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

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.

[1]  Grunér,et al.  Green-function approach to the radiation-field quantization for homogeneous and inhomogeneous Kramers-Kronig dielectrics. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[2]  T Honjo,et al.  Long-distance distribution of time-bin entangled photon pairs over 100 km using frequency up-conversion detectors. , 2007, Optics express.

[3]  Barnett,et al.  Quantization of the electromagnetic field in dielectrics. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[4]  Thomas Lorünser,et al.  High-fidelity transmission of polarization encoded qubits from an entangled source over 100 km of fiber. , 2007, Optics express.

[5]  Reza Matloob,et al.  Electromagnetic field quantization in a linear isotropic dielectric , 2004 .

[6]  A. Zeilinger,et al.  Speakable and Unspeakable in Quantum Mechanics , 1989 .

[7]  Anders Karlsson,et al.  Low-frequency dispersion characteristics of a multilayered coaxial cable , 2013 .

[8]  A. Khrennikov,et al.  Epr-bohm experiment and Bell’s inequality: Quantum physics meets probability theory , 2008 .

[9]  H. Weinfurter,et al.  Entanglement-based quantum communication over 144km , 2007 .

[10]  Arkady Plotnitsky.  Epistemology and Probability , 2010 .

[11]  W Tittel,et al.  Distribution of time-bin entangled qubits over 50 km of optical fiber. , 2004, Physical review letters.

[12]  Reza Matloob.  ELECTROMAGNETIC FIELD QUANTIZATION IN AN ABSORBING MEDIUM , 1999 .

[13]  Andrei Khrennikov,et al.  Contextual Approach to Quantum Formalism , 2009 .

[14]  D. S. Jones.  The theory of generalised functions: Table of Laplace transforms , 1982 .

[15]  S. Nordebo,et al.  Quantization of propagating modes in optical fibres , 2012 .

[16]  M. Shahriar,et al.  Long distance, unconditional teleportation of atomic states via complete Bell state measurements. , 2000, Physical review letters.

[17]  G. Lyon.  Al , 2014 .

[18]  G. Agrawal.  Fiber‐Optic Communication Systems , 2021 .

[19]  Sae Woo Nam,et al.  Distribution of time-energy entanglement over 100 km fiber using superconducting single-photon detectors. , 2008, Optics express.

[20]  H. Nussenzveig.  Causality and dispersion relations , 2012, American Journal of Physics.

[21]  L. Mandel,et al.  Optical Coherence and Quantum Optics , 1995 .

[22]  G. Roger,et al.  Experimental Test of Bell's Inequalities Using Time- Varying Analyzers , 1982 .

[23]  F. Olver.  Asymptotics and Special Functions , 1974 .

[24]  Guillaume Adenier,et al.  Is the fair sampling assumption supported by EPR experiments , 2007 .

[25]  Nicolas Gisin,et al.  Quantum teleportation over the Swisscom telecommunication network , 2007 .

[26]  Gerard 't Hooft,et al.  On the free-will postulate in Quantum Mechanics , 2007 .

[27]  Sven Nordebo,et al.  Distance dependence of entangled photons in waveguides , 2012 .

[28]  K. Michielsen,et al.  A local realist model for correlations of the singlet state , 2006 .

[29]  Aaron J. Miller,et al.  Detection-loophole-free test of quantum nonlocality, and applications. , 2013, Physical review letters.

[30]  Arkady Plotnitsky,et al.  Epistemology and Probability: Bohr, Heisenberg, Schrödinger, and the Nature of Quantum-Theoretical Thinking , 2009 .

[31]  Barnett,et al.  Electromagnetic field quantization in absorbing dielectrics. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[32]  H. Takesue.  Long-distance distribution of time-bin entanglement generated in a cooled fiber. , 2005, Optics express.

[33]  Igor Volovich,et al.  Quantum field theory and distance effects for polarization correlations in waveguides , 2009 .

[34]  H. Weinfurter,et al.  Free-Space distribution of entanglement and single photons over 144 km , 2006, quant-ph/0607182.

[35]  T. Miya,et al.  Ultimate low-loss single-mode fibre at 1.55 μm , 1979 .

[36]  R. Morrow,et al.  Foundations of Quantum Mechanics , 1968 .

[37]  Andrei Khrennikov,et al.  Foundations of Probability and Physics , 2002 .

[38]  H. Weinfurter,et al.  Violation of Bell's Inequality under Strict Einstein Locality Conditions , 1998, quant-ph/9810080.

[39]  J. Bell,et al.  Speakable and Unspeakable in Quatum Mechanics , 1988 .

[40]  A. Shimony,et al.  Proposed Experiment to Test Local Hidden Variable Theories. , 1969 .

[41]  A. Zeilinger,et al.  Bell violation using entangled photons without the fair-sampling assumption , 2012, Nature.

[42]  K. Laiho,et al.  Spatial modes in waveguided parametric down-conversion , 2009, 0904.4668.

[43]  Igor Volovich,et al.  Local realism, contextualism and loopholes in Bell's experiments , 2002 .

[44]  G. Agrawal.  Fiber-Optic Communication Systems: Agrawal/Fiber-Optic , 2010 .

[45]  Willem M. de Muynck.  Interpretations of quantum mechanics, and interpretations of violation of Bell's inequality , 2001 .