statis- tical Physics 82, 1575–1646 (1996), arXiv:gr-qc/9412067

    1996 arXiv

  19. [27]

    Measurements accord- ing to Consistent Histories,

    Elias Okon and Daniel Sudarsky, “Measurements accord- ing to Consistent Histories,” Studies in History and Phi- losophy of Science Part B: Studies in History and Phi- losophy of Modern Physics 48, Part A, 7–12 (2014), arXiv:1309.0792

    2014 arXiv

  20. [28]

    Solution to the Lorentzian quantum re- ality problem,

    Adrian Kent, “Solution to the Lorentzian quantum re- ality problem,” Physical Review A 90, 012107 (2014), arXiv:1311.0249. 6

    2014 arXiv

  21. [29]

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

    C. Jess Riedel, Wojciech H. Zurek, and Michael Zwolak, “Objective past of a quantum universe: Redundant records of consistent histories,” Physical Review A 93, 032126 (2016), arXiv:1312.0331

    2016 arXiv

  22. [30]

    Quantum Mere- ology: Factorizing Hilbert Space into Subsystems with Quasi-Classical Dynamics,

    Sean M. Carroll and Ashmeet Singh, “Quantum Mere- ology: Factorizing Hilbert Space into Subsystems with Quasi-Classical Dynamics,” Physical Review A 103, 022213 (2020), arXiv:2005.12938

    2020 arXiv

  23. [31]

    Macroscopic Reality from Quantum Complexity,

    Don Weingarten, “Macroscopic Reality from Quantum Complexity,” Foundations of Physics 52, 45 (2022), arXiv:2105.04545

    2022 arXiv

  24. [32]

    Contrary Inferences for Classical Histories within the Consistent Histories Formulation of Quantum Theory,

    Adamantia Zampeli, Georgios E. Pavlou, and Pet- ros Wallden, “Contrary Inferences for Classical Histories within the Consistent Histories Formulation of Quantum Theory,” (2022), arXiv:2205.15893

    2022

  25. [33]

    Emergence of Objectivity for Quan- tum Many-Body Systems,

    Harold Ollivier, “Emergence of Objectivity for Quan- tum Many-Body Systems,” Entropy 24, 277 (2022), arXiv:2202.06832

    2022 arXiv

  26. [34]

    First Principles Numerical Demonstration of Emergent Decoherent Histories,

    Philipp Strasberg, Teresa E. Reinhard, and Joseph Schindler, “First Principles Numerical Demonstration of Emergent Decoherent Histories,” Physical Review X 14, 041027 (2024), arXiv:2304.10258

    2024 arXiv

  27. [35]

    Alternative Decohering Histories in Quantum Mechanics,

    M. Gell-Mann and J. B. Hartle, “Alternative Decohering Histories in Quantum Mechanics,” in Proceedings of the 25th International Conference on High Energy Physics, edited by K. K. Phua and Y. Yamaguchi (World Scien- tific, Singapore, 1990)

    1990

  28. [36]

    Equivalent sets of histories and multiple quasiclassical realms,

    Murray Gell-Mann and James B. Hartle, “Equivalent sets of histories and multiple quasiclassical realms,” (1994), arXiv:gr-qc/9404013

    1994 arXiv

  29. [37]

    Quantum Darwinism,

    Wojciech H. Zurek, “Quantum Darwinism,” Nature Physics 5, 181–188 (2009), arXiv:0903.5082

    2009 arXiv

  30. [38]

    Classical Branch Structure from Spatial Redundancy in a Many-Body Wave Function,

    C. Jess Riedel, “Classical Branch Structure from Spatial Redundancy in a Many-Body Wave Function,” Physical Review Letters 118, 120402 (2017), arXiv:1608.05377

    2017 arXiv

  31. [39]

    thesis, University of Queensland, Queens- land, Australia (to appear 2025)

    Jordan Taylor, Non-Interfering Structures in Wavefunc- tions, Ph.D. thesis, University of Queensland, Queens- land, Australia (to appear 2025)

    2025

  32. [40]

    In higher dimensions, the boundary is less understood [53]

    Strictly speaking, it’s only in one dimension that area-law entanglement characterizes states that are efficiently clas- sically representable. In higher dimensions, the boundary is less understood [53]

  33. [41]

    Wiseman and Gerard J

    Howard M. Wiseman and Gerard J. Milburn, Quantum Measurement and Control, 1st ed. (Cambridge University Press, 2014)

    2014

  34. [42]

    Wavefunction branching: When you can’t tell pure states from mixed states,

    Jordan K. Taylor and Ian P. McCulloch, “Wavefunction branching: When you can’t tell pure states from mixed states,” Quantum 9, 1670 (2025), arXiv:2308.04494

    2025 arXiv

  35. [43]

    Quantum circuit complexity,

    A. Chi-Chih Yao, “Quantum circuit complexity,” in Pro- ceedings of the 34th Annual Symposium on Foundations of Computer Science, 1993(1993) pp. 352–361

    1993

  36. [44]

    Quantum Computation as Geometry,

    Michael A. Nielsen, Mark R. Dowling, Mile Gu, and An- drew C. Doherty, “Quantum Computation as Geometry,” Science 311, 1133–1135 (2006), arXiv:quant-ph/0603161

    2006 arXiv

  37. [45]

    Quantum complex- ity in gravity, quantum field theory, and quantum infor- mation science,

    Stefano Baiguera, Vijay Balasubramanian, Pawel Ca- puta, Shira Chapman, Jonas Haferkamp, Michal P. Heller, and Nicole Yunger Halpern, “Quantum complex- ity in gravity, quantum field theory, and quantum infor- mation science,” (2025), arXiv:2503.10753

    2025

  38. [46]

    The typical-state paradox: Diagnos- ing horizons with complexity,

    Leonard Susskind, “The typical-state paradox: Diagnos- ing horizons with complexity,” Fortschritte der Physik 64, 84–91 (2016), arXiv:1507.02287

    2016 arXiv

  39. [47]

    Quantum complexity and negative curvature,

    Adam R. Brown, Leonard Susskind, and Ying Zhao, “Quantum complexity and negative curvature,” Physical Review D 95, 045010 (2017), arXiv:1608.02612

    2017 arXiv

  40. [48]

    Second law of quantum complexity,

    Adam R. Brown and Leonard Susskind, “Second law of quantum complexity,” Physical Review D 97, 086015 (2018), arXiv:1701.01107

    2018 arXiv

  41. [49]

    Path integral optimization as circuit complexity,

    Hugo A. Camargo, Michal P. Heller, Ro Jefferson, and Johannes Knaute, “Path integral optimization as circuit complexity,” Physical Review Letters 123, 011601 (2019), arXiv:1904.02713

    2019 arXiv

  42. [50]

    Universality in long-distance ge- ometry and quantum complexity,

    Adam R. Brown, Michael H. Freedman, Henry W. Lin, and Leonard Susskind, “Universality in long-distance ge- ometry and quantum complexity,” Nature 622, 58–62 (2023), arXiv:2111.12700

    2023 arXiv

  43. [51]

    Polynomial Equivalence of Complexity Geometries,

    Adam R. Brown, “Polynomial Equivalence of Complexity Geometries,” Quantum 8, 1391 (2024), arXiv:2205.04485

    2024 arXiv

  44. [52]

    Weingarten has even recently proposed that these branches could explain the appearance of dark matter and dark energy [54], albeit by relying on philosophical assumptions about observers that are hard to assess

  45. [53]

    On the hardness of detecting macroscopic superpositions,

    Scott Aaronson, Yosi Atia, and Leonard Susskind, “On the hardness of detecting macroscopic superpositions,” (2020), arXiv:2009.07450

    2020 arXiv

  46. [54]

    Theory of Quantum Error Correction for General Noise,

    Emanuel Knill, Raymond Laflamme, and Lorenza Vi- ola, “Theory of Quantum Error Correction for General Noise,” Physical Review Letters 84, 2525–2528 (2000), arXiv:quant-ph/9908066

    2000 arXiv

  47. [55]

    Complexity and order in approximate quan- tum error-correcting codes,

    Jinmin Yi, Weicheng Ye, Daniel Gottesman, and Zi- Wen Liu, “Complexity and order in approximate quan- tum error-correcting codes,” Nature Physics 20, 1798– 1803 (2024), arXiv:2310.04710

    2024 arXiv

  48. [56]

    Area laws and efficient de- scriptions of quantum many-body states,

    Yimin Ge and Jens Eisert, “Area laws and efficient de- scriptions of quantum many-body states,” New Journal of Physics 18, 083026 (2016), arXiv:1411.2995

    2016 arXiv

  49. [57]

    Vacuum Branching, Dark Energy, Dark Matter,

    Don Weingarten, “Vacuum Branching, Dark Energy, Dark Matter,” (2023), arXiv:2308.05569

    2023 arXiv

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.