Quantum cryptography exploits the fact that an unknown quantum state cannot be accurately copied or measured without disturbance. By using such elementary quantum states to represent binary information it is possible, therefore, to construct communication systems with verifiable levels of security that are 'guaranteed' by fundamental quantum mechanical laws. This paper describes recent progress at BT Laboratories in the development of practical optical fiber- based quantum cryptography system. These developments include interferometric systems operating in the 1.3 micrometers - wavelength fiber transparency window over point-to-point links up to approximately 50km in length and on multi-user passive optical networks. We describe how this technology performs on fiber links installed in BT's public network and discuss issues such as cross-talk with conventional data channels propagating at different wavelengths in the same fiber.

An experimental free-space quantum key distribution (QKD) system has been tested over an outdoor optical path of approximately 1 km under nighttime conditions at Los Alamos National Laboratory. This system employs the Bennett 92 protocol; here we give a brief overview of this protocol, and describe our experimental implementation of it. An analysis of the system efficiency is presented as well as a description of our error detection protocol, which employs a 2D parity check scheme. Finally, the susceptibility of this system to eavesdropping by various techniques is determined, and the effectiveness of privacy amplification procedures is discussed. Our conclusions are that free-space QKD is both effective and secure; possible applications include the rekeying of satellites in low earth orbit.

The positive operator valued measure (POVM), also known as the probability operator valued measure, is useful in quantum information processing. The POVM consists of a set of non-negative quantum-mechanical Hermitian operators that add up to the identity. The probability that a quantum system is in a particular state is given by the expectation value of the POVM operator corresponding to that state. Following a brief review of the mathematics and history of POVMs in quantum theory, and a pedagogical discussion of the quantum mechanics of photonic qubits, a particular implementation of a POVM for use in the measurement of photonic qubits is reviewed.

Decoherence is studied in an attractive proposal for an actual implementation of a quantum computer based on trapped ions.Emphasis is placed on the decoherence arising from the vibrational motion of the ions, which is compared with that due to spontaneous emission from excited states of the ions. The calculations is made tractable by exploiting the vast difference in time scales between the vibrational excitations and the intra-ionic electronic excitations. Since the latter are several orders of magnitude faster, an adiabatic approximation is used to integrate them out and find the inclusive probability for the electronic state of the ions to evolve as it would in the absence of vibrational coupling, and the ions to evolve into any state whatsoever. The decoherence time is found at zero temperature and for any number of ions N in the computer. Comparison is made with the spontaneous emission decoherence, and the implications for how trap voltages and other parameters should be scaled with N are discussed.

We present an extension of the projection synthesis technique which allows, at least in principle, the determination of the probability distribution of any physical observable of a quantized optical field mode. This involves directly measuring a quantity proportional to the squared modulus of the projection of an input pure state onto the eigenstate associated with the observable to be measured. It is found that we need to synthesize a specific reference state conditioned upon the property under investigation. A general expression for these reference states is given. We provide the specific reference states needed to synthesize a measurement of canonical phase. A variant on homodyne detection is investigated using projection synthesis and we form the probability operator measure (POM) required to characterize the measurement. The POM is not that which is formed in conventional balanced homodyne detection. As an application, we utilize these results to form the POM and a quasi probability distribution function associated with a measurement scheme used to distinguish between nonorthogonal coherent states.

We describe an on-going experimental investigation of a newly predicted mechanism for the production of nonlinear interactions between two photons. This mechanism involves nonlocal cooperative effects between pairs of atoms and exists only at the quantum level. An optical approach to quantum computing based on this effect may have many practical advantages.

This paper explores the limitations that interaction between the physical qubits making up a quantum computer may impose on the computer's performance. For computers using atoms as qubits, magnetic dipole-dipole interactions are likely to be dominant; various types of errors which they might introduce are considered here. The strength of the interaction may be reduce by increasing the distance between qubits, which in general will make the computer slower. For ion-chain based quantum computers the slowing down due to this effect is found to be generally more sever than that due to other causes. In particular, this effect alone would be enough to make these systems unacceptably slow for large-scale computation, whether they use the center of mass motion as the 'bus' or whether they do this via an optical cavity mode.

Quantum computers are able to operate on coherent superpositions of states, and to isolate a single global property of the set of computed quantities via interference. In principle, this permits them to solve certain problems exponentially faster thana classical computer, but not one has yet succeeded in implementing a true quantum computer on more than two quantum bits. Recently, however, it has been found that an ensemble of independent and identical quantum computers can perform mots of the same feats than a single quantum computer could, while at the same time bringing massive classical parallelism to bear on its computations. Such an ensemble quantum computer can be realized, to a limited extent, by nuclear magnetic resonance (NMR) spectroscopy on ordinary liquids at room temperature and pressure. This simple implementation depends on special kinds of mixed states, called pseudo-pure states, whose preparation entails a loss of signal that is exponential in the number of spins. While this would appear to limit such an implementation to ca. 8-10 spins in the foreseeable future, NMR spectroscopy has now permitted the first experimental demonstrations of all the basic features of quantum computing. We claim, moreover, that the product operator formalism, on which the theory of NM R spectroscopy is based, provides an efficient framework within which to analyze algorithms and decoherence effects in quantum computing more generally. This is illustrated by presenting our recent experimentally implementation of a quantum error correcting code.

Strongly coupled cavity QED systems show great promise for coherent processing of quantum information in the contexts of quantum computing, communication and cryptography. We present here current progress in experiments for which single atoms are strongly coupled to the mode of a high finesse optical resonator.

Wave Function Rearrangement Quantum Devices (WFR QD) make it possible to create CMOS-like circuits. The major problem of logic design for WFR QD is providing logically inverting conductivity in the upper and lower quantum wells. It is shown that when the quantum wells have collinear conductivity, one quantum device correctly realizes only self-dual Boolean functions. A new configuration of WFR QD is suggested in which the upper and lower quantum wells have orthogonal conductivity. In this case, when extra separation and conjaction pads are incorporated, one WFR QD can realize an arbitrary Boolean function in the parallel-serial form.

Implementation of the present form of the Shor factoring algorithm for numbers large enough to interest cryptographers and number theorists may pose problems of precision of measurement that apparently have received less attention than the problems of maintaining coherence during the algorithm's unitary transformations on its quantum registers. Hence, those whose primary interest is a major advancement of computational power may reasonably ask if other physical phenomena or other algorithm design principles might pose milder technical difficulties while providing desired computations. Recalling that Hopfield and Tank's neural network formula for solving the traveling salesman problem was originally inspired by the Hamiltonians of spin glasses has led to a possible spin-relaxation method for solving factorization problems. The search process starts at quasi-Monte Carlo points that in research on numerical integration have been shown to be adequate samples of unit hypercubes. Feasibility of implementation of this method has not been shown, with two evident types of difficulty: initializing a spin system to the quasi-Monte Carlo points, and achieving the needed wide dynamic range of couplings between spins. As real spin system both evolve unitarily under conditions where coupling to the rest of the world can be neglected and display relaxation behavior where coupling is significant, there may be a useful complementarily between unitary transformations and relaxation processes in implementing different phases of a computation, and alternating between them would provide some degree of noise suppression comparable to that found in conventional digital technology. The strategy of equipartitioning searches provides a possible framework for factoring some computations into feasible portions.

We discuss a difference model of the linear harmonic oscillator based on the Meixner polynomials. As limit and special cases, it contains difference oscillator models in terms of the Kravchuk and Charlier polynomials, as well as the wavefunctions of the linear harmonic oscillator in quantum mechanics. We show that the dynamical group is SU(1,1) and construct explicitly the corresponding coherent state. The reproducing kernel for the wavefunctions of the Meixner model is also found.

Overlap integrals over the full real line for a family of q- extensions of the linear harmonic oscillator wave functions in quantum mechanics are evaluated. In particular, an explicit form of the squared norms for these q-wave functions is obtained. The classical Fourier-Gauss transform connects the families with different values 0 < q < 1 and q < 1 of the deformation parameter q. An explicit expansion of the q-Hermite polynomials of Rogers in terms of the ordinary Hermite polynomials emerges as a by-product.

Two-level quantum system, described by non-relativistic Schroedinger equations in a matrix form with a potential, causing quantum deterministic chaos through the cascade of period doubling bifurcations has been considered. Bifurcations in this case correspond to series of quantum nutation of nutations. It was shown that quantum computation underlie the working of biological neural networks.

This paper proposes a novel solid state quantum CCN gate having a lock structure, which is effective to maintain quantum mechanical coherence and reduce both the bit error and the phase error. The stability of the dipole-dipole interaction in quantum dot array is estimated. Furthermore, the spatiotemporal dynamics of quantum computing process involving the quantum entangled pure states is illustrated.