Following Einstein, Podolsky, and Rosen (EPR) original argument, we derive a pair of inequalities for the uncertainties in the sum of the momenta and in the difference of the positions of an entangled two-particle system. We prove that only entangled systems can satisfy both EPR-inequalities, in violation of the limits imposed by classical statistics. We propose an operational approach that allows applying the EPR inequalities to two-photon systems, as well. In particular, we demonstrate a scheme that allows implementing the EPR gedanken-experiment and verifying the EPR inequalities on systems of pairs of photons. We report the experimental results obtained in this kind of quantum interference and imaging experiment: SPDC two-photon system satisfies both EPR inequalities. The experimental verification of the EPR inequalities represents a practical way to experimentally distinguish entanglement from classical correlation in momentum and/or position variables for systems of two particles/photons. We emphasize the practical consequences of the EPR inequalities: only entanglement allows one to go beyond the limitations imposed by Heisenberg uncertainty on systems of classically correlated particles/photons. In this context we review a recent experiment of two-photon diffraction and quantum lithography.

Many of the schemes utilizing photon states under investigation for Quantum Information Processing (QIP) technology involve active and passive optical components. In order to be able to establish fidelity levels for these schemes, the performance of these optical components and their coupling efficiencies require careful and accurate characterization. Correlated photons, the basis of entangled photon states, offer a direct means of measuring detector quantum efficiency and source radiance in the photon counting regime. Detector and source calibration by correlated photon techniques therefore address some of the key factors critical to QIP technology and the developing techniques of correlated/entangled photon metrology. Work is being undertaken at NPL to establish the accuracy limitations of the correlated photon technique for detector and source calibration. This paper will report on investigations concerning the characterization of silicon avalanche photodiode detectors using the correlated photon technique.

We discuss a classical model allowing one to visualize and characterize the optical mode of the single photon generated by means of a conditional measurement on a biphoton produced in parametric down-conversion. The model is based on Klyshko's advanced wave interpretation, but extends beyond it, providing a precise mathematical description of the advanced wave. The optical mode of the conditional photon is shown to be identical to the mode of the classical difference-frequency field generated due to nonlinear interaction of the partially coherent advanced wave with the pump pulse. With this "nonlinear advanced wave model" most coherence properties of the conditional photon become manifest, which permits one to intuitively understand many recent results, in particular, in quantum imaging.

Quantum tomography of cw homodyne detected field quadratures (QHT) is used for investigating quantum states of radiation fields. We apply QHT to the measurement of the transmittance of optical samples illuminated by vacuum squeezed radiation produced by a type-I degenerate OPO operating below threshold. The field reconstructed by QHT contains information about the transmittance of different absorbers illuminated by a very small number of photons.

Quantum metrology utilizes nonclassical states (of light) to outperform the accuracy limits of its classical counterpart. We demonstrate the relevance of photon number Fock states and polarization entanglement for the experimental realization of interferometric quantum metrology applications.

Recently, several researchers have been able to measure precisely the contribution of the Casimir force to the dynamics of micro-electromechanical devices. Thus there is no doubt of the importance of these physics at the nanometer scale in metallic films. However, almost twenty years ago, it was estimated that the ratio of the Casimir energy to the Coulomb energy stored by a production, metal-oxide-semiconductor field effect transistor (MOSFET), having a gate oxide thickness of 50 nm, in a state of charge inversion should be of order 10%. Yet today's production MOSFET technologies are engineered with gate oxide thickness on the order of 2 nm, implying a Casimir-to-Coulomb energy ratio of well over 100% by using the original calculation. If this were correct, the Casimir effect would of necessity be a major factor in the design and in the resulting performance of current MOS technologies. This does not appear to be the case. In this light, the purpose of this paper is twofold: 1) To demonstrate that by including more precise physics the original estimate was too high, and 2) To propose a practicable method of measuring the strength of the Casimir effect in the MOS system.

The process of up-conversion is shown to enable superior single-photon detectors in the infrared, compared to InGaAs and germanium Avalanche Photodiodes (APDs) (normally used for IR single photon detection). After up-converting an infrared photon to a visible one in a non-linear crystal-Periodically Poled Lithium Niobate (PPLN)-we use a silicon APD to efficiently detect the frequency up-shifted IR photon. We have demonstrated this process at the "high-intensity" level and at the single-photon level, where the up-converted state is effectively a superposition of the single photon Fock state and the vacuum state. We achieve an 80% conversion efficiency over the width of the pulse, and show that this process is coherent, a necessary ingredient for many applications.

We report an experimental implementation of deterministic preparation and measurement of single-photon two-qubit entangled states, in which the polarization and the spatial modes of a single-photon each represent a quantum bit. It is demonstrated that all four single-photon two-qubit entangled states (Bell states) can be easily prepared and measured deterministically using linear optical elements alone. We also discuss how this scheme can be used for implementing recently proposed single-photon two-qubit quantum cryptography.

We show theoretically that two-photon correlation time for a biphoton, a pair of entangled photons generated in the process of parametric down conversion, is limited by the inverse frequency width of the single-photon spectrum, which is limited by the dispersion of the nonlinear material used for the pair generation. The dispersion is determined by the transparency window of the material, which provides the ultimate limitation for the two-photon correlation time. We discuss several experimental approaches enabling realization of such a limiting case.

We investigate the coupling efficiency of parametric downconversion light (PDC) into single and multi-mode optical fibers as a function of the pump beam diameter, crystal length and walk-off. We outline two different theoretical models for the preparation and collection of either single-mode or multi-mode PDC light (defined by, for instance, multi-mode fibers or apertures, corresponding to bucket detection). Moreover, we define the mode-matching collection efficiency, important for realizing a single-photon source based on PDC output into a well-defined single spatial mode. We also define a multimode collection efficiency that is useful for single-photon detector calibration applications.

The Visible Light Photon Counter (VLPC) has the capability to discriminate photon number states, in contrast to conventional photon counters which can only detect the presence or absence of photons. We use this capability, along with the process of parametric down-conversion, to generate photon number states. We first investigate single photon generation, using a modified Hanbury-Brown Twiss (HBT) intensity interferometer to verify the single photon nature of the light. We then use a second VLPC to experimentally demonstrate generation of 2,3 and 4 photons with high fidelity. We investigate the effect of the detection efficiency of the VLPC on the generation rate and fidelity of the created states.

A scheme to distinguish entangled two-photon-polarization states (ETP) from two independent it entangled one-photon-polarization states is proposed. Using this scheme, the experimental generation of ETP by parametric down-conversion is confirmed through the anti-correlations between three orthogonal two-photon-polarization states. The estimated fraction of ETP among the correlated photon pairs is 37% in the present experimental setup.

Possible schemes to implement the basic quantum gates for quantum computation have been presented based on cavity quantum electrodynamics (QED) systems. We then discuss schemes to implement several important quantum algorithms such as the discrete quantum fourier transform (QFT) algorithm and Grover's quantum search algorithm based on these quantum gates. Some other applications of cavity QED based systems including the implementations of a quantum disentanglement eraser and an entanglement amplifier are also discussed.

A modified coherent state is created by mixing a coherent state with optical field from parametric down-conversion in a beam splitter. A two-photon interference effect will cancel the two-photon state. This modified coherent state has ad-vantage over the conventional weak coherent state currently used widely in quantum cryptography. We make numerical analysis on the improvement in secure data rate and transmission distance with the modified coherent state. With a three-photon interference effect to cancel the three-photon state, further improvement is shown to be possible in a newly proposed protocol for quantum cryptography.

We present a quantum theory for generating two-photon states by means of four-wave mixing in optical fiber. We start with an interaction Hamiltonian that can correctly describe all nonlinear interactions among the four waves present in the fiber, namely, the frequency non-degenerate pumps, signal, and idler, including the terms responsible for self-phase modulation (SPM), cross-phase modulation (XPM), and four-photon scattering (FPS). The exact form of this Hamiltonian is obtained through comparison between the classical and quantum equations of motion. The two-photon state is then calculated by means of first-order perturbation theory. It turns out that only the FPM and the pump SPM terms contribute to the formation of the two-photon state. The entangled nature of this state is verified in a coincidence counting experiment. The results of the theoretical calculation agree well with experimental data.

We review an experimental demonstration of a simple irreversible circuit of two probabilistic exclusive-OR (XOR) gates for single-photon qubits. We describe the operation of the individual linear-optics gates and the overall circuit in terms of two-photon and three-photon quantum interference effects. We also discuss future plans for quantum circuits using single-photon qubits from stored parametric down-conversion sources.

We show that single qubit quantum fingerprinting without shared randomness is feasible with linear optics and is demonstrably superior to its classical counterpart. Furthermore a shared source of entanglement, provided for example by a parametric down converter, permits 100% reliable quantum fingerprinting, which outperforms classical fingerprinting even with arbitrary amounts of shared randomness.

We analytically demonstrate a quantum memory based on coherence transfer for manipulating quantum states of photons interacting with a macroscopic medium. The present quantum memory has potential for quantum information and communications using entanglement storage and retrieval. Using this technique the quantum coherent control of a quantum state is effectively possible by simply varying the classical laser parameters.

This paper discusses simulation of quantum computing applications solving important physics and engineering problems. Methodologies are developed for quantum computing solutions of the Navier Stokes Equation, Dirac's Equation, and Schrodinger's Equation in complex domains. Turbulent Navier Stokes solutions were generated in complex geometries including urban domains. A quantum computing algorithm is also developed for the processing of sound which has a greater than classical efficiency in compression when run on a quantum computer. The algorithm also has interesting and useful properties on a classical computer, but without the superior speed and storage properties realized on a quantum computer.

Our last experimental results on the realization of a measurement-conditional unitary operation at single photon level are presented. This gate operates by rotating by 90° the polarization of a photon produced by means of Type-II Parametric Down Conversion conditional to a polarization measurement on the correlated photon. We then propose a new scheme for measuring the quantum efficiency of a single photon detection apparatus by using this set-up. We present experimental results obtained with this scheme compared with traditional biphoton calibration. Our results show the interesting potentiality of the suggested scheme.

We have tested the experimental prerequisites for a Space-to-Ground quantum communication link between satellites and an optical ground station. The feasibility of our ideas is being tested using the facilities of the ASI Matera Laser Ranging Observatory (MLRO) and existing geodetic satellites such as Lageos 1 and 2. Specific emphasis is put on the necessary technological modifications of the existing infrastructure to achieve single photon reception from an orbiting satellite.

In this paper we analyze the turbulence affects on a quantum-key distribution (QKD system and demonstrate them experimentally. We demonstrate a QKD scheme, in which we transform polarization states to time slots. This transformation to the time domain eliminates the need for numerous detectors or moving parts, and simplifies the system architecture by achieving a compact, lightweight and reliable system. These attributes are broadly recognized as being important features of future mobile quantum communication applications such as will be found in satellites and airplanes. We have demonstrated the feasibility of our design.

In 2000, an attractive new quantum cryptography was discovered by H.P.Yuen based on quantum communication theory. It is applicable to direct encryption, for example quantum stream cipher based on Yuen protocol(Y-00), with high speeds and for long distance by sophisticated optical devices which can work under the average photon number per signal light pulse: <n> = 1000 ~ 10000. In addition, it may provide information-theoretic security against known/chosen plaintext attack, which has no classical analogue. That is, one can provide secure communication, even the system has H(K)<