Linear optics with photon counting is a prominent candidate for practical quantum computing. The protocol by Knill, Laflamme, and Milburn [2001, Nature (London) 409, 46] explicitly demonstrates that efficient scalable quantum computing with single photons, linear optical elements, and projective measurements is possible. Subsequently, several improvements on this protocol have started to bridge the gap between theoretical scalability and practical implementation. The original theory and its improvements are reviewed, and a few examples of experimental two-qubit gates are given. The use of realistic components, the errors they induce in the computation, and how these errors can be corrected is discussed.

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Linear optical quantum computing with photonic qubits

We review the current status of single-photon-source and single-photon-detector technologies operating at wavelengths from the ultraviolet to the infrared. We discuss applications of these technologies to quantum communication, a field currently driving much of the development of single-photon sources and detectors.

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Invited review article: Single-photon sources and detectors

This review covers the latest developments in continuous-variable quantum-state tomography of optical fields and photons, placing a special emphasis on its practical aspects and applications in quantum-information technology. Optical homodyne tomography is reviewed as a method of reconstructing the state of light in a given optical mode. A range of relevant practical topics is discussed, such as state-reconstruction algorithms (with emphasis on the maximum-likelihood technique), the technology of time-domain homodyne detection, mode-matching issues, and engineering of complex quantum states of light. The paper also surveys quantum-state tomography for the transverse spatial state (spatial mode) of the field in the special case of fields containing precisely one photon.

https://arxiv.org/pdf/quant-ph/0511044.pdf

Continuous-variable optical quantum-state tomography

The development of silicon-compatible optical components that simultaneously amplify and process a broad range of wavelength channels is critical for future data communication technology based on photonic chips. Until now, such devices have only been able to amplify a single wavelength channel. Now, using nanoscale silicon waveguides designed for the purpose, Foster et al. have achieved broadband amplification. The key is the exploitation of a nonlinear optical effect known as four-wave mixing. This process can also be used for other all-optical functions previously only possible in extended lengths of optical fibre. Phase-matched four-wave mixing can take place with high efficiency in a suitably designed silicon waveguide — this advance could allow for the implementation of dense wavelength channels for optical processing in an all-silicon photonic chip. Developing an optical amplifier on silicon is essential for the success of silicon-on-insulator (SOI) photonic integrated circuits. Recently, optical gain with a 1-nm bandwidth was demonstrated using the Raman effect1,2,3,4,5,6,7,8,9, which led to the demonstration of a Raman oscillator10,11, lossless optical modulation12 and optically tunable slow light13. A key strength of optical communications is the parallelism of information transfer and processing onto multiple wavelength channels. However, the relatively narrow Raman gain bandwidth only allows for amplification or generation of a single wavelength channel. If broad gain bandwidths were to be demonstrated on silicon, then an array of wavelength channels could be generated and processed, representing a critical advance for densely integrated photonic circuits. Here we demonstrate net on/off gain over a wavelength range of 28 nm through the optical process of phase-matched four-wave mixing in suitably designed SOI channel waveguides. We also demonstrate wavelength conversion in the range 1,511–1,591 nm with peak conversion efficiencies of +5.2 dB, which represents more than 20 times improvement on previous four-wave-mixing efficiencies in SOI waveguides14,15,16,17. These advances allow for the implementation of dense wavelength division multiplexing in an all-silicon photonic integrated circuit. Additionally, all-optical delays18, all-optical switches19, optical signal regenerators20 and optical sources for quantum information technology21, all demonstrated using four-wave mixing in silica fibres, can now be transferred to the SOI platform.

Broad-band optical parametric gain on a silicon photonic chip

Several kinds of nonlinear optical effects have been observed in recent years using silicon waveguides, and their device applications are attracting considerable attention. In this review, we provide a unified theoretical platform that not only can be used for understanding the underlying physics but should also provide guidance toward new and useful applications. We begin with a description of the third-order nonlinearity of silicon and consider the tensorial nature of both the electronic and Raman contributions. The generation of free carriers through two-photon absorption and their impact on various nonlinear phenomena is included fully within the theory presented here. We derive a general propagation equation in the frequency domain and show how it leads to a generalized nonlinear Schrodinger equation when it is converted to the time domain. We use this equation to study propagation of ultrashort optical pulses in the presence of self-phase modulation and show the possibility of soliton formation and supercontinuum generation. The nonlinear phenomena of cross-phase modulation and stimulated Raman scattering are discussed next with emphasis on the impact of free carriers on Raman amplification and lasing. We also consider the four-wave mixing process for both continuous-wave and pulsed pumping and discuss the conditions under which parametric amplification and wavelength conversion can be realized with net gain in the telecommunication band.

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Nonlinear optical phenomena in silicon waveguides: Modeling and applications

We present a fiber-based source of polarization-entangled photons that is well suited for quantum communication applications in the 1550 nm band of standard fiber-optic telecommunications. Polarization entanglement is created by pumping a nonlinear-fiber Sagnac interferometer with two time-delayed orthogonally polarized pump pulses and subsequently removing the time distinguishability by passing the parametrically scattered signal and idler photon pairs through a piece of birefringent fiber. Coincidence detection of the signal and idler photons yields biphoton interference with visibility greater than 90%, while no interference is observed in direct detection of either signal or idler photons. All four Bell states can be prepared with our setup and we demonstrate violations of the Clauser-Horne-Shimony-Holt form of Bell's inequality by up to 10 standard deviations of measurement uncertainty.

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Optical-Fiber Source of Polarization-Entangled Photons in the 1550 nm Telecom Band

We demonstrate greatly improved results for the production of correlated photon-pairs using the four-photon scattering process in silica fiber. We achieve a true-coincidence-count to accidental-coincidence-count ratio greater than 10, when the photon-pair production rate is about 0.04 /pulse. This represents a four-fold improvement over our previous results. The contribution of spontaneous Raman scattering, the primary cause of uncorrelated photons that degrades the fidelity of this source, is reduced by decreasing the wavelength detuning between the correlated photons and the pump photons and by using polarizers to remove the cross-polarized Raman-scattered photons. Excess Raman scattering could be further suppressed by cooling the silica fiber. Even without cooling the fiber, the achieved 10 to 1 ratio of true-coincidence to accidental-coincidence makes the fiber source of correlated photon-pairs a useful tool for realizing various quantum-communication protocols.

https://www.rle.mit.edu/quantummuri/publications/Additions4_05/Kumar_10.pdf

All-fiber photon-pair source for quantum communications: Improved generation of correlated photons.

We study the purity of correlated photon pairs generated in a dispersion-shifted fiber at various temperatures. The ratio of coincidence to accidental-coincidence counts greater than 100 can be obtained as the fiber is cooled to liquid-nitrogen temperature (77 K). We then generate polarization-entangled photon pairs by using a compact counterpropagating scheme. Two-photon interference with visibility >98% and Bell's inequality violation by >8 standard deviations of measurement uncertainty are observed at 77 K, without subtracting the accidental-coincidence counts due to background Raman photons.

Generation of high-purity telecom-band entangled photon pairs in dispersion-shifted fiber.

The nonzero response time of the Kerr [χ3] nonlinearity determines the quantum-limited noise figure of χ3 parametric amplifiers. This nonzero response time of the nonlinearity requires coupling of the parametric amplification process to a molecular-vibration phonon bath, causing the addition of excess noise through Raman gain or loss at temperatures above 0 K. The effect of this excess noise on the noise figure can be surprisingly significant. We derive analytical expressions for this quantum-limited noise figure for phase-insensitive operation of a χ3 amplifier and show good agreement with published noise-figure measurements.

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Raman-noise-induced noise-figure limit for Χ(3) parametric amplifiers

We report measurement of the noise statistics of spontaneous parametric fluorescence in a fiber parametric amplifier with single-mode, single-photon resolution. We employ optical homodyne tomography for this purpose, which also provides a self-calibrating measurement of the noise figure of the amplifier. The measured photon statistics agree with quantum-mechanical predictions, and the amplifier’s noise figure is found to be almost quantum limited.

Paul L. Voss

Papers

Optical-Fiber Source of Polarization-Entangled Photons in the 1550 nm Telecom Band

All-fiber photon-pair source for quantum communications: Improved generation of correlated photons.

Generation of high-purity telecom-band entangled photon pairs in dispersion-shifted fiber.

Raman-noise-induced noise-figure limit for Χ(3) parametric amplifiers

Measurement of the photon statistics and the noise figure of a fiber-optic parametric amplifier.