Foundations of Physics

, Volume 44, Issue 4, pp 389–405 | Cite as

Photon Flux and Distance from the Source: Consequences for Quantum Communication

  • Andrei KhrennikovEmail author
  • Börje Nilsson
  • Sven Nordebo
  • Igor Volovich


The paper explores the fundamental physical principles of quantum mechanics (in fact, quantum field theory) that limit the bit rate for long distances and examines the assumption used in this exploration that losses can be ignored. Propagation of photons in optical fibers is modelled using methods of quantum electrodynamics. We define the “photon duration” as the standard deviation of the photon arrival time; we find its asymptotics for long distances and then obtain the main result of the paper: the linear dependence of photon duration on the distance when losses can be ignored. This effect puts the limit to joint increasing of the photon flux and the distance from the source and it has consequences for quantum communication. Once quantum communication develops into a real technology (including essential decrease of losses in optical fibres), it would be appealing to engineers to increase both the photon flux and the distance. And here our “photon flux/distance effect” has to be taken into account. This effect also may set an additional constraint to the performance of a loophole free test of Bell’s type—to close jointly the detection and locality loopholes.


Photon propagation Optical fibre Photon duration Linear dependence of photon duration on the distance Loophole free Bell test Photon flux/distance effect 



The work was supported by the following funding agencies: MPNS COST Action MP1006 (Fundamental Problems in Quantum Physics), Austrian Academy of Science (visiting professor fellowship of A. Khrennikov at Vienna University and Atom Institute, 2013). The authors would like to thank both reviewers for valuable comments and advices which improved essentially clarity of the paper.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Andrei Khrennikov
    • 1
    Email author
  • Börje Nilsson
    • 1
  • Sven Nordebo
    • 2
  • Igor Volovich
    • 3
  1. 1.International Center for Mathematical Modeling in Physics, Engineering, Economics, and Cognitive Science, Department of MathematicsLinnæus UniversityVäxjöSweden
  2. 2.Department of Physics and Electrical EngineeringLinnæus UniversityVäxjöSweden
  3. 3.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia

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