Top PDF Classical and quantum nonlinear optical information processing

Classical and quantum nonlinear optical information processing

Classical and quantum nonlinear optical information processing

The abundant amount of prior work credited above provides ample evidence that nonlinear optics resem- bles fluid dynamics to a certain degree. In order to use nonlinear optics as a useful and practical computational tool for fluid dynamics, however, simply drawing analogies between the two kinds of dynamics is not enough. One must be able to show an exact correspondence or, at the very least, an approaching convergence between a problem in nonlinear optics and a problem in fluid dynamics, in order to produce any useful prediction of fluid dynamics via nonlinear optics. Moreover, as computers nowadays have enough capabilities to simulate two-dimensional fluids, the mere correspondence between optics and two-dimensional fluid dynamics con- sidered in most of the prior work would not motivate the use of metaphoric optical computing in preference to conventional digital computing. A three-dimensional fluid modeling, on the other hand, requires a pro- cessing capability orders of magnitude higher than that available in today’s supercomputers, so metaphoric optical computing would need to compute such problems much more efficiently to compete with electronic computers and the Moore’s law.
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Classical processing algorithms for Quantum Information Security

Classical processing algorithms for Quantum Information Security

allow for a relaxation of the security assumptions typically made in QKD security proofs, opening the way to the so-called device independent security (see e.g., [56, 57, 58]. The two families of QKD schemes described above can be further distinguished into three main categories, which differ in the information coding technique: discrete-variables coding (DV-C), continuous-variables coding (CV-C) and distributed-phase-reference co- ding (DPR-C). DV-C is the first technique which has been proposed for QKD and, to date, is probably the most used. According to this approach, information is encoded in a discrete quantum degree of freedom of photons; in particular, widely used solutions are photon polarization for free-space implementations and phase coding for fiber-based im- plementations. The receiver uses a photon detector and only the events which resulted in a detection are taken into account for key distillation. DV-C protocols have the main advantage that, if the quantum channel is error-free and no eavesdropper is tampering with it, the legitimate parties immediately share a perfect secret key. On the other hand, they suffer from a low efficiency of photon detectors, high dark count rates and rather long dead-times, thus resulting in high overall losses [51]. These limitations were the dri- ving reasons for the introduction of CV-C protocols, which are based on the measurement of quadrature components of light by means of homodyne detection (see, e.g., [59, 60]). Despite getting rid of hardware limitations of photon detectors, however, in CV-C imple- mentations losses translate into noise, 1 resulting in a decrease of the signal-to-noise ratio. This entails an overhead in the information reconciliation procedure, which is now required to deal with noisier signals. In order to overcome the drawbacks of both the DV-C and the CV-C protocols, some experimental groups proposed a new approach to QKD, where the raw key bits are encoded into discrete quantum states (as for DV-C) and the quantum channel is monitored by observing the phase coherence of subsequent pulses. In that way, the communication efficiency can be improved with respect to DV-C and CV-C schemes. As previously mentioned, this class of protocols is referred to as DPR-C; examples of such protocols can be found in [61] and in [62].
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Modelling of Optical Gates for Quantum Information Processing.

Modelling of Optical Gates for Quantum Information Processing.

The single-qubit rotation by using STIRAP technique [107] (briefly pre- sented in Sec. 4.2) was developed in 2002. Type-I DQD configurations to implement single- and two- qubit rotations by using STIRAP have also been introduced before [19]. Our contribution here is that we show how to overcome the limitations of the scheme in Ref. [19] by using the novel type-II DQD-in- a-nanowire system instead of the conventional type-I configuration. By cal- culating the transition dipole moments, we quantitatively illustrate type-II QDs are significantly better than type-I QDs for quantum gating by STI- RAP. By developing a multiband formalism we show that a charged-exciton featuring a mixed-hole part acting as an intermediate state provides essential coupling with three ground-states of a DQD to perform qubit rotations by STIRAP. We then introduce a system consisting of two neighboring DQDs in a nanowire each encoding one qubit. By using the configuration-interaction method, we show that the strong Coulomb interaction between the charges, which causes a significant shift of the STIRAP transition frequencies, can be exploited to efficiently perform high fidelity conditional two-qubit CNOT op- eration on the two qubits. Importantly, we also show that the implementation is robust against the decoherence posed by spin and charge fluctuations in the environment.
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Benchmarking integrated linear-optical architectures for quantum information processing

Benchmarking integrated linear-optical architectures for quantum information processing

In this article we bridge this gap, presenting a complete analysis of the performance of the main photonic architectures under imperfect operational conditions. The three interferometric layouts have been investigated in the general case, by admitting different levels of losses and noise in unitary transformations of increasing size. Specifically, following the approach commonly adopted for reconfigurable quantum circuits 24 , 25 , i.e. by model- ling beam splitters as Mach-Zehnder interferometers with variable phases and two cascaded symmetric beam splitters, noise was added to their reflectivities and to phases in both Mach-Zehnders and outer phase shifters. For our numerical benchmark we employ as figures of merit the fidelity 39 , 52 , 55 , 56 and the total variation distance (TVD) 53 – 56 , as good estimators of the distance between ideal and imperfect implementations in relevant applica- tions. In particular, while depending also on external factors like purity and degree of distinguishability between the input photons, the TVD has been already identified as a key figure of merit for the goodness of multiphoton experiments 53 – 56 (see Supplementary Note 3). The article is structured as follows. First, we briefly discuss the interferometric structure of the triangular, square and fast designs, whose main characteristics are outlined in Fig. 1 . Thereafter, we compare the performances of the first two schemes, which were shown to be universal for unitary evolutions, for the implementation of Haar-random transformations of increasing size. Finally, we com- pare the operation of the three schemes for the implementation of Fourier and Sylvester interferometers, which represent the fundamental building blocks in a significant number of relevant quantum information protocols. Our analysis highlights the advantages and limitations of each scheme, providing an essential reference point for the design of future larger-scale photonic technologies, whose optimal configurations may well benefit from a joint integration.
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Classical and quantum dynamics of optical frequency conversion

Classical and quantum dynamics of optical frequency conversion

Scanning the monolith ensures that the cavity experiences a wide range of dispersions, and thus does not limit the possible resonances of the signal and idler. The output of the scanning grating is monitored with a silicon photodiode (EG & G FND-100). Fig. 7.2 shows the scanning grating output for the most nondegenerate case, A = 31nm. This is the broadest nondegeneracy reported to date for this system. The large peak in the centre of the plot is the fundamental, at 1064 nm. The peak at the far left of the plot is the signal, that at the far right is the idler. The signal intensity is 4.3% of the 1064nm peak; the idler is much weaker. This may be intrinsic, i.e. idler production is weaker than signal, however it is more probable that this is due to the very steep roll-off in quantum efficiency in silicon photodetectors between 1000 & 1100 nm. The signal wavelength of 1033 nm agrees well w ith the calculated maximum of nonlinear gain centred at 1031 nm.
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Non-Hermitian quantum and classical integrated nonlinear photonics

Non-Hermitian quantum and classical integrated nonlinear photonics

Chapter 7 Conclusion and outlook Quantum and classical properties of light propagating in the nonlinear opti- cal waveguides spark significant of research driven by fundamental interest and applications. Nonlinear waveguide arrays can be used to efficiently generate en- tangled photon pairs and simultaneously shape their spatial correlations through quantum walks. Such integrated photon sources can find applications in the development of on-chip quantum communication and computation devices. In recent years the quantum optics of attenuating media was developed. Firstly, be- cause quantum information protocols are inevitably affected by noise, secondly photonic structures composed of coupled waveguides with lossy regions offer new possibilities for shaping optical beams and pulses. Finally, there has been in- creased interest in nonlinear hybrid plasmonic waveguide as surface plasmon po- laritons offer increased field confirmation and minituisation.
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Information Geometry in Classical and Quantum Systems

Information Geometry in Classical and Quantum Systems

This linear relationship holds for all D and D 0 . In contrast, for the cubic process, the relation is not linear, and the log-log plot on the right in Fig. 2 shows a power-law dependence with the power-law index p. This power-law index p varies between 1.52 and 1.91 and depends on the width (∝ D 1/2 0 ) of initial PDF and stochastic forcing amplitude D, as shown in [18]. This demonstrates that nonlinear interaction tends to change geometric structure of a non-equilibrium process from linear to power-law scalings. In either cases here, L ∞ has a smooth variation with y 0 with its minimum value at y 0 = 0 since the equilibrium point 0 is stable. This will be compared with the behaviour in chaotic systems in
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Photonic quantum information processing

Photonic quantum information processing

mechanism that is employed. Finally, the feed-forward nature of linear opti- cal quantum computing means that we require fast, low-loss optical switches. This is currently a major challenge. An actual implementation of a linear optical quantum computer will not use bulk optical elements, but rather have a chip-based architecture in which microscopic waveguides are wired into programmable circuits. Beam splitters can then be constructed from evanescently coupled waveguides. By adjusting the distance between the waveguides, the transmission coefficient can in principle be carefully calibrated. Recently, photon sources have been placed in or on top of waveguides, which allows for directional coupling of the photon into the waveguide depending on the spin of the photon source [53, 54, 55]. This new technology can be employed for alternative Bell pair generation methods based on photon which-path erasure and spin readout.
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Nonlinear Optical Spatial Filtering for Medical Image Processing

Nonlinear Optical Spatial Filtering for Medical Image Processing

Optical spatial filtering using nonlinear optical materials has become very popular for implantation in optical information processing [15] such as edge enhancement and medical image processing [5] [6] [16]. A Fourier plan of the lens contains terms including: spatial frequency, the magnitude (positive and negative) and the phase. These values capture all information regarding two dimensional images at the Fourier plane. The spatial fre- quency is the frequency across the space that can be mapped out to the different spatial frequencies to different points in the focal plane in a 4f-image system with the nonlinear material at the Fourier plane. Therefore the Fourier spectrum contains low spatial frequencies at the center and high spatial frequency at the edge. Therefore intensity dependent nonlinear absorption can be used to filter out undesired spatial frequency bands in the Fou- rier spectrum of the image (low spatial frequencies at the center with high intensities and low spatial frequencies at the edges with low intensities). Spatial filtering with nonlinear optical materials has been demonstrated by many authors, Xuan et al. used two photon absorption and Raman scattering in nonlinear material such as ace- tone and CS 2 for contrast improvement [17]. C. S. Yelleswarapu et al. [6] demonstrated the use of power limit- ing mechanism for self-adaptive, all optical Fourier imaging processes. Kothapalli et al. used nonlinear filtering technique that exploited photo control light modulation characteristic of bacteriorhodospin (bR) films for early detection of microcalcifications [18].
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Eigenvalue inequalities in quantum information processing

Eigenvalue inequalities in quantum information processing

Part I (Chapters 1–4) explores what is possible if the two parties may use only classical communication. A well-known result by M. Nielsen says that this is inti- mately connected to the majorization relation: if x is the vector of eigenvalues of the initial state, then y can be the vector of eigenvalues of the final state if and only if x is majorized by y. It was recently observed that it is possible for x ⊗ z to be majorized by y ⊗ z, even if x is not majorized by y; physically, this means that the presence of a state with eigenvalues z is a catalyst that allows a certain transformation to occur.
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Implementation of quantum information processing faces the

Implementation of quantum information processing faces the

is still sufficiently low. Conclusions and outlook In summary, we have proposed the application of NEMS as a universal quantum transducer for spin–spin interactions. Com- pared with direct magnetic coupling or probabilistic optical en- tanglement schemes, our approach enables the implementation of long-range and deterministic spin-entanglement operations as well as the design and control of multispin interactions by simple electric circuitry. The universality of the basic underlying concept, namely to use the mechanical resonator for a coherent conversion of magnetic into electric dipoles, also opens a wide range of possibilities for the integration of electronic and nuclear spins with other charge-based quantum systems. Specifically, it might be interesting to consider hybrid architectures by coupling spins with transmission-line cavities 27 , charge qubits 29 and trapped ions 31,32 or atoms 30 . Moreover, this technique can be applicable for a remote magnetic sensing of ‘dark’ spins in a condensed-matter or biological environment that is incompatible with direct laser illumination. In a broader perspective, the quantum transducer ability of NEMS can therefore be seen as one of the fundamental applications of
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Commercial Prospects for Quantum Information Processing

Commercial Prospects for Quantum Information Processing

3.4.1 ‘S MALL ’ Q UANTUM S IMULATIONS Quantum simulations explore physical systems that are themselves highly quantum in nature. This is a potential early application because a quantum simulator is thought to be useful with only a small number of qubits. In addition, the laboratory environment is much more forgiving of technical problems than the commercial environment, so devices could be released by manufacturers early in the technology lifecycle. Below 30 qubits, simulations could, in general, be performed as quickly on a classical computer. Above about 30 qubits, a quantum computer can outperform any conceivable classical computer, for some applications, and in particular for quantum simulations of many-bodied problems. An example application is the study of dipole- dipole interactions: classical simulations of crystal unit-cells are limited to approximately 200 independent atoms before the classical algorithms used become unstable. If a quantum computer could improve this performance then it would be of great value to the field of materials research.
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Reservoir engineering for quantum information

processing

Reservoir engineering for quantum information processing

Chapter 4 Reservoir Engineering 4.1 Introduction The previous two chapters have both been focused on developing the theoretical tools we require for this one. We now turn to the task of applying this to cavity QED systems that can be used to perform useful quantum information processing tasks. The motivation for us here thus comes from limitations of current exper- iments with optical cavities. Recent progress in experiments with these optical cavities has mainly been motivated by potential applications in quantum informa- tion processing. These applications often require the simultaneous trapping of at least two atomic qubits inside a single resonator field mode. It has been shown that the common coupling to a quantised mode can be used to implement quantum gate operations [110, 100, 111, 101, 112] and the controlled generation of entanglement [113, 94, 114, 51, 115]. However, the practical realisation of these schemes with current technologies is experimentally challenging. The reason is that strong atom- cavity interactions require relatively small mode volumes and high quality mirrors;
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Entanglement and Optimal Quantum Information Processing

Entanglement and Optimal Quantum Information Processing

We also would like to admit that many physical realizations of QCM’s has been demonstrated recently. An optical implementation of the universal 1 → 2 QCM ( 2.24 ) for an arbitrary input qubit state based on parametric down-conversion has been demonstrated to have fidelity 0.810 ± 0.008 [ 123 ] which is in a good agreement with the theoretical prediction 5/6 = 0.833. Another physical realization of the universal QCM was achieved by using optical fibers doped with erbium ions. The universal cloning transformation based on this technique was shown to have fidelity F ≈ 0.82 which is again in good agreement with the theoretical prediction [ 46 ]. Also, several realistic theoretical schemes for the physical realization of a QCM on atoms in a cavity have been recently proposed [ 46 ]. However, to our knowledge no experimental results are available at the moment. Also, some physical realizations of universal and equatorial 1 → N QCMs where N = 2, 3... has been already reported. Apart of the optimal cloning transformations, a single-qubit state independent transformation — universal NOT operation ( 2.43 ) — has been experimentally demon- strated with an optical setup to have fidelity 0.630 ± 0.008 which is in a good agree- ment with the theoretical prediction 2/3 ≈ 0.666 [ 123 ]. However, it is worth noticing that while most of efforts has been devoted to physical realizations of 1 → N QCMs where N = 2, 3..., no attention has been paid to realization of universal and equa- torial N → N + K QCMs. Therefore, it is hard to judge whether such cloning machines and corresponding optimal multiqubit state independent transformations can be efficiently realized in practice.
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Investigating information geometry in classical and quantum systems through information length

Investigating information geometry in classical and quantum systems through information length

D/γ y 0 by taking the limit of t → ∞ (y → 0) in Equation (A10). In contrast, for the cubic process, the relation is not linear, and the log-log plot on the right in Figure 2 shows a power-law dependence with the power-law index p. This power-law index p varies between 1.52 and 1.91 and depends on the width ( ∝ D 1/2 0 ) of initial PDF and stochastic forcing amplitude D, as shown in [16]. This indicates that nonlinear force breaks the linear scaling of geometric structure and changes it to power-law scalings. In either cases here, L ∞ has a smooth variation with y 0

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Novel optical devices for information processing

Novel optical devices for information processing

control. Since data is transmitted in the form of optical pulses over fiber optic net- works, problems arise when several pulse trains simultaneously request right of the same route. Certain mechanisms will be helpful if they can save the pulse trains of low priorities to yield for the high priority one. Currently, no good optical buffer memo- ries exist to deal with this need, and so the optical signal must first be converted to an electronic signal, which severely limits the overall network speed. In 1999, Hau et al. reported that the group velocity of light was slowed down to the unusual 17 m/s in an ultra cold atomic gas [7]. This has spurred ultraslow light research for applica- tions in optical buffers, delay lines and quantum information storage. For the sake of commercial competitiveness, ultraslow light has to be realized at room temperature by solid-state devices. However, there is an inherent conflict between the delay time and bandwidth, which limits the device capacities to an unacceptable value. The capacity limit is represented by the delay-time-bandwidth product which is related to the length of an optical pulse stream that can be buffered by this technique. Here, we will study the problem of delay-time-bandwidth product in slow light and a discuss a possible solution.
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Fractional Transforms in Optical Information Processing

Fractional Transforms in Optical Information Processing

As we have mentioned in the introduction, some frac- tional transforms arise under consideration of di ff erent problems: description of paraxial diffraction in free space and in a quadratic refractive index medium, resolution of the nonstationary Schr¨odinger equation in quantum mechanics, phase retrieval, and so forth. Other fractional transforms can be constructed for their own sake, even if their direct ap- plication may not be obvious yet. In particular, in Section 9 we consider a general algorithm for the fractionalization of a given linear cyclic integral transform. The application of a particular fractional transform for optical information pro- cessing then depends on its properties and on the possibility of its experimental realization in optics.
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Nonlinear Fourier transform for optical data processing and transmission:advances and perspectives

Nonlinear Fourier transform for optical data processing and transmission:advances and perspectives

By performing the NFT of a given profile q ( z, t ) , we segre- gate two distinct components: the dispersive nonlinear radia- tion and the non-dispersive solitons, although either of these two can be absent for specific profiles. For normal dispersion, the inputs localised in time cannot nucleate solitons. For the dis- persive part of the nonlinear spectrum, the NLSE evolution pro- duces exactly the linear phase rotation of spectral components as we have for linear systems. For the anomalous dispersion, the solitons, associated with the complex “nonlinear frequen- cies” (eigenvalues), in addition to the rotation of soliton phases can involve either the motion as a whole or a more nontrivial beating dynamics of bound states–the so-called multi-soliton breathers [27, 33], although inside the NFT domain the solitonic degrees of freedom remain decoupled. Note that NFT methods are much richer, more flexible and versatile with respect to the system design and performance compared to just soliton-based techniques, studied previously in many details [26, 27, 33]. In the NFT methods dealing with the discrete part of nonlinear spectrum (solitonic eigenvalues), the information carriers are not the fundamental solitons themselves but the NFT parameters (nonlinear spectral data) attributed to a multisolution pulse. In this sense, the traditional soliton-based transmission emerges as the simplest (and not necessarily optimal) subclass of the NFT methods. The NFT communications are, to some extent, the extension of not only the soliton-based approach but also of the coherent communication idea itself: While for the latter both signal’s amplitude and phase are used for modulation, the NFT approach goes further and employs the nonlinear charac- teristics of the signal.
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Research on nonlinear and quantum optics at the photonics and
quantum information group of the University of Valladolid

Research on nonlinear and quantum optics at the photonics and quantum information group of the University of Valladolid

Palabras clave: Solitones ópticos, Ecuación no lineal de Helmholtz, Gestión de la Dispersión, Multiplexación de información cuántica, Computación cuántica, Materiales no lineales ABSTRACT: We outline the main research lines in Nonlinear and Quantum Optics of the Group of Photonics and Quantum Information at the University of Valladolid. These works focus on Optical Soli- tons, Quantum Information using Photonic Technologies and the development of new materials for Nonlinar Optics. The investigations on optical solitons cover both temporal solitons in disper- sion managed fiber links and nonparaxial spatial solitons as described by the Nonlinear Helmholtz Equation. Within the Quantum Information research lines of the group, the studies address new photonic schemes for quantum computation and the multiplexing of quantum data. The investiga- tions of the group are, to a large extent, based on intensive and parallel computations. Some asso- ciated numerical techniques for the development of the activities described are briefly sketched.
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Harnessing the Exchange Interaction for Quantum Information Processing

Harnessing the Exchange Interaction for Quantum Information Processing

1. Stationary Qubit Model One of the most popular communication models in classical communication is the bus-based model. In this model, the bus/register is the primary unit of information processing and information is mediated between buses using flying bits. In the world of quantum information processing, this has traditionally been done by carrier particles such as photons. We can observe short-range and yet effective mediation done by the exchange interaction in spin-systems. In our stationary-qubit model, we have an integrated computing-and-communication system. Each compu- tation unit comprises of an array of spins being driven through channels, such as electrons driven by surface acoustic waves in semiconductor heterostructures, and made to interact at specific locations in the system.
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