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Random exclusion codes: Quantum advantages of single-shot communication

Joonwoo Bae1,*, Kieran Flatt1,†, Teiko Heinosaari2,‡, Oskari Kerppo3,§, Karthik Mohan1,∥, Andrés Muñoz-Moller2,¶, and Ashutosh Rai1,#

  • *Contact author: joonwoo.bae@kaist.ac.kr
  • †Contact author: kflatt@kaist.ac.kr
  • ‡Contact author: teiko.heinosaari@jyu.fi
  • §Contact author: oskari.kerppo@quanscient.com
  • ∥Contact author: karthikmohan@kaist.ac.kr
  • Contact author: andres.d.munozmoller@jyu.fi
  • #Contact author: ashutosh.rai@kaist.ac.kr
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Phys. Rev. Research 8, 013171 – Published 17 February, 2026

DOI: https://doi.org/10.1103/196j-lmzl

Abstract

Useful applications of quantum information technologies can be found by identifying tasks in which quantum resources outperform their classical counterparts. In this work, we introduce a two-party communication primitive, random exclusion code (REC), which is a single-shot prepare-and-measure protocol where a sender encodes a random message into a shorter sequence and a receiver attempts to exclude a randomly chosen letter in the original message. We present quantum advantages in RECs in two ways: probability and dimension. We show that RECs with quantum resources achieve higher success probabilities than classical strategies. We verify that, with the additional constraint that successful outcomes occur uniformly and without error, the quantum resources required to describe detection events of RECs have a smaller dimension than classical ones. We also show that a guessing counterpart, random access codes, may not have a dimension advantage over classical resources. Our results elucidate various possibilities of achieving quantum advantages in two-party communication.

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References (46)

  1. A. Winter, Winter's Principle, Quantum Information (Benasque, Spain, 2013).
  2. A. Holevo, Probabilistic and Statistical Aspects of Quantum Theory (Edizioni della Normale, 2011).
  3. A. Holevo, The capacity of the quantum channel with general signal states, IEEE Trans. Inf. Theory 44, 269 (1998).
  4. B. Schumacher and M. D. Westmoreland, Sending classical information via noisy quantum channels, Phys. Rev. A 56, 131 (1997).
  5. A. Ambainis, D. Leung, L. Mancinska, and M. Ozols, Quantum random access codes with shared randomness, arXiv:0810.2937.
  6. A. Ambainis, D. Kravchenko, S. Sazim, J. Bae, and A. Rai, Quantum advantages in (n,d)↦1 random access codes, New J. Phys. 26, 123023 (2024).
  7. A. Tavakoli, A. Hameedi, B. Marques, and M. Bourennane, Quantum random access codes using single d-level systems, Phys. Rev. Lett. 114, 170502 (2015).
  8. C. Carmeli, T. Heinosaari, and A. Toigo, Quantum random access codes and incompatibility of measurements, Europhys. Lett. 130, 50001 (2020).
  9. C. W. Helstrom, Quantum detection and estimation theory, J. Stat. Phys. 1, 231 (1969).
  10. J. Bae and L.-C. Kwek, Quantum state discrimination and its applications, J. Phys. A: Math. Theor. 48, 083001 (2015).
  11. S. M. Barnett and S. Croke, Quantum state discrimination, Adv. Opt. Photonics 1, 238 (2009).
  12. J. A. Bergou, Quantum state discrimination and selected applications, J. Phys.: Conf. Ser. 84, 012001 (2007).
  13. C. M. Caves, C. A. Fuchs, and R. Schack, Conditions for compatibility of quantum-state assignments, Phys. Rev. A 66, 062111 (2002).
  14. M. Pusey, J. Barrett, and T. Rudolph, On the reality of the quantum state, Nat. Phys. 8, 475 (2012).
  15. S. Bandyopadhyay, R. Jain, J. Oppenheim, and C. Perry, Conclusive exclusion of quantum states, Phys. Rev. A 89, 022336 (2014).
  16. T. Heinosaari and O. Kerppo, Antidistinguishability of pure quantum states, J. Phys. A: Math. Theor. 51, 365303 (2018).
  17. R. Uola, T. Bullock, T. Kraft, J.-P. Pellonpää, and N. Brunner, All quantum resources provide an advantage in exclusion tasks, Phys. Rev. Lett. 125, 110402 (2020).
  18. A. F. Ducuara, P. Lipka-Bartosik, and P. Skrzypczyk, Multiobject operational tasks for convex quantum resource theories of state-measurement pairs, Phys. Rev. Res. 2, 033374 (2020).
  19. N. Harrigan and R. W. Spekkens, Einstein, incompleteness, and the epistemic view of quantum states, Found. Phys. 40, 125 (2010).
  20. J. S. Bell, On the Einstein Podolsky Rosen paradox, Phys. Phys. Fiz. 1, 195 (1964).
  21. N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, Bell nonlocality, Rev. Mod. Phys. 86, 419 (2014).
  22. S. Pironio, A. Acín, S. Massar, A. B. de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, Random numbers certified by Bell's theorem, Nature (London) 464, 1021 (2010).
  23. A. Acín, N. Brunner, N. Gisin, S. Massar, S. Pironio, and V. Scarani, Device-independent security of quantum cryptography against collective attacks, Phys. Rev. Lett. 98, 230501 (2007).
  24. I. Šupić and J. Bowles, Self-testing of quantum systems: A review, Quantum 4, 337 (2020).
  25. I. Šupić, D. Cavalcanti, and J. Bowles, Device-independent certification of tensor products of quantum states using single-copy self-testing protocols, Quantum 5, 418 (2021).
  26. J. Crickmore, Ph.D. thesis, Quantum elimination measurements, Heriot-Watt University, 2020, http://hdl.handle.net/10399/4310.
  27. S. J. D. Phoenix, S. M. Barnett, and A. Chefles, Three-state quantum cryptography, J. Mod. Opt. 47, 507 (2000).
  28. T. Heinosaari, O. Kerppo, L. Leppäjärvi, and M. Plávala, Simple information-processing tasks with unbounded quantum advantage, Phys. Rev. A 109, 032627 (2024).
  29. N. Johnston, V. Russo, and J. Sikora, Tight bounds for antidistinguishability and circulant sets of pure quantum states, Quantum 9, 1622 (2025).
  30. V. Havlíček and J. Barrett, Simple communication complexity separation from quantum state antidistinguishability, Phys. Rev. Res. 2, 013326 (2020).
  31. M. Srikumar, S. D. Bartlett, and A. Karanjai, How contextuality and antidistinguishability are related, arXiv:2411.09919.
  32. B. Stratton, C.-Y. Hsieh, and P. Skrzypczyk, Operational interpretation of the Choi rank through exclusion tasks, Phys. Rev. A 110, L050601 (2024).
  33. R. Duan, S. Severini, and A. Winter, On zero-error communication via quantum channels in the presence of noiseless feedback, IEEE Trans. Inf. Theory 62, 5260 (2016).
  34. G. Chiribella, S. Roy, T. Guha, and S. Saha, Communication power of a noisy qubit, Phys. Rev. Lett. 134, 080803 (2025).
  35. M. Farkas, N. Miklin, and A. Tavakoli, Simple and general bounds on quantum random access codes, Quantum 9, 1643 (2025).
  36. D. Saha, D. Das, A. K. Das, B. Bhattacharya, and A. S. Majumdar, Measurement incompatibility and quantum advantage in communication, Phys. Rev. A 107, 062210 (2023).
  37. T. Heinosaari and O. Kerppo, Communication of partial ignorance with qubits, J. Phys. A: Math. Theor. 52, 395301 (2019).
  38. T. Heinosaari, O. Kerppo, and L. Leppäjärvi, Communication tasks in operational theories, J. Phys. A: Math. Theor. 53, 435302 (2020).
  39. O. Kerppo, Ph.D. Thesis, Quantum communication tasks, University of Turku, 2023, https://urn.fi/URN:ISBN:978-951-29-9127-3.
  40. T. Heinosaari and O. Kerppo, Maximal elements of quantum communication, Quantum 8, 1515 (2024).
  41. P. E. Frenkel and M. Weiner, Classical information storage in an n-level quantum system, Commun. Math. Phys. 340, 563 (2015).
  42. J. E. Cohen and U. G. Rothblum, Nonnegative ranks, decompositions, and factorizations of nonnegative matrices, Linear Algebra Appl. 190, 149 (1993).
  43. H. Fawzi, J. Gouveia, P. A. Parrilo, R. Z. Robinson, and R. R. Thomas, Positive semidefinite rank, Math. Program. 153, 133 (2015).
  44. T. Lee, Z. Wei, and R. de Wolf, Some upper and lower bounds on psd-rank, Math. Program. 162, 495 (2017).
  45. M. Dall'Arno, E. Passaro, R. Gallego, and A. Acín, Robustness of device-independent dimension witnesses, Phys. Rev. A 86, 042312 (2012).
  46. N. Brunner, M. Navascués, and T. Vértesi, Dimension witnesses and quantum state discrimination, Phys. Rev. Lett. 110, 150501 (2013).

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Phys. Rev. Research 8, 013171– Published 17 February, 2026
  • Received 18 June 2025
  • Accepted 12 January 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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