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Wavefunction branching: when you can't tell pure states from mixed states

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Taylor, Jordan K., McCulloch, Ian P.·2025·Quantum
DOI 10.22331/q-2025-03-25-1670
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Abstract

We propose a definition of wavefunction "branchings": quantum superpositions which can't be feasibly distinguished from the corresponding mixed state, even under time evolution. Our definition is largely independent of interpretations, requiring only that it takes many more local gates to swap branches than to distinguish them. We give several examples of states admitting such branch decompositions. Under our definition, we argue that attempts to get relative-phase information between branches will fail without frequent active error correction, that branches are effectively the opposite of good error-correcting codes, that branches effectively only grow further apart in time under natural evolution, that branches tend to absorb spatial entanglement, that branching is stronger in the presence of conserved quantities, and that branching implies effective irreversibility. Identifying these branch decompositions in many-body quantum states could shed light on the emergence of classicality, provide a metric for experimental tests at the quantum/ classical boundary, and allow for longer numerical time evolution simulations. We see this work as a generalization of the basic ideas of environmentally-induced decoherence to situations with no clear system/ environment split.

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  • For GHZ states, the interference proxy is n, the distinguishability proxy is 1, and the branch factor is n-1.

    “So C I = n, C D = 1, and B = n -1.”

    From Towards violations of Local Friendliness with quantum computers (2025) · cites this paper as [48]

    Section 3.1 (p. 5) says the GHZ interference complexity grows with the number of qubits, while distinguishing its two components requires one operation on one qubit. The equations that would give the exact proxy values and branch factor are not decoded in our copy, so it does not verify B = n − 1. (LLM, conf=0.83)

    Experimental — accuracy not yet measured

  • For two random n-qubit states produced by circuits with depth D0 and D1, C_I = O((D0 + D1)n) and C_D = O(min(D0, D1)n).

    “It can be shown [48] that C I = O((D 0 + D 1 )n) and C D = O(min(D 0 , D 1 )n)(11)”

    From Towards violations of Local Friendliness with quantum computers (2025) · cites this paper as [48]

  • Error-correcting codes have bad branch factors.

    “As considered in [48], error-correcting codes have bad branch factors.”

    From Towards violations of Local Friendliness with quantum computers (2025) · cites this paper as [48]

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Cited by

Sorted by citations

Authors
Taylor, J. K., & McCulloch, I. P.
Affiliations
The University of Queensland (AU)
ORCID
Venue
Quantum
Publisher
Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
Published
2025-03-25
Volume
9
Pages
1670
ISSN
2521-327X (ISSN-L)
DOI
10.22331/q-2025-03-25-1670
OpenAlex
W4408830641
Cited by
6
References
2
Citations by year
2026: 2 · 2025: 4
FWCI
2.19
Type
journal article
Language
en
Open access
Licence
Locations
  • Quantum (publishedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion, cc-by)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • arXiv (Cornell University) (cc-by)
Funders
  • National Science and Technology Council (112-2811-M-007-044, 113-2112-M-007-MY2)
  • Australian Research Council (ARC) Discovery Project (DP190101515, DP200103760)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
Keywords
branch decomposition, quantum superposition, mixed states, quantum-to-classical transition, emergence of classicality, environmental decoherence, error correction, irreversibility, spatial entanglement, relative phase, quantum many-body states

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