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Estimation of initial one photon temporal modes in waveguides using the asymptotic radiation zone

Nilsson, Börje (author)
Linnéuniversitetet,Institutionen för matematik (MA)
Nordebo, Sven (author)
Linnéuniversitetet,Institutionen för fysik och elektroteknik (IFE)
Khrennikov, Andrei (author)
Linnéuniversitetet,Institutionen för matematik (MA)
 (creator_code:org_t)
2014
2014
English.
In: Physica Scripta. - 0031-8949 .- 1402-4896. ; T163
  • Journal article (peer-reviewed)
Abstract Subject headings
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  • 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.

Subject headings

NATURVETENSKAP  -- Fysik (hsv//swe)
NATURAL SCIENCES  -- Physical Sciences (hsv//eng)
NATURVETENSKAP  -- Matematik (hsv//swe)
NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

asymptotic radiation zone
waveguide
initial quantum state
arrival times
maximum-likelihood function
non-convex optimization problem
Fysik
Physics
Matematik
Mathematics

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ref (subject category)
art (subject category)

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Nilsson, Börje
Nordebo, Sven
Khrennikov, Andr ...
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NATURAL SCIENCES
NATURAL SCIENCES
and Physical Science ...
NATURAL SCIENCES
NATURAL SCIENCES
and Mathematics
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Physica Scripta
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Linnaeus University

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