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Unspeakable coherence concentration

Benjamin Stratton1,2,*, Chung-Yun Hsieh2, and Paul Skrzypczyk2

  • 1Quantum Engineering Centre for Doctoral Training, H. H. Wills Physics Laboratory and Department of Electrical & Electronic Engineering, University of Bristol, Bristol BS8 1FD, United Kingdom
  • 2H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom

  • *Contact author: ben.stratton@bristol.ac.uk
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Phys. Rev. A 113, 062429 – Published 11 June, 2026

DOI: https://doi.org/10.1103/fj8w-v1bb

Abstract

Unspeakable coherence is a key feature separating quantum and classical physics. Modeled as asymmetry with respect to a continuous transformation generated by a physically relevant observable, such as the Hamiltonian or angular moment, unspeakable coherence has been shown to be the relevant notion of coherence for achieving quantum advantage in the tasks of metrology, reference frame alignment, and work extraction, among others. A question of both practical and foundational value is: Given some copies of a state with low coherence, can we prepare a more coherent state via coherence nonincreasing operations? Here, we study this question in the minimal limiting case: Given two uncorrelated copies of a coherent state, can one, via globally coherence nonincreasing unitaries, increase the coherence in a subsystem? We fully solve this problem for qubits, identifying the optimal unitaries and revealing the existence of bound coherence. This is then used to create a completely constructive multiqubit coherence enhancement protocol, where only effective-qubit unitaries are used. Unexpectedly, in this protocol, we show that there exist states for which the ratio of the input-output coherence can be amplified unboundedly. Extending beyond qubits, we derive two fundamental upper bounds on the amount of local coherence that can be increased and prove a no-go theorem showing that certain global correlations cannot be converted to local coherence.

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References (28)

  1. V. Giovannetti, S. Lloyd, and L. Maccone, Quantum metrology, Phys. Rev. Lett. 96, 010401 (2006).
  2. J. Chen, Review on quantum communication and quantum computation, J. Phys.: Conf. Ser. 1865, 022008 (2021).
  3. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition (Cambridge University, Cambridge, 2010).
  4. E. Chitambar and G. Gour, Quantum resource theories, Rev. Mod. Phys. 91, 025001 (2019).
  5. I. Marvian and R. W. Spekkens, How to quantify coherence: Distinguishing speakable and unspeakable notions, Phys. Rev. A 94, 052324 (2016).
  6. T. Baumgratz, M. Cramer, and M. B. Plenio, Quantifying coherence, Phys. Rev. Lett. 113, 140401 (2014).
  7. M. Lostaglio, D. Jennings, and T. Rudolph, Description of quantum coherence in thermodynamic processes requires constraints beyond free energy, Nat. Commun. 6, 6383 (2015).
  8. T. V. Kondra, R. Ganardi, and A. Streltsov, Coherence manipulation in asymmetry and thermodynamics, Phys. Rev. Lett. 132, 200201 (2024).
  9. M. Lostaglio, K. Korzekwa, D. Jennings, and T. Rudolph, Quantum coherence, time-translation symmetry, and thermodynamics, Phys. Rev. X 5, 021001 (2015).
  10. N. Shiraishi and R. Takagi, Arbitrary amplification of quantum coherence in asymptotic and catalytic transformation, Phys. Rev. Lett. 132, 180202 (2024).
  11. I. Marvian, Coherence distillation machines are impossible in quantum thermodynamics, Nat. Commun. 11, 25 (2020).
  12. M. Lostaglio and M. P. Müller, Coherence and asymmetry cannot be broadcast, Phys. Rev. Lett. 123, 020403 (2019).
  13. I. Marvian and R. W. Spekkens, No-broadcasting theorem for quantum asymmetry and coherence and a trade-off relation for approximate broadcasting, Phys. Rev. Lett. 123, 020404 (2019).
  14. J. Åberg, Catalytic coherence, Phys. Rev. Lett. 113, 150402 (2014).
  15. F. Ding, X. Hu, and H. Fan, Amplifying asymmetry with correlating catalysts, Phys. Rev. A 103, 022403 (2021).
  16. R. Takagi and N. Shiraishi, Correlation in catalysts enables arbitrary manipulation of quantum coherence, Phys. Rev. Lett. 128, 240501 (2022).
  17. S. D. Bartlett, T. Rudolph, and R. W. Spekkens, Reference frames, superselection rules, and quantum information, Rev. Mod. Phys. 79, 555 (2007).
  18. I. Marvian, R. W. Spekkens, and P. Zanardi, Quantum speed limits, coherence, and asymmetry, Phys. Rev. A 93, 052331 (2016).
  19. A. Winter and D. Yang, Operational resource theory of coherence, Phys. Rev. Lett. 116, 120404 (2016).
  20. G. Gour and R. W. Spekkens, The resource theory of quantum reference frames: manipulations and monotones, New J. Phys. 10, 033023 (2008).
  21. C.-Y. Hsieh, B. Stratton, H.-C. Weng, and V. Scarani, Informational nonequilibrium concentration, Phys. Rev. A 111, 052423 (2025).
  22. I. Marvian and R. W. Spekkens, Modes of asymmetry: The application of harmonic analysis to symmetric quantum dynamics and quantum reference frames, Phys. Rev. A 90, 062110 (2014).
  23. N. Brunner, N. Linden, S. Popescu, and P. Skrzypczyk, Virtual qubits, virtual temperatures, and the foundations of thermodynamics, Phys. Rev. E 85, 051117 (2012).
  24. K. Fan, Maximum properties and inequalities for the eigenvalues of completely continuous operators, Proc. Natl. Acad. Sci. USA 37, 760 (1951).
  25. B. Stratton, https://github.com/benstratton6/Unspeakable CoherenceConcentration (2025).
  26. T. Apostol, Mathematical Analysis: A Modern Approach to Advanced Calculus (Pearson, Hoboken, 1974).
  27. R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge University, Cambridge, 1985).
  28. J. von Neumann, Some Matrix-Inequalities and Metrization of Matric Space (Tomsk University Review, Tomsk, 1937).

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Phys. Rev. A 113, 062429– Published 11 June, 2026
  • Received 19 December 2025
  • Accepted 28 April 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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