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

作     者：Nilsson, Borje Nordebo, Sven Khrennikov, Andrei 

作者机构：Linnaeus Univ Dept Math SE-35195 Vaxjo Sweden Linnaeus Univ Dept Phys & Elect Engn SE-35195 Vaxjo Sweden 

出 版 物：《PHYSICA SCRIPTA》 (物理学报)

年 卷 期：2014年第T163卷第T163期

页      面：014023-014023页

核心收录：

学科分类：07[理学] 0702[理学-物理学] 

主　　题：asymptotic radiation zone waveguide initial quantum state arrival times maximum-likelihood function non-convex optimization problem 

摘      要：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.