RSS feeds
РусскийEnglish
Issue 10, 2026
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

2026

 / 

October

←  →

Methodological notes


Relativistic quantum key distribution between stationary objects based on coherent states

†  a,  b, c
a Quantum Technology Center of Lomonosov Moscow State University, Leninskie Gory 1, build. 35, Moscow, 119991, Russian Federation
b Academy of Cryptography of the Russian Federation, PO Box 100, Moscow, 119331, Russian Federation
c Osipyan Institute of Solid State Physics, Russian Academy of Sciences, Akademika Osip'yana str. 2, Chernogolovka, Moscow Region, 142432, Russian Federation

The combined constraints of quantum mechanics and special relativity open new possibilities for quantum communications. This paper discusses a relativistic quantum key distribution (QKD) protocol over open space. The protocol does not require single-photon states, but rather attenuated coherent states of laser radiation. With a small average number of photons in coherent states, states with different relative phase values cannot be reliably distinguished. There is no need to use deceptive states, as in the decoy state method, which are mandatory for non-relativistic QKD protocols. This simplifies the optical design at the receiving end and eliminates the need for active elements — a phase modulator. An intensity modulator is not required at the transmitting end, which is necessary for implementing the decoy state method in non-relativistic systems. The protocol enables key distribution with high line losses of approximately ≈ 60 dB. The protocol uses only two information states, eliminating the need for base agreement. All registered packets are used in the key, increasing the speed of key distribution. The most suitable application for relativistic QKD systems is key distribution between stationary objects, such as cellular base stations or other objects between which laying fiber optic cables is expensive or practically impossible. Unlike the analysis of the cryptographic strength of non-relativistic QKD systems, which uses rather sophisticated mathematical apparatus, the analysis of the strength of relativistic QKD is presented at a level that is intuitively understandable for a physics audience. It does not require prior specialized knowledge and is accessible to graduate students and senior university undergraduates familiar with the fundamentals of quantum optics, quantum information science, and quantum cryptography, as taught in standard university courses.

Typically, an English full text is available in about 1 month from the date of publication of the original article.

Correspondence should be addressed to
Keywords: special relativity, quantum cryprography in free space, coherent states
PACS: 03.30.+p, 03.67.Dd, 89.70.−a (all)
DOI: 10.3367/UFNe.2026.08.040188
URL: https://ufn.ru/en/articles/2026/10/f/
Citation: Kulik S P, Molotkov S N "Relativistic quantum key distribution between stationary objects based on coherent states" Phys. Usp. 69 (10) (2026)

Received: 16th, October 2024, revised: 13th, April 2026, 31st, August 2026

Оригинал: Кулик С П, Молотков С Н «Релятивистское квантовое распределение ключей между стационарными объектами на когерентных состояниях» УФН 196 1086–1097 (2026); DOI: 10.3367/UFNr.2026.08.040188

Similar articles (20) ↓

  1. I.M. Arbekov, S.N. Molotkov “Extraction of quantum randomness” Phys. Usp. 64 617–634 (2021)
  2. Gaite José “The relativistic virial theorem and scale invariance” Phys. Usp. 56 919–931 (2013)
  3. A.S. Trushechkin, E.O. Kiktenko et al “Security of the decoy state method for quantum key distribution” Phys. Usp. 64 88–102 (2021)
  4. I.M. Arbekov, S.N. Molotkov “Quantum random number generators, extraction of provably random bit sequences from Markov chain trajectories” Phys. Usp. 67 919–937 (2024)
  5. M.I. Shirokov “Signal velocity in quantum electrodynamics” Sov. Phys. Usp. 21 345–358 (1978)
  6. V.P. Bykov, V.I. Tatarskii “Perturbation theory for resolvents as applied to problems in radiation theory” Sov. Phys. Usp. 34 (2) 167–184 (1991)
  7. E.D. Trifonov “On quantum statistics for ensembles with a finite number of particles” Phys. Usp. 54 723–727 (2011)
  8. V.L. Gorshenin, B.N. Nougmanov, F.Ya. Khalili “On 'Schrödinger's cat' fringes” Phys. Usp. 67 938–942 (2024)
  9. S.I. Syrovatskii “On the problem of the ’retardation’ of the relativistic contraction of moving bodies” Sov. Phys. Usp. 19 273–274 (1976)
  10. Ya.B. Zel’dovich, L.P. Grishchuk “Gravitation, the general theory of relativity, and alternative theories” Sov. Phys. Usp. 29 780–787 (1986)
  11. V.P. Bykov “Basic properties of squeezed light” Sov. Phys. Usp. 34 (10) 910–924 (1991)
  12. G.D. Fleishman “Transition radiation of a relativistic particle moving along a curve” Sov. Phys. Usp. 34 (1) 86–96 (1991)
  13. A.V. Belinskii “Bell’s theorem without the hypothesis of locality” Phys. Usp. 37 219–222 (1994)
  14. V.A. Bordovitsyn, I.M. Ternov, V.G. Bagrov “Spin light” Phys. Usp. 38 1037–1047 (1995)
  15. N.V. Evdokimov, D.N. Klyshko et al “Bell’s inequalities and EPR-Bohm correlations: working classical radiofrequency model” Phys. Usp. 39 83–98 (1996)
  16. G. Oppen “Objects and environment” Phys. Usp. 39 617–622 (1996)
  17. A.V. Belinskii “Bell’s theorem for trichotomic observables” Phys. Usp. 40 305–316 (1997)
  18. Yu.I. Hovsepyan “Some notes on the relativistic Doppler effect” Phys. Usp. 41 941–944 (1998)
  19. Yu.L. Klimontovich “Entropy and information of open systems” Phys. Usp. 42 375–384 (1999)
  20. V.I. Ritus “Permutation asymmetry of the relativistic velocity addition law and non-Euclidean geometry” Phys. Usp. 51 709–721 (2008)

The list is formed automatically.
© 1918–2026 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions