Coherent optical implementations of the fast Fourier transform and their comparison to the optical implementation of the quantum Fourier transform

Optical structures to implement the discrete Fourier transform (DFT) and fast Fourier transform (FFT) algorithms for discretely sampled data sets are considered. In particular, the decomposition of the FFT algorithm into the basic Butterfly operations is described, as this allows the algorithm to be fully implemented by the successive coherent addition and subtraction of two wavefronts (the subtraction being performed after one has been appropriately phase shifted), so facilitating a simple and robust hardware implementation based on waveguided hybrid devices as employed in coherent optical detection modules. Further, a comparison is made to the optical structures proposed for the optical implementation of the quantum Fourier transform and they are shown to be very similar

Considerations for the extension of coherent optical processors into the quantum computing regime

Previously we have examined the similarities of the quantum Fourier transform to the classical coherent optical implementation of the Fourier transform (R. Young et al, Proc SPIE Vol 87480, 874806-1, -11). In this paper, we further consider how superposition states can be generated on coherent optical wave fronts, potentially allowing coherent optical processing hardware architectures to be extended into the quantum computing regime. In particular, we propose placing the pixels of a Spatial Light Modulator (SLM) individually in a binary superposition state and illuminating them with a coherent wave front from a conventional (but low intensity) laser source in order to make a so-called ‘interaction free’ measurement. In this way, the quantum object, i.e. the individual pixels of the SLM in their superposition states, and the illuminating wavefront would become entangled. We show that if this were possible, it would allow the extension of coherent processing architectures into the quantum computing regime and we give an example of such a processor configured to recover one of a known set of images encrypted using the well-known coherent optical processing technique of employing a random Fourier plane phase encryption mask which classically requires knowledge of the corresponding phase conjugate key to decrypt the image. A quantum optical computer would allow interrogation of all possible phase masks in parallel and so immediate decryption

QR factorization equalisation scheme for mode devision multiplexing transmission in fibre optics

Optical communication systems play a major role in handling worldwide Internet traffic. Internet traffic has been increasing at a dramatic rate and the current optical network infrastructure may not be able to support the traffic growth in a few decades. Mode division multiplexing is introduced as a new emerging technique to improve the optical network capacity by the use of the light modes as individual channels. One of the main issues in MDM is mode coupling which is a physical phenomenon when light modes exchange their energy between each other during propagation through optical fiber resulting in inter-symbol interference (ISI). Many studies based on Least Mean Square (LMS) and Recursive Least Square (RLS) have taken place to mitigate the mode coupling effect. Still, most approaches have high computational complexity and hinders high-speed communication systems. Blind equalisation approach does not need training signals, thus, will reduce the overhead payload. On the other hand, QR factorization shows low computational complexity in the previous research in the radio domain. The combination of these two concepts shows significant results, as the use of low complexity algorithms reduces the processing needed to be done by the communication equipment, resulting in more cost effective and smaller equipment, while having no training signal saves the bandwidth and enhances the overall system performance. To the best knowledge of the researcher, blind equalisation based on QR factorization technique has been not used in MDM equalisation to date. The research goes through the four stages of the design research methodology (DRM) to achieve the purpose of the study. The implementation stage is taken two different simulators has been used, the first one which is the optical simulator is used to collect the initial optical data then, MATLAB is used to develop the equalisation scheme. The development starts with the derivation of the system’s transfer function (H) to be used as the input to the developed equalizer. Blind equalisation based on QR factorization is chosen as a way to introduce an efficient equalization to mitigate ISI by narrowing the pulse width. The development stages include a stage where the channel estimation is taken place. Statistical properties based on the standard deviation (STD) of the powers of the input and output signals has been used for the blind equalisation’s channel estimation part. The proposed channel estimation way has the ability in estimating the channel with an overall mean square error (MSE) of 0.176588301 from the initial transmitted signal. It is found that the worst channel has an MSE of 0.771365 from the transmitted signal, while the best channel has and MSE of 0.000185 from the transmitted signal. This is done by trying to avoid the issues accompanied with the development of the previous algorithms that have been utilized for the same goal. The algorithm mentioned in the study reduces the computational complexity problem which is one of the main issues that accompany currently used tap filter algorithms, such as (LMS) and (RLS). The results from this study show that the developed equalisation scheme has a complexity of O(N) compared with O(N2) for RLS and at the same time, it is faster than LMS as its calculation CPU time is equal to 0.005242 seconds compared with 0.0077814 seconds of LMS. The results are only valid for invertible and square channel matrices

On the Chirp Function, the Chirplet Transform and the Optimal Communication of Information

—The purpose of this extended paper is to provide a review of the chirp function and the chirplet transform and to investigate the application of chirplet modulation for digital communications, in particular, the transmission of binary strings. The significance of the chirp function in the solution to a range of fundamental problems in physics is revisited to provide a background to the case and to present the context in which the chirp function plays a central role, the material presented being designed to show a variety of problems with solutions and applications that are characterized by a chirp function in a fundamental way. A study is then provided whose aim is to investigate the uniqueness of the chirp function in regard to its use for convolutionalcodinganddecoding,thelattercase(i.e.decoding) being related to the autocorrelation of the chirp function which provides a unique solution to the deconvolution problem. Complementary material in regard to the uniqueness of a chirp is addressed through an investigation into the selfcharacterizationofthechirpfunctionuponFouriertransformation. This includes a short study on the eigenfunctions of the Fourier transform, leading to a uniqueness conjecture which is based on an application of the Bluestein decomposition of a Fourier transform. The conjecture states that the chirp function is the only phase-only function to have a self-characteristic Fourier transform, and, for a specific scaling constant, a conjugate eigenfunction. In the context of this conjecture, we consider the transmission of information through a channel characterized by additive noise and the detection of signals with very low Signal-to-Noise Ratios. It is shown that application of chirplet modulation can provide a simple and optimal solution to the problem of transmitting binary strings through noisy communication channels, a result which suggests that all digital communication systems should ideally by predicated on the application of chirplet modulation. In the latter part of the paper, a method is proposed for securing the communication of information (in the form of a binary string) through chirplet modulation that is based on prime number factorization of the chirplet (angular) bandwidth. Coupled with a quantum computer for factorizing very large prime numbers using Shor’s algorithm, the method has the potential for designing a communications protocol specifically for users with access to quantum computing when the factorization of very large prime numbers is required. In thisrespect,and,inthefinalpartofthepaper,weinvestigatethe application of chirplet modulation for communicating through the ‘Water-Hole’. This includes the introduction of a method for distinguishing between genuine ‘intelligible’ binary strings through the Kullback-Leibler divergence which is shown to be statistically significant for a number of natural languages

A Survey of Signal Processing Problems and Tools in Holographic Three-Dimensional Television

Cataloged from PDF version of article.Diffraction and holography are fertile areas for application of signal theory and processing. Recent work on 3DTV displays has posed particularly challenging signal processing problems. Various procedures to compute Rayleigh-Sommerfeld, Fresnel and Fraunhofer diffraction exist in the literature. Diffraction between parallel planes and tilted planes can be efficiently computed. Discretization and quantization of diffraction fields yield interesting theoretical and practical results, and allow efficient schemes compared to commonly used Nyquist sampling. The literature on computer-generated holography provides a good resource for holographic 3DTV related issues. Fast algorithms to compute Fourier, Walsh-Hadamard, fractional Fourier, linear canonical, Fresnel, and wavelet transforms, as well as optimization-based techniques such as best orthogonal basis, matching pursuit, basis pursuit etc., are especially relevant signal processing techniques for wave propagation, diffraction, holography, and related problems. Atomic decompositions, multiresolution techniques, Gabor functions, and Wigner distributions are among the signal processing techniques which have or may be applied to problems in optics. Research aimed at solving such problems at the intersection of wave optics and signal processing promises not only to facilitate the development of 3DTV systems, but also to contribute to fundamental advances in optics and signal processing theory. © 2007 IEEE

Modematching an optical quantum memory

We analyse the off-resonant Raman interaction of a single broadband photon, copropagating with a classical `control' pulse, with an atomic ensemble. It is shown that the classical electrodynamical structure of the interaction guarantees canonical evolution of the quantum mechanical field operators. This allows the interaction to be decomposed as a beamsplitter transformation between optical and material excitations on a mode-by-mode basis. A single, dominant modefunction describes the dynamics for arbitrary control pulse shapes. Complete transfer of the quantum state of the incident photon to a collective dark state within the ensemble can be achieved by shaping the control pulse so as to match the dominant mode to the temporal mode of the photon. Readout of the material excitation, back to the optical field, is considered in the context of the symmetry connecting the input and output modes. Finally, we show that the transverse spatial structure of the interaction is characterised by the same mode decomposition.Comment: 17 pages, 4 figures. Brief section added treating the transverse spatial structure of the memory interaction. Some references added. A few typos fixe

The Optical Frequency Comb as a One-Way Quantum Computer

In the one-way model of quantum computing, quantum algorithms are implemented using only measurements on an entangled initial state. Much of the hard work is done up-front when creating this universal resource, known as a cluster state, on which the measurements are made. Here we detail a new proposal for a scalable method of creating cluster states using only a single multimode optical parametric oscillator (OPO). The method generates a continuous-variable cluster state that is universal for quantum computation and encoded in the quadratures of the optical frequency comb of the OPO. This work expands on the presentation in Phys. Rev. Lett. 101, 130501 (2008).Comment: 20 pages, 8 figures. v2 corrects minor error in published versio

Implementation of Quantum Key Distribution Protocols

As a wide spectrum of the human activity rapidly transitions to a digital environment, the need for secure and efficient communication intensifies. The currently used public key distribution cryptosystems, such as the Rivest-Shamir-Adleman (RSA) protocol, source their security from the computational difficulty of certain mathematical problems. While widely successful, the security these cryptosystems offer remains heuristic and the development of Quantum computers may render them obsolete. The security that Quantum Key Distribution (QKD) guarantees, stems not from the mathematical complexity of the encryption algorithms but from the laws of Quantum Physics. Implementations of QKD protocols, however, rely on imperfect instruments and devices for information encoding, transmission and detection. Device imperfections limit the rate of information exchange and introduce vulnerabilities which can be exploited by a potential eavesdropper. This work explores practical aspects of QKD as it matures beyond proof-of-principle experiments, focusing on the Measurement Device Independent - QKD, a novel Quantum Communication protocol that offers an exceptional balance between security and efficiency. At the heart of the MDI-QKD lies the Hong-Ou-Mandel (HOM) interference which characterizes the indistinguishability of the photon states that the communicating parties independently send. This study examines the HOM interference in a realistic lab environment and concludes that exceptional interference visibility can be achieved using typical commercially available optical devices and detectors, further demonstrating the applicability of the MDI-QKD protocol. An important limiting factor for every Quantum Communication protocol is the transmission medium. Fiber - based optical networks suffer significant losses that prohibit Quantum Communication beyond metropolitan scales. While Free Space communication is an attractive alternative for long distance communication, is susceptible to losses due to the atmospheric Turbulence of the channel. As a means to improve the key generation efficiency, this work examines and experimentally demonstrates the Prefixed-Threshold Real Time Selection (P-RTS) scheme, which improves the free-space communication efficiency by rejecting detections that occur while the channel transmittance drops below a predetermined threshold