This PDF file contains the front matter associated with SPIE Proceedings Volume 6573, including the Title Page, Copyright information, Table of Contents, and the Conference Committee listing.

Currently there is interest in the possibility of using quantum-mechanically entangled light to enhance the spatial resolution of sensors. Here I review some applications of equations in quantum-mechanical form to the design of sensors and related systems. In order to consider comparing equations against experiments, we will need to distinguish models comprised of mathematical formulas, whether quantum-mechanical or classical, from experiments with devices such as lasers and light detectors. The following sections sketch: * two known ways to connect quantum models to experiments (one statistical-mechanical, the other by way of probabilities); * an approximate way to translate from equations of classical electromagnetism to the quantum language of photons and detection probabilities, concentrating on interferometric effects; * quantum-mechanically suggested possibilities and obstacles for light-based radar (lidar) to enhance positional accuracy and spatial resolution; * a recently proved universal gap between, on one hand, quantum-mechanical models composed of equations and, on the other hand, experiments with devices, with the consequent need and opportunities for a designer to choose models as descriptions of measured behavior.

We present a review of our recent results for the comparative evaluation of the induced exchange interaction and quantum noise mediated by the bosonic environment in two-qubit systems. We report new calculations for P-donor-electron spins in Si-Ge type materials. Challenges and open problems are discussed.

The model of quantum computation developed by Kitaev (¹ ,∮4.1) shows that a perfect, error-free, quantum computer can lead to reliable classical outputs, despite the need to apply a necessarily probabilistic measurement. In this paper we extend the analysis to account for necessarily imperfect quantum computation. The analysis presented here is required to establish the utility of practical quantum computation even given the assumption that fault-tolerance techniques are successfully applied. This is due to the fact that the application of currently known fault-tolerance techniques does not permanently and completely remove errors. To this end we have introduced a mathematical relation that compares the accuracy of a necessarily imperfect quantum computation to a prescribed performance bound. Finally, we discuss several mathematical aspects of this bound and its usefulness in analyzing quantum computing protocols.

We design and implement a SIMD scheduler that returns the distribution of quantum operations when taking into account communication and layout constraints. We define the ion-motion path interface for trapped ion quantum computing architectures and analyze the design constraints involved in assembling the control circuitry necessary to implement this interface. Finally, we describe an Instruction Set Architecture (ISA) that we can use to optimize and provide a library of fault-tolerant building blocks for scalable quantum computation.

Much of the theory of quantum computing assumes the capacity to apply a chosen sequence of unitary transformations to the state of a quantum register (sometimes called a memory). It is widely recognized that this "application of a unitary transformation" requires an external influence. Here we relate the physics of external influences to the well established framework of quantum-mechanical scattering problems, in order to show how scattering is conceptually necessary to quantum computers, even in the idealization of zero temperature and no imperfections. For a single-qubit quantum register, infinitely slow limiting cases are shown in which scattering indeed results in a unitary transformation of the register. Implications for "transformation-induced decoherence" are developed and related to questions of errors and error correction.

This paper deals with the progress made in applications of quantum computing in control and optimization. It concentrates on applying the geometric technique in order to investigate a finite control problem of a two-level quantum system, resonance control of a three-level system, simulation of bilinear quantum control systems, and optimal control using the Bellman principle. We show that a quantum object described by a Schroedinger equation can be controlled in an optimal way by electromagnetic modes. We also demonstrate an application of these techniques and an algebra-geometric approach to the study of dynamic processes in nonlinear systems. The information processing by means of controlled quantum lattices is discussed: we present new mathematical models of classical (CL) and quantum-mechanical lattices (QML) and their application to information processing. system-theoretical results on the observability, controllability and minimal realizability theorems are formulated for cl. The cellular dynamaton (CD) based on quantum oscillators is presented. Cellular's quantum computational search procedure can provide the basis for implementing adaptive global optimization algorithms. A brief overview of the procedure is given and a framework called lattice adaptive search is set up. A method of Yatsenko and one introduced by the authors fit into this framework and are compared.

Topological quantum computation provides efficiency with fault-tolerant and error-correction to overcome decoherence problem. Here we investigate a class of topological quantum computation device. We discuss a method of constructing topological quantum scheme based on quantum walk for the state space.

To achieve scalability of NMR computers, one needs a large number of highly polarized spins in liquid nuclearspin systems at finite temperature. In quantum computing terminology, such spin-half states are (almost) pure qubit states. Producing highly polarized spins (almost pure qubit states) out of non-polarized spins (non-pure qubit states) is sometimes called "purification". From a thermodynamic point of view, purification can be viewed as cooling spins to a very low temperature. In this work, we study how classical data compression codes can be used to design cooling algorithms for both short and long molecules. We argue that so designed cooling (purification) algorithms potentially outperform other methods in terms of the closeness of the output state to the ideal pure state, which in turn implies lower output temperature. We also analyze how the mismatch of the algorithm's computational basis and the actual eigenbasis of the spins' density matrix will affect the cooling (purification) performance.

Some of our previous research showed some interesting results regarding the effect of non-zero temperature on a specified quantum computation. For example, our analysis revealed that more Grover iterations are required to amplify the amplitude of the solution in a quantum search problem when the system is found at some finite temperature. We want to further study the effects of temperature on quantum entanglement using a finite temperature field theoretical description. Such a framework could prove to be useful for the understanding of computational dynamics inside a quantum computer. Other issues that we will address in our discussion include analytical descriptions of the effects of the temperature in the Von Newman entropy and others as a measure of entanglement.

We consider a database with one target item. Partial search is designed to find a part of the database [a block] containing the target item. After a user finds the target block he/she might want to make another partial search: subdivide the target block into sub-blocks and look for a sub-block containing the target item. An example: if we need to go to a hotel, we first look at a State map [to find highways] and then at a town map [to find a local approach to the hotel]. Number of queries necessary for sequential searches is calculated in the paper. Sequential partial search can be done faster the first one.

We study the quantum complexity of algorithms for optimal graph traversal problems. We look at eulerian tours, optimal postman tours, approximation of travelling salesman tours and self avoiding walks. We present quantum algorithms and quantum lower bounds for these problems. Our results improve the best classical algorithms for the corresponding problems.

Quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given in a black box, but the aim is to compute function value for arbitrary input using as few queries as possible. In this paper we concentrate on quantum query algorithm designing tasks. The main aim of research was to find new efficient algorithms and develop general algorithm designing techniques. We present several exact quantum query algorithms for certain problems that are better than classical counterparts. Next we introduce algorithm transformation methods that allow significant enlarging of sets of exactly computable functions. Finally, we propose quantum algorithm designing methods. Given algorithms for the set of sub-functions, our methods use them to design more complex one, based on algorithms described before. Methods are applicable for input algorithms with specific properties and preserve acceptable error probability and number of queries.

Weak values are the outcomes of weak measurements and were discovered by studying the time-symmetric aspects of quantum mechanics. This resulted in new approaches to quantum cryptography and new resources for quantum information. In this article, new non-statistical aspects of weak measurements are introduced. Contary to past results, this outcome is not rare, suggesting that weak values are a property of every individual pre-and-post-selected system.

Quantum information processing's objective is to utilize revolutionary computing capability based on harnessing the paradigm shift offered by quantum computing to solve classically hard and computationally challenging problems. Some of our computationally challenging problems of interest include: the capability for rapid image processing, rapid optimization of logistics, protecting information, secure distributed simulation, and massively parallel computation. Currently, one important problem with quantum information processing is that the implementation of quantum computers is difficult to realize due to poor scalability and great presence of errors. Therefore, we have supported the development of Quantum eXpress and QuIDD Pro, two quantum computer simulators running on classical computers for the development and testing of new quantum algorithms and processes. This paper examines the different methods used by these two quantum computing simulators. It reviews both simulators, highlighting each simulators background, interface, and special features. It also demonstrates the implementation of current quantum algorithms on each simulator. It concludes with summary comments on both simulators.

Quantum experiments are described in terms of time-dependent networks of quantum bits, each qubit representing an elementary information gateway. The emphasis is on the signal properties of apparatus rather than on systems under observation (SUOs), with the quantum states of the theory (the labstates) representing the observer's information about the state of their apparatus, rather than of any SUO. The formalism gives an efficient quantum register description related to the formalism of quantum computation. Experiments conventionally described by the PVM and POVM formalisms are treated in identical terms, the formalism providing an efficient modular approach to quantum optics experiments of arbitrary complexity.

We study the phase estimation abilites of photonic N00N states, propagating in an attenuating medium, is analyzed. It is shown that N00N states of a given number of enangled photons N, never achieve the 1/N Heisenberg limit if the propagation occurs through lossy medium. It is also shown that a signal comprised of an attenuated separable state of N photons will actually produce a better phase estimate than a signal comprised of an equally attenuated N00N state unless the transmittance of the medium is very high. Thus, for most practical applications in realistic scenarios with attenuation, the resolution of N00N state-based phase estimation not only does not achieve the Heisenberg Limit, but is actually worse than the 1/(square root of)N Standard Quantum Limit. This performance deficit becomes more pronounced as the number, N, of photons in the signal increases.

I first review positive-operator and projection valued measures in quantum mechanics, and then address a few applications in quantum key distribution (QKD). The positive operator valued measure (POVM) is useful in the design of a quantum key receiver. The projection valued (PV) measure is useful in the design of QKD eavesdropping devices. In this case the measurement determines correlations with the measurements made by the lefitimate receiver and therewith the maximum information gain by the probe. It is essential to know the latter for privacy amplification.

The theoretical framework for a principled procedure to encrypt/decrypt covert information (code)into/from the null spaces of a hierarchy of statistical distributions possessing ill-conditioned eigenstructures, is suggested. The statistical distributions are inferred using incomplete constraints, employing the generalized nonextensive thermostatistics (NET) Fisher information as the measure of uncertainty. The hierarchy of inferred statistical distributions possess a quantum mechanical connotation for unit values of the nonextensivity parameter. A systematic strategy to encrypt/decrypt code via unitary projections into the null spaces of the ill-conditioned eigenstructures, is presented.

Cryptology and information security are set to play a more prominent role in the near future. In this regard, quantum communication and cryptography offer new opportunities to tackle ICT security. Quantum Information Processing and Communication (QIPC) is a scientific field where new conceptual foundations and techniques are being developed. They promise to play an important role in the future of information Security. It is therefore essential to have a cross-fertilizing development between quantum technology and cryptology in order to address the security challenges of the emerging quantum era. In this article, we discuss the impact of quantum technology on the current as well as future crypto-techniques. We then analyse the assumptions on which quantum computers may operate. Then we present our vision for the distribution of security attributes using a novel form of trust based on Heisenberg's uncertainty; and, building highly secure quantum networks based on the clear transmission of single photons and/or bundles of photons able to withstand unauthorized reading as a result of secure protocols based on the observations of quantum mechanics. We argue how quantum cryptographic systems need to be developed that can take advantage of the laws of physics to provide long-term security based on solid assumptions. This requires a structured integration effort to deploy quantum technologies within the existing security infrastructure. Finally, we conclude that classical cryptographic techniques need to be redesigned and upgraded in view of the growing threat of cryptanalytic attacks posed by quantum information processing devices leading to the development of post-quantum cryptography.

A six-user quantum key distribution over a bus network spanning a total distance 30km of standard telecommunication-grade fiber is demonstrated. Each user on the network has one unique address wavelength channel for establishing secure quantum cryptographic keys with a central network server. The address wavelengths are all in the C-band region of between 1553 nm and 1557 nm, making the system compatible with present fiber-optic communication network infrastructures. The quantum bit error rate measurements made on the network agree favorably with theoretically calculated values.

Based on the law of quantum mechanics we present a simple authorization scheme: Quauth. The description of the scheme is given in details. The authorization is accomplished through a quantum channel by one way communication. We show that eavesdropper gets no information about key no matter how many times s/he is listening on the channel. The scheme is robust against both the passive and active attacks. By induction we prove that the scheme is information theoretically secure.

Quantum correlations or entanglement is a basic ingredient for many applications of quantum information theory.One important application using quantum entanglement exploits the correlation nature of entangled photon states is quantum key distribution, which is proven unbreakable in principle and provides the highest possible security that is impossible in classical information theory. However, generating entangled photon pairs is not a simple task -- only approximately one out of a million pump photons decay into a signal and idler photon pair. This low rate of entangled photon pairs is further reduced by the overhead required in order for the rectification of the inevitable errors due to channel imperfections or caused by potential eavesdroppers. As a consequence, quantum key distribution suffers from a low bit rate, which is in the order of hundreds to thousands bits per second or below. On the other hand, the classical public key distribution does not impose a tight limit on the transmission rate. However, it is subject to the risks of eavesdroppers sitting in the middle of the insecure channel. In this paper, we propose a hybrid key distribution method which uses public key distribution method to generate a raw key, and then uses entanglement assisted communication to modify the raw key by inserting a number of quantum bits in the raw key. Building upon the foundation of the unconditional security of quantum key distribution, we use the privacy amplification to make the affection of inserted bits expand to a whole key. Our quantum entanglement assisted key distribution scheme greatly improves the efficiency of key distribution while without compromising the level of security achievable by quantum cryptography.

Let K be a 3-stranded knot (or link), and let L denote the number of crossings in of K. Let ε₁ and ε₂ be two positive real numbers such that ε₂≤1. In this paper, we create two algorithms for computing the value of the Jones polynomial V_K(t) at all points t=exp(iφ) of the unit circle in the complex plane such that |φ|≤2π/3. The first algorithm, called the classical 3-stranded braid (3-SB) algorithm, is a classical deterministic algorithm that has time complexity O(L). The second, called the quantum 3-SB algorithm, is a quantum algorithm that computes an estimate of V_K (exp (iφ)) within a precision of ε₁ with a probability of success bounded below by 1-ε₂. The execution time complexity of this algorithm is O(nL), where n is the ceiling function of (ln(4/ε₂))/2ε²₁ . The compilation time complexity, i.e., an asymptotic measure of the amount of time to assemble the hardware that executes the algorithm, is O(L).

We review the q-deformed spin network approach to Topological Quantum Field Theory and apply these methods to produce unitary representations of the braid groups that are dense in the unitary groups. The simplest case of these models is the Fibonacci model, itself universal for quantum computation. We here formulate these braid group representations in a form suitable for computation and algebraic work.

Using the Kauffman-Lomonaco method, some two-qutrits universal quantum gates are derived from the nine-dimensional unitary solutions of the Yang-Baxter equations associated with algebraic structures like the partial transpose operator and the dihedral group, which admit three dimensional representations. The Yang-Baxterization method given by Zhang-Kauffman-Ge is continuously used to obtain two-qutrits quantum gates and certain Hamiltonians for the evolution of the quantum gates are obtained, being such Hamiltonians interpreted as physical Hamiltonians of chain of particles of spin 1. Finally, the generalization for systems of two qudits is presented in the case of Yang-Baxterization of representations of braided monoidal algebra like the BH algebra and the bicolored Birman-Wenzl-Muraki algebra. For these algebras the corresponding two-qudits quantum gates are constructed jointly with the associated Hamiltonians interpreted like physical chains of particles with spin d. It is conjectured that the derived two-qdits quantum gates and the Hamiltonians may be implemented over bi-dimensional lattice systems like anyons systems or more generally over any physical systems ruled by the Yang-Baxter equations.

A martingale appears in conclusive Bayesian discrimination of two quantum states subjected to a sequence of optimal weak measurements. This martingale is solely a function of the two system states and their respective probabilities at the time of each measurement, and it directly determines the evolving probability of discrimination error. Also, it is constant if and only if the states are pure. For strictly mixed quantum states the martingle is constant just on average, with the consequence that, with some probability, the realized discrimination error probability conditioned on prior measurements may be less (better) than the optimal Helstrom error probability. So for mixed states conditionally superoptimal discrimination is possible. This phenomenon is demonstrated numerically in an example.

An overview of the Quantum Repeater techniques based on Entanglement Distillation and Swapping is provided. Beginning with a brief history and the basic concepts of the quantum repeaters, the article primarily focuses on the communication model based on the quantum repeater techniques, which mainly consists of two fundamental modules --- the Entanglement Distillation module and the Swapping module. The realizations of Entanglement Distillation are discussed, including the Bernstein's Procrustean method, the Entanglement Concentration and the CNOT-purification method, etc. The schemes of implementing Swapping, which include the Swapping based on Bell-state measurement and the Swapping in Cavity QED, are also introduced. Then a comparison between these realizations and evaluations on them are presented. At last, the article discusses the experimental schemes of quantum repeaters at present, documents some remaining problems and emerging trends in this field.

This paper focuses on "time-extended" properties that quantum mechanics represents as existing at a given moment, but which cannot be measured at a given moment. Several examples are presented in which the energy cannot be measured in a short time. The essence of these examples is an attempt to measure the momenta (or the energy) of an ideal quantum clock by having an interaction that lasts only a short time, where this short time is defined with respect to the internal time which is conjugate to this momenta. However, this momenta and this time cannot both be definite at once, even though quantum mechanics claims that a definite energy should be definite at a definite time. However, the momenta can be definite at a definite external parameter time, rather than this internal time. From the internal perspective, however, it is shown that the energy cannot be defined at a given internal time and therefore, this aspect of "time-extension" is completely quantum in origin, unlike the classical aspect of "energy is frequency." An additional consequence of time extended properties is that the connection between the internal time before and after the energy measurement is made uncertain. This suggests that the complementarity between energy and time is deeper than the notion that precise measurements of energy take a long time. Going beyond the "negative" statements about what cannot be measured (which characterize most of the discussions of the energy-time uncertainty relation), a positive aspect of ΔEΔt > 1 is demonstrated in a closed system based on causality. In this example, if one were to argue that energy really existed at a definite moment in time, then causality could be called into question. The standard understanding of the relationship between energy and time is that if the energy is conserved then we can calculate what the energy is at any point in time and thus we should be able to speak about energy as actually existing at that definite moment in time. This section challenges that assertion and is motivated by the question: "is there an example in physics of a property that the formalism tells us exists at a given moment, but which cannot be checked at a given time?"

As a resource, quantum entanglement provides enormous power to quantum information processing and quantum communication. We focus on new properties of entanglement as revealed by quantum weak measurements. Weak measurements are performed between a pre-selected and post-selected states, one, or both or which are entangled.

Many quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given by a black box. As in the classical version of decision trees, different kinds of quantum query algorithms are possible: exact, with bounded error and even nondeterministic. In this paper, we study the latter class of algorithms. We introduce a new notion in addition to already studied nondeterministic algorithms and introduce dual nondeterministic quantum query algorithms. We examine properties of such algorithms and prove relations with exact and nondeterministic quantum query algorithm complexity. As a result and as an example of the application of discovered properties, we demonstrate a gap of n vs. 2 between classical deterministic and dual nondeterministic quantum query complexity for a specific Boolean function. Finally, we show an approach how to construct examples where quantum nondeterministic complexity of an algorithm is O(1), however classical deterministic algorithm for the same function would require O(n) queries.