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Estimation of initial one photon temporal modes in waveguides using the asymptotic radiation zone
Linnaeus University, Faculty of Technology, Department of Mathematics.
Linnaeus University, Faculty of Technology, Department of Physics and Electrical Engineering.ORCID iD: 0000-0002-7018-6248
Linnaeus University, Faculty of Technology, Department of Mathematics.ORCID iD: 0000-0002-9857-0938
2014 (English)In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. T163, 014023Article in journal (Refereed) Published
Abstract [en]

There are two optic fibre properties in particular that obstruct the transfer over long distances in quantum communications. One of them is dispersion, which reduces the maximum bit rate. In classical communication with modern highly purified fibres, dispersion is the major limiting factor. The other property is the material loss that causes fluctuations in addition to a general annihilation with distance of photons. It is believed that losses are the major limiting factor in quantum communication over long distances if the bit rate is not an issue. Of major interest in quantum communication is the photon source. It is therefore a high priority to develop methods for the determination of properties like initial temporal modes, repeatability, independence of sequentially emitted photons, etc., for a source emitting single photons in a given spatial mode. In the current paper we suggest that the source properties can be estimated using statistics of the run times of the photons. This requires that the fibre is modelled with sufficient accuracy. To simplify the analysis, it is assumed that the fibre losses can be neglected and that the photons are independent and identically generated. Energy detection in one spin state is employed, making the modelling scalar. The one photon initial temporal mode is found by maximizing a maximum-likelihood function based on running time statistics. Unfortunately, this optimization problem is, in general, not convex. However, for photon detection in the so-called asymptotic radiation zone, where the probability density can be determined to a sufficient degree with asymptotic methods, the optimization problem is convex. In the current paper, quantum tomography in fibres based on this convex optimization method is presented, and its generalization to more complicated situations like the introduction of losses in the modelling is discussed.

Place, publisher, year, edition, pages
2014. Vol. T163, 014023
Keyword [en]
asymptotic radiation zone, waveguide, initial quantum state, arrival times, maximum-likelihood function, non-convex optimization problem
National Category
Physical Sciences Mathematics
Research subject
Natural Science, Physics; Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-41403DOI: 10.1088/0031-8949/2014/T163/014023ISI: 000349832400024Scopus ID: 2-s2.0-84919628465OAI: oai:DiVA.org:lnu-41403DiVA: diva2:798312
Available from: 2015-03-26 Created: 2015-03-26 Last updated: 2017-01-10Bibliographically approved

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Nilsson, BörjeNordebo, SvenKhrennikov, Andrei
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