We describe a phase-encoded quantum key distribution system the uses continuous control of receiver-interferometer path length to maintain alignment with the transmitter. In this fiber-based system, a small number of training frames are sent over the quantum channel that allow the receiver to compensate for drift in the transmitter and receiver interferometers due to slow changes in temperature. The system is self-starting after disruption and can maintain a quantum bit error rate of less than 7% for phase drift rates of 0.5 deg/sec. The control system design is described and measured system data is compared with simulations.

We present results of experimental demonstration of secure Quantum Key Distribution (QKD) at Elsag spa based on the implementation of BB84 protocol using polarization entangled states produced in the nonlinear process of type-II spontaneous parametric down conversion (SPDC). This enables us to avoid the use of active polarization modulation components and increases the overall key distribution rate. The high quality of polarization-entangled state generated by parametric down conversion and the high efficiency of coupling entangled-photon pairs into a single-mode optical fiber has enabled us to perform QKD with quantum bit-error rate compatible with acceptable security levels. The complete software system architecture includes a QKD protocol implementing all phases of the key distillation process. The system runs in a server and two users configuration on three different PCs connected over a local area network (LAN). Friendly graphical user interfaces (GUI) are available to start and to monitor the whole key generation and distillation process.

Users of a quantum cryptographic system face a problem of deciding on the ignorance of a maximally adroit eavesdropper concerning their key material. It is known that there can be no sure, positive, lower bound on any plausible measure of ignorance, and for this reason we characterize the problem as the making of an informed guess, meaning a guess that employs a rule that can be shown to work except in unlikely cases. As the measure of an eavesdropper's ignorance concerning n bits of sifted key material less some number k of bits found in error and discarded, we analyze Renyi entropy of arbitrary order R, for 1 ≤ R ≤ 2. We offer a rule for deciding on Renyi entropy based on a tighter bound on the relevant probability distributions than has been available. To this end, we employ a recently derived approximation to the cumulative binomial distribution which is uniformly accurate over a larger domain than previously available approximations. This results in a longer distilled key than that obtained from looser bounds, as well as generalizing the order R. Some numerical examples are presented.

Quantum cryptography has attracted much recent attention due to its potential for providing secret communications that cannot be decrypted by any amount of computational effort. This is the first analysis of the secrecy of a practical implementation of the BB84 protocol that simultaneously takes into account and presents the full set of analytical expressions for effects due to the presence of pulses containing multiple photons in the attenuated output of the laser, the finite length of individual blocks of key material, losses due to error correction, privacy amplification, and authentication, errors in polarization detection, the efficiency of the detectors, and attenuation processes in the transmission medium. The analysis addresses eavesdropping attacks on individual photons rather than collective attacks in general. Of particular importance is the first derivation of the necessary and sufficient amount of privacy amplification compression to ensure secrecy against the loss of key material which occurs when an eavesdropper makes optimized individual attacks on pulses containing multiple photons. It is shown that only a fraction of the information in the multiple photon pulses is actually lost to the eavesdropper.

We report on the construction of polarization-entangled photon sources for quantum key distribution (QKD) testbed using nonlinear optical process of spontaneous parametric down-conversion (SPDC) pumped by a 266-nm and 351-nm continuous wave (cw) and a 415-nm femtosecond-pulsed laser sources. The efficient coupling of down-converted photons at 702 nm and 830 nm into optical single-mode fiber has enabled us to increase the rate of entangled-photon pairs available for transmission over communication channels with a high degree of polarization entanglement. The detection and characterization of the entangled-photon-state properties has been performed using commercially available Silicon avalanche photodiodes (APD) as well as using a novel photon-number-resolving cryogenic photodetector, which has been developed by our colleagues at the Boulder Division of NIST and brought to BU for tests with elements of the future DARPA Quantum Network.

This paper gives a criterion for detecting the entanglement of a quantum state, and uses it to study the relationship between topological and quantum entanglement. It is fundamental to view topological entanglements such as braids as entanglement operators and to associate to them unitary operators that are capable of creating quantum entanglement. The entanglement criterion is used to explore this connection.

By quantum mechanics principle, two remote parties that have never interacted each other can be entangled through entanglement swapping operation done by a third party. Currently existing entanglement swapping experiments are done probabilistically by post-selection, i.e., once a successful swapping is verified, the resultant entanglement is destructed. We propose a simple non-post-selection scheme to probabilistically make the high quality quantum entanglement swapping with the spontaneous parametric down conversion(SPDC) process. After the swapping, two spatially separated parties who have never interacted each other are entangled through a single photon entangled state. Our scheme only requires the normal photon detectors which can distinguish the vacuum and non-vacuum Fock states.

A quantum state which can be written as a convex sum of product states is a separable state; such a convex sum allows for a local description. There are many different local descriptions for a given separable state, and some new results about the minimal number of product states in the convex sum wil be given in this paper. Any quantum state is either entangled or separable. However it is very difficult to tell whether a given state is separable or entangled. This difficulty has not been solved yet although a lot of separability criteria have already be proposed. The various separability criteria will also be discussed.

In this paper we show how to construct two continuous variable and one continuous functional quantum hidden subgroup (QHS) algorithms. These are respectively quantum algorithms on the additive group of reals R, the additive group R/Z of the reals R mod 1, i.e., the circle, and the additive group Paths of L² paths x:[0,1] → Rⁿ in real n-space Rⁿ.

We employ quantum mechanical principles in the computability exploration of the class of classically noncomputable Hilbert's tenth problem which is equivalent to the Turing halting problem in Computer Science. The Quantum Adiabatic Theorem enables us to establish a connection between the solution for this class of problems and the asymptotic behavior of solutions of a particular type of time-dependent Schrodinger equations. We then present some preliminary numerical simulation results for the quantum adiabatic processes corresponding to various Diophantine equations.

If a large Quantum Computer (QC) existed today, what type of physical problems could we efficiently simulate on it that we could not simulate on a classical Turing machine? In this paper we argue that a QC could solve some relevant physical "questions" more efficiently. The existence of one-to-one mappings between different algebras of observables or between different Hilbert spaces allow us to represent and imitate any physical system by any other one (e.g., a bosonic system by a spin-1/2 system). We explain how these mappings can be performed showing quantum networks useful for the efficient evaluation of some physical properties, such as correlation functions and energy spectra.

For a real number r > 0, let F(r) be the family of all stationary completely ergodic quantum sources with von Neumann entropy rates less than r. We prove that, for any r > 0, there exists a blind, source-independent block compression scheme which compresses every source from F(r) to rn qubits per input block length n with arbitrarily high fidelity for all large n. As our second result, we show that the stationarity and the ergodicity of a quantum source {ρm}_m=1^∞ are preserved by any trace-preserving completely positive linear map of the tensor product form ε^⊗m, where a copy of ε acts locally on each spin lattice site. We also establish ergodicity criteria for so called classically-correlated quantum sources.

We present a modificaton of Simon's Algorithm that in some cases is able to fit experimentally obtained data to appropriately chosen trial functions with high probability. Modulo constants pertaining to the reliability and probability of success of the algorithm, the algorithm runs using only O[polylog(|Y|)] queries to the quantum database and O[polylog(|X|,|Y|)] elementary quantum gates where |X| is the size of the experimental data set and |Y| is the size of the parameter space. We discuss heuristics for good performance, analyze the performance of the algorithm in the case of linear regression, both one-dimensional and multidimensional, and outline the algorithm's limitations.

In recent years, computer graphics has emerged as a critical component of the scientific and engineering process, and it is recognized as an important computer science research area. Computer graphics are extensively used for a variety of aerospace and defense training systems and by Hollywood's special effects companies. All these applications require the computer graphics systems to produce high quality renderings of extremely large data sets in short periods of time. Much research has been done in "classical computing" toward the development of efficient methods and techniques to reduce the rendering time required for large datasets. Quantum Computing's unique algorithmic features offer the possibility of speeding up some of the known rendering algorithms currently used in computer graphics. In this paper we discuss possible implementations of quantum rendering algorithms. In particular, we concentrate on the implementation of Grover's quantum search algorithm for Z-buffering, ray-tracing, radiosity, and scene management techniques. We also compare the theoretical performance between the classical and quantum versions of the algorithms.

We investigate the storage and retrieval of an image in a multi-particle quantum mechanical system. Several models are studied and compared with corresponding classical digital methods. We consider a situation in which qubits replace classical bits in an array of pixels and show several advantages. For example, we consider the situation in which 4 different values are randomly stored in a single qubit and show that quantum mechanical properties allow better reproduction of original stored values compared with classical (even stochastic) methods. The retrieval process is uniquely quantum (involves measurement in more than one bases). The independence and the finiteness of the stored copies of the image play an important role in the quantum protocol being better than the classical one. Other advantages of quantum storage of an image are found in its security.

This paper presents a quantum optimization problem and solid-state quantum computing architectures. Quantum approach to global optimization and NP-complete problems are considered. Our approach to global optimization based on quantum mechanical entanglement, quantum resonant tunneling, cellular automaton and geometric control methods. A quantum optimization algorithm combines the properties of classical simulated annealing with the possibility of quantum tunneling between the minima. Quantum computation exploits the property of quantum states to implement quantum parallelism for global nonconvex optimization problem. This paper considers new mathematical models of classical (CL) and quantum-mechanical lattices (QML). System-theoretic results on the observability, controllability and minimal realizability theorems are formulated for CL. The cellular dynamaton (CD) based on quantum oscillators is presented. We investigate the conditions when stochastic resonance can occur through the interaction of dynamical neurons with intrinsic deterministic noise and an external periodic control.

We have developed a new class of superconducting single-photon detectors (SSPDs) for ultrafast counting of infrared (IR) photons for secure quantum communications. The devices are operated on the quantum detection mechanism, based on the photon-induced hotspot formation and subsequent appearance of a transient resistive barrier across an ultrathin and submicron-wide superconducting stripe. The detectors are fabricated from 3.5-nm-thick NbN films and they operate at 4.2 K inside a closed-cycle refrigerator or liquid helium cryostat. Various continuous and pulsed laser sources have been used in our experiments, enabling us to determine the detector experimental quantum efficiency (QE) in the photon-counting mode, response time, time jitter, and dark counts. Our 3.5-nm-thick SSPDs reached QE above 15% for visible light photons and 5% at 1.3 - 1.5 μm infrared range. The measured real-time counting rate was above 2 GHz and was limited by the read-out electronics (intrinsic response time is <30 ps). The measured jitter was <18 ps, and the dark counting rate was <0.01 per second. The measured noise equivalent power (NEP) is 2 x 10^-18 W/Hz^1/2 at λ = 1.3 μm. In near-infrared range, in terms of the counting rate, jitter, dark counts, and overall sensitivity, the NbN SSPDs significantly outperform their semiconductor counterparts. An ultrafast quantum cryptography communication technology based on SSPDs is proposed and discussed.

Based on resonant atomic interactions with classical fields and dispersive couplings with quantized cavity fields we discuss schemes for the implementation of certain quantum computing algorithms. In particular we discuss implementations of Grover's algorithm and the quantum Fourier transform.

Ever since Knill, Laflamme and Milburn [Nature (London) 409, 46 (2001)] showed that nondeterministic quantum logic operations could be performed with linear optical elements, additional photons (ancilla) and projective measurements, the idea of linear-optics quantum computation has attracted considerable interest. Our group has recently demonstrated several devices of this kind. We give an overview of recent experimental results, including the quantum parity check, the destructive controlled-NOT, and a cyclical quantum memory. The need for high-efficiency detection of single photons, and for detectors capable of distinguishing photon number will be discussed. Some experimental improvements towards meeting that need will be presented.

Algorithmic cooling is a method devised by Boykin, Mor Rowchodhury, Vatan and Vrijen (PNAS Mar '02) for initializing NMR systems in general and NMR quantum computers in particular. The algorithm recursively employs two steps. The first is an adiabatic entropy compression of the computation qubits of the system. The second step is an isothermal heat transfer from the system to the environment through a set of reset qubits that reach thermal relaxation rapidly. To allow experimental algorithmic cooling, the thermalization time of the reset qubits must be much shorter than the thermalization time of the computation qubits. We investigated the effect of the paramagnetic material Chromium Acetylacetonate on the thermalization times of computation qubits (carbons) and reset qubit (hydrogen). We report here the accomplishment of an improved ratio of the thermalization times from T₁(H)/T₁(C) of approximately 5 to around 15. The magnetic ions from the Chromium Acetylacetonate interact with the reset qubit reducing their thermalization time, while their effect on the less exposed computation qubits is found to be weaker. An experimental demonstrating of non adiabatic cooling by thermalization and magnetic ion is currently performed by our group based on these results.

Future quantum information processing devices will require the use of exotic quantum states, such as specially crafted entangled states, to achieve certain desired computations on demand. Thus far, synthesis schemes for such states have been devised on a case-by-case basis using ad hoc techniques. In this paper we present a systematic method for finding a quantum circuit that can synthesize any pure or mixed n-qubit state. We then give examples of the use of our algorithm for finding synthesis pathways for especially exotic quantum states such as maximal mixed states. It is not known how to prepare general instances of such states by other means. Thus our quantum state synthesis algorithm should be of use not only in quantum information processing, but also in experimental quantum physics.

An essential component of any quantum computer is the quantum memory, the content of which is a pure quantum state. A program to study the quantum memory is initiated here, where the spatial variables are of central importance. The presence of the spatial variables makes it possible to apply the powerful and well-developed theory of scattering: The fundamental operations of writing on, reading and resetting the quantum memory are all performed through scattering from the memory. The requirement that the quantum memory must remain in a pure state after scattering implies that the scattering is of a special type, and only certain incident waves are admissible. Models based on the coupled-channel Schrodinger equation for potential scattering are formulated, where there is indeed the required large collection of admissible incident waves. On the basis of these models, certain types of decoherence are unavoidable. Such decoherence and the necessity of using the relativistic Schrodinger equation are discussed. One of the implications of quantum memory is the possible lack of security for the quantum key distribution in quantum cryptography.

We propose a method of single photon detection of infrared (IR) photons at potentially higher efficiencies and lower noise than allowed by traditional IR band Avalanche Photodiodes (APD). By up-converting the photon from IR, e.g., 1550 nm, to a visible wavelength in a nonlinear crystal, we can utilize the much higher efficiency of visible wavelength APDs. We have used a nonlinear crystal -- Periodically Poled Lithium Niobate (PPLN) -- and a pulsed 1064-nm Nd:YAG laser to perform the up-conversion to a 631-nm photon. When properly quasi-phase-matched, PPLN provides a large enough second order nonlinear susceptibility that near unit conversion efficiency of the IR photon into the visible should be possible. We have been able to observe peak conversion efficiencies as high as 80%, and have demonstrated scaling down to the single photon level while maintaining a background of 3 x 10^-4 dark counts/count. Since the PPLN only acts on one polarization of the single photon, we also propose a 2-crystal extension of this scheme whereby orthogonal polarizations may be up-converted coherently, thereby enabling complete quantum state transduction.

A fully optical method to perform any quantum computation with optical waveguide modes is proposed by supplying the prescriptions for a universal set of quantum gates. The proposal for quantum computation is based on implementing a quantum bit with two normal modes of multi-mode waveguides. The proposed universal set of gates has the potential of being more compact and easily realized than other optical implementations, since it is based on planar lightwave circuit technology and can be constructed by using Mach-Zehnder interferometer configurations having semiconductor optical amplifiers with very high refractive nonlinearity in its arms.

Following a review of the physics of quantum decoherence, an instructive comparison is made between the mathematical description of qubit decoherence due to interaction with the environment, and certain aspects of the problem of Wigner's friend.

Methods for quantifying environmentally induced decoherence in quantum systems are investigated. We formulate criteria for measuring the degree of decoherence and consider several representative examples, including a spin interacting with the modes of a bosonic, e.g., phonon, bath. We formulate an approach based on the operator norm measuring the deviation of the actual density matrix from the ideal one which would describe the system without environmental interactions.

In light of the lessons learned in the last 35 years from the quantum statistical mechanics description of phase transitions, I argue that the dichotomy in the evolution of quantum systems proposed by von Neumann, and pursued by Wigner in spite of the Einstein--Bohr criticisms on the attendent lack of resolution in terms of classical reality, fails to take into account the middle term suggested by the existence of superselection rules, Wigner's own discovery (with Wightmann and Wick). I claim that the part of the measurement problem concerned with the stable transfer of microscopic information to macroscopic physics can be treated entirely within the framework of a deterministic, conservative evolution of the joint system, i.e. without requiring the type of evolution von Neumann proposed besides that governed by the Schroedinger equation. I sustain this claim with the use of an exactly solvable model akin to the x-y model of statistical mechanics and involving its thermodynamical limit.

We consider semiconductor double dot system with single electron localized in it as quantum bit (qubit) candidate for quantum computing purposes. The interaction of qubit with environment (phonon bath) and detector (quantum point contact) lead to modification of electron dynamics. Phonon induced decoherence rates are obtained. Detector current noise spectrum is derived.

Quantum lattice gas algorithms are developed for the coupled-nonlinear Schrodinger (coupled-NLS) equations, equations that describe the propagation of pulses in birefringent fibers. When the cross-phase modulation factor is unity, the coupled-NLS reduce to the Manakov equations. The quantum lattice gas algorithm yields vector solitons for the fully integrable Manakov system that are in excellent agreement with exact results. Simulations are also presented for the interaction between a turbulent 2-soliton mode and a simple NLS 2-soliton mode. The quantum algorithm requires 4 qubits for each spatial node, with quantum entanglement required only between pairs of qubits through a unitary collision operator. The coupling between the qubits is achieved through a local phase change in the absolute value of the paired qubit wave functions. On symmetrizing the unitary streaming operators, the resulting quantum algorithm, which is unconditionally stable, is accurate to O(ε²).

Individual members of an ensemble of identical systems coupled to a common probe can become entangled with one another, even when they do not interact directly. We investigate how this type of multipartite entanglement is generated in the context of a system consisting of an ensemble of N two-level atoms resonantly coupled to a single mode of the electromagnetic field. In the case where N=2, the dynamical evolution is studied in terms of the entanglements in the different bipartite divisions of the system, as quantified by the I-tangle. We also propose a generalization of the so-called residual tangle that quantifies the inherent three-body correlations in this tripartite system. This allows us to give a complete characterization of the phenomenon of entanglement sharing in the case of the two-atom Tavis-Cummings model. We also introduce an entanglement monotone which constitutes a lower bound on the I-tangle of an arbitrary bipartite system. This measure is seen to be useful in quantifying the entanglement in various bipartite partitions of the TCM in the case where N > 2, i.e., when there is no known analytic form for the I-tangle.

We present the status of our work implementing a single photon on-demand source based on a multiplexed arrangement of parametric downconverters. An array of downconverters with multiplexed outputs makes it possible to create light pulses with increased probability of containing a single photon, while suppressing the probability of producing more than one photon. This is crucial for quantum cryptographic applications. Our current setup implements the scheme in a greatly simplified manner that produces photons along with a measure of the likelihood that the light pulse emitted is just a single photon. This implementation uses a virtual array of downconverters and an array of staggered length optical fibers allowing a single detector to measure a herald photon output by a series of downconverters. This single detector arrangement is a great savings considering the cost of such detectors. The timing of the herald tells us which path the herald took, which in turn, provides information on the single vs. multiphoton probabilities. So far, our work shows that the individual correlated photon peaks are clearly resolvable with our 2.4 ns delay line steps and the 1 ns full width half maximum (FWHM) of the correlated photon peaks, and that we can observe four correlated photon peaks simultaneously, a requirement to fully implement our scheme. Our current efforts are to increase the brightness and utility of the system for incorporation into a quantum communication testbed.

In this paper we present a model for quantum measurement. This scheme consists of using two polarization-entangled photons that are orthogonal to each other to probe the atom from which we want to extract some information. The atom we use here is a two-level rubidium. These levels are the 5P_3/2 and 5P_1/2 and is illustrated in Fig 1. Our initial results indicate that such a scheme can slow down the rate of measurement-induced decoherence.