We consider the problem of identifying the degree of correlation θ in the depolarization rates of an array of qubits, such as might be found in a holding register in a quantum information processing architecture. We treat this as a problem in quantum channel identification and use the quantum Fisher information about θ in the channel output to compare different candidate probe states. We consider channel probes in general pure N-qubit cat states and find that partial entanglement is always suboptimal; the best cat probe state is either separable or maximally entangled, and we lay out for any given depolarizing rate p and correlation θ, the (p, θ)-regions for which separable and maximally entangled probes each yield the most information. In the case of very large qubit arrays, we find that the quantum Fisher information obtained about θ using any pure cat probe state is asymptotically independent of the state and identically equal to the information available about a classical coin's bias from a single coin toss. Finally, we turn our attention to arrays of N qudits (with common dimension D) that are depolarizing with some correlation θ. We consider both separable and maximally entangled cat probe states and find and compare their quantum Fisher informations in both the large N and large D regimes.

We report on progress for a couple of experiments on manipulating cold atoms on a chip for quantum sensing. The first experiments are directed towards developing a compact atom interferometer on an atom chip using a double-well potential. The interferometer uses ⁸⁷Rb atoms magnetically confined in an atomic waveguide produced by wires on the surface of a lithographically patterned chip. Finite element modeling of combinations of different current configurations with various external bias fields indicated a means of coherently splitting the atomic cloud through dynamically adjusting the currents and bias fields. In these experiments we investigate real-time transformations between different double-well configurations adiabatically and non-adiabatically, and study their effects on the initially trapped atoms. Coherence properties of the two atomic wavepackets are examined. In another set of experiments we investigate the properties of bosons confined to (quasi) one dimension in our magnetic waveguide. When the atom-atom repulsive interaction becomes much larger than the kinetic energy, bosons confined in one dimension can enter a new state of matter, the Tonks-Girardeau gas, in which they behave like non-interacting fermions. However, the bosons can still occupy the same momentum state and therefore the gas cannot be fully described by either Bose-Einstein or Fermi-Dirac statistics. This transition has been observed in optical lattices but not in magnetic atom chip waveguides. We discuss the conditions for obtaining a Tonks-Girardeau gas with ⁸⁷Rb atoms in our atom chip waveguide as well as a novel signature for observing the transition in our system.

A technique to drive stimulated Raman transition between spin and/or momentum states of ultracold ⁸⁷Rb atoms confined on an atomchip trap is discussed. We present our experimental and theoretical approach to an all-optical manipulation of the atoms using an optical frequency comb emitted by a modelocked ultrafast pulsed laser.

We present a single electron transistor (SET) based on an individual phosphorus dopant atom in an epitaxial silicon environment. Using scanning tunneling microscope (STM) hydrogen lithography, the single impurity is deterministically placed with a spatial accuracy of ± 1 lattice site within a donor-based transport device. Low temperature transport measurements confirm the presence of the single donor and show that the donor charge state can be precisely controlled via gate voltages. We observe a charging energy that is remarkably similar to the value expected for isolated P donors in bulk silicon, which is in sharp contrast to previous experiments on single-dopant transport devices. We show that atomistic modeling can fully capture the effects of the highly-doped transport electrodes on the electronic states of the donor, thus highlighting the high level of control over the electrostatic device properties afforded by a deterministic single donor architecture. Our fabrication method therefore opens the door for the realization of a scalable donor-based qubit architecture in silicon.

Double-well potentials have extensive applications in many branches of physics and have resulted in devices that are useful for precision sensing as well as quantum information processing. Here, we present a theoretical analysis of the transverse phonon coupling between a pair of trapped ions as described by a double-well system. Typically the phonons in trapped ions are used as an intermediary in quantum information processing, but here we focus on the dynamics of the phonons themselves. The double-well system is a special case of the more generalized Bose-Hubbard Model, with exactly two sites available to store particles. We draw an analogy to another double-well system in solid state physics: a Josephson junction containing a thin insulating barrier between two superconductors. Applications of the Josephson junction include superconducting quantum interference devices (SQUIDs), which have emerged as sensitive magnetometers and also as qubits for quantum computation. Another analogy is the recent demonstrations of matter-wave interference with Bose-Einstein condensates in double-well traps, which have also shown great promise for applications in precise inertial and gravitational field sensing. We will also discuss experimental techniques that can be applied to control and manipulate this double-well system.

Secret keys can be established through the use of a Quantum channel monitored through classical channel which can be thought of as being error free. The quantum channel is subject to massive erasures and discards of erroneously measured bit values and as a result the error correction mechanism to be used must be accordingly modified. This paper addresses the impact of error correction (known as Reconciliation) on the secrecy of the retained bits and issues concerning the efficient software implementation of the Low Density Parity Check algorithm in the Quantum Key Distribution environment. The performance of three algorithmic variants are measured through implementations and the collected sample data suggest that the implementation details are particularly important

We develop an improvement to the weak laser pulse BB84 scheme for quantum key distribution, which utilizes entanglement to increase the security of the scheme and enhance its resilience to the photon-number-splitting attack. This protocol relies on the non-commutation of phase and number to detect an eavesdropper performing quantum nondemolition measurement on photon number. The potential advantages and disadvantages of this scheme are compared to the coherent decoy state protocol.

A quantum gate is a logically and thermodynamically reversible situation that effects a unitary transformation of qubits of superimposed information, and essentially constitutes a situation for a reversible quantum decision. A quantum decision is a symmetry break, and the effect of the function of a Szilard engine is a symmetry break. A quantum gate is a situation in which a reversible quantum decision can be made, and so if a logically and thermodynamically reversible Szilard engine can be theoretically constructed then it would function as a quantum gate. While the traditionally theorized Szilard engine is not thermodynamically reversible, if one of the bounding walls of a Szilard engine were to be constructed out of the physical information by which it functions in such a manner as to make that information available to both sides of the wall simultaneously, then such a Szilard engine would be both logically and thermodynamically reversible, and thus capable of function as a quantum gate. A theoretical model of the special case of a reversible Szilard engine functioning as a quantum gate is presented and discussed, and since a quantum decision is made when the shutter of a Szilard engine closes, the coherence of linked reversible Szilard engines should be considered as a state during which all of the shutters of linked Szilard engines are open simultaneously.

A brief review is given of possible Finsler metrics de…ned on the SU(2ⁿ) group tangent bundle which may be suitable for quantum circuit optimiza- tion.

In this paper we study an improved semantics of some basic elements in quantum computation, which can be helpful to build quantum compiler and quantum operating system.

Here we propose a new design paradigm for a superconducting nanowire single photon detector that uses a multi-layer architecture that places the electric leads beneath the nanowires. This allows for a very large number of detector elements, which we will call pixels in analogy to a conventional CCD camera, to be placed in close proximity. This leads to signicantly better photon number resolution than current single and multi-nanowire meanders, while maintaining similar detection areas. We discuss the reset time of the pixels and how the design can be modied to avoid the latching failure seen in extremely short superconducting nanowires. These advantages give a multi-layer superconducting number-resolving photon detector signicant advantages over the current design paradigm of long superconducting nanowire meanders. Such advantages are desirable in a wide array of photonics applications.

The idea of this work was to generalize the Donkor model (Quantum Information and Computation IX, edited by Eric Donkor, Andrew R. Pirich, Howard E. Brandt, Proc. of SPIE Vol. 8057) about the application of induced dipole-dipole forbidden transitions to quantum computation. Using computer algebra we were able to reproduce the original Donkor model. Then we applied some modifications to this model and obtained the respective solutions. It is expected that this model has applications for quantum computation.

The design for an all optical XOR gate is proposed. The basic idea is to split the input beams and let them cancel or strengthen each other selectively or flip the encoded information based on their polarization properties. The information is encoded in terms of polarization of the beam. Polarization of a light beam is well understood hence the design should be feasible to implement. The truth table of the optical circuit is worked out and compared with the expected truth table. Then it is demonstrated that the design complies with the linear behavior of the XOR function. In the next section, based on a similar idea, the design of an all optical CNOT gate is proposed. The truth table for the gate is verified. Then, it is discussed how this approach can be used for Linear Optics Quantum Computation (LOQC). It is shown that with a Hadamard gate and a rotation gate, the CNOT gate makes up a universal set of quantum gates based on linear optics. This novel approach requires no additional power supply, extra input beam or ancilla photon to operate. It also doesn't require the expensive and complex single photon source and detector. Only narrowband laser sources are required to operate these gates.

For classical simulation, the quantum Fourier transform (QFT) requires very large matrix operations. Previous work has shown that the semi-classical quantum Fourier transform (SCQFT) can use these individual coefficients to perform the QFT using only single-quantum bit (qubit) unitary gates and measurement operators. However, the SCQFT requires these individual decomposed qubits of the quantum system as input to the algorithm. We devise two methods to find separable approximations of quantum systems to serve as inputs to the SCQFT. We introduce an application of the approach on classical radio frequency signals represented through a quantum model. The resulting decomposition and QFT are computed on several simulated results, and an example is given using an experimental signal.

The International Second (SI) is defined in terms of a resonant frequency of cesium imagined at 0 K, differing from any measurable resonant frequency by an offset calculated from a chosen wave function. As proved in prior work, the choice of wave function cannot be determined by measured data but requires a reach beyond anything measurable or calculable, thereby bringing incalculablility, along with an element of free choice, into the definition and the realization of the second. A clock that realizes the second contains a variable-frequency oscillator controlled by a measurement model running in a computational process, and the chosen wave function is embodied in the measurement model. Embedded in a computational process, the measurement model, with its dependence on the chosen wave function, acts as an active agent, responding to incalculable detections by calculating numbers that adjust the oscillator. Because the choice of realization of a proper clock influences the measured numbers that give evidence of spacetime curvature, the chosen wave function for cesium clocks affects spacetime curvature, inviting exploration of offsets of imagined proper clocks from measurable frequencies in interesting situations, such as stellar interiors.

The Battle of the Sexes game is analyzed from quantum game theory using quantum initial states as possible strategies for two players. Quantum circuits are presented as schemes of development proposing also the use of Yang-Baxter operators as quantum gates in the circuits. This formalism is implemented using a Computer Algebra Software (CAS) due to its complex and long mathematical treatment. Payoff matrices of the players are given as the results for each case shown. Biology and finances applications are also proposed.

Quantum mutual information defined in terms of von Neumann entropy captures and quantifies all correlations, quantum and classical, between the two parts of a bipartite quantum system. Within this framework entanglement is the most distinguished type of quantum correlation, and a rich body of theory and experiment establishes that entanglement is a potent and fungible resource for quantum information processing broadly. Bipartite systems can exhibit quantum correlations beyond entanglement. Such non-classical states are called discordant in general and strictly discordant (or dissonant) when the quantum state is separable. We show that strict discord can increase the amount of information available from probing a quantum channel. We focus in this study on the qubit depolarizing channel, using quantum Fisher information to measure the information available about the channel depolarizing probability. We consider channel probes prepared, along with an ancilla, in a separable two-qubit Bell-diagonal state. We prove for Bell-diagonal probes of the qubit depolarizing channel that, in the absence of entanglement and controlling for marginal purity and degree of classical correlation, any increase in strict discord between the probe and ancilla yields an accompanying increase in available statistical information about the channel depolarizing probability.

Nielsen, et al.^{1, 2} proposed a view of quantum computation where determining optimal algorithms is equivalent to extremizing a geodesic length or cost functional. This view of optimization is highly suggestive of an action principle of the space of N-qubits interacting via local operations. The cost or action functional is given by the cost of evolution operators on local qubit operations leading to causal dynamics, as in Blute et. al.³ Here we propose a view of information geometry for quantum algorithms where the inherent causal structure determines topology and information distances^{4, 5} set the local geometry. This naturally leads to geometric characterization of hypersurfaces in a quantum cellular automaton. While in standard quantum circuit representations the connections between individual qubits, i.e. the topology, for hypersurfaces will be dynamic, quantum cellular automata have readily identifiable static hypersurface topologies determined via the quantum update rules. We demonstrate construction of quantum cellular automata geometry and discuss the utility of this approach for tracking entanglement and algorithm optimization.

Local availability of mathematics and number scaling provide an approach to a coherent theory of physics and mathematics. Local availability of mathematics assigns separate mathematical universes, x, to each space time point, x.. The mathematics available to an observer, Ox, at x is contained in x . Number scaling is based on extending the choice freedom of vector space bases in gauge theories to choice freedom of underlying number systems. Scaling arises in the description, in x, of mathematical systems in y . If ay or ψy is a number or a quantum state in y, then the corresponding number or state in x is ry,xax or ry,xψx. Here ax and ψx are the same number and state in x as ay and ψy are in y . If y = x+ μdx is a neighbor point of x, then the scaling factor is r_y,x = exp( A(x) • μdx) where A is the gradient of a scalar field. The effects of scaling and local availability of mathematics on quantum theory show that scaling has two components, external and internal. External scaling is shown above for ay and ψy. Internal scaling occurs in expressions with integrals or derivatives over space time. An example is the replacement of the position expectation value, ∫ψ*(y)yψ(y)dy, by ∫_x r_y,ψ_x* x(yx)yxψx(yx)dy_x. This is an integral in x . The good agreement between quantum theory and experiment shows that scaling is negligible in a space region, L, in which experiments and calculations can be done, and results compared. L includes the solar system, but the speed of light limits the size of L to a few light years. For observers in L and events outside L, at cosmological distances, scaling is not limited by theory experiment agreement requirements.

This paper generalizes the AJL algorithm for quantum computation of the Jones polynomial to continuous ranges of values on the unit circle for the Jones parameter and shows that the Kauffman-Lomonaco 3-strand algorithm for the Jones polynomial is a special case of this generalization. We then describe a quantum algorithm for the Jones polynomial that is related to Khovanov homology.

Possible quantum algorithms for generalized Khovanov homology and the Rasmussen's invariant are proposed. Such algorithms are resulting from adaptations of the recently proposed Kauffman's algorithm for the standard Khovanov homology. The method that was applied consists in to write the relevant quantum invariant as the trace of a certain unitary operator and then to compute the trace using the Hadamard test. We apply such method to the quantum computation of the Jones polynomial, HOMFLY polynomial, Chromatic polynomial, Tutte polynomial and Bollobàs- Riordan polynomial. These polynomials are quantum topological invariants for knots, links, graphs and ribbon graphs respectively. The Jones polynomial is categorified by the standard Khovanov homology and the others polynomials are categorified by generalized Khovanov homologies, such as the Khovanov-Rozansky homology and the graph homologies. The algorithm for the Rasmussen's invariant is obtained using the gauge theory; and the recently introduced program of homotopyfication is linked with the super-symmetric quantum mechanics. It is claimed that a new program of analytification could be development from the homotopyfication using the celebrated Atiyah-Singer theorem and its super-symmetric interpretations. It is hoped that the super-symmetric quantum mechanics provides the hardware for the implementation of the proposed quantum algorithms.

The main goal of this paper is to apply the Yang-Baxter-Rowell equation in topological quantum computation, using the symbolic computational software Maple. Initially, using Maple, I reproduced the Dye classification of the 4x4 unitary solutions of the Yang-Baxter equation. Then, also using Maple, I reproduced the solutions given by Rebecca Chen to the Yang-Baxter-Rowell equation. Finally, the obtained solutions were applied to the problem of topological quantum categorification of the chromatic polynomial for graphs. It was claimed that the Yang-Baxter-Rowell operators, considered as quantum gates, can be incorporated in quantum circuit models and quantum games, such as the Grover algorithm and the game Battle of the Sexes. It is expected that a future investigation can provide a more complete classification of the solution to the Yang-Baxter-Rowell equation and its possible applications on topological quantum computation.

While entanglement is believed to underlie the power of quantum computation and communication, it is not generally well understood for multipartite systems. Recently, it has been appreciated that there exists proper no-signaling probability distributions derivable from operators that do not represent valid quantum states. Such systems exhibit supra-correlations that are stronger than allowed by quantum mechanics, but less than the algebraically allowed maximum in Bell-inequalities (in the bipartite case). Some of these probability distributions are derivable from an entanglement witness W, which is a non-positive Hermitian operator constructed such that its expectation value with a separable quantum state (positive density matrix) ρ_sep is non-negative (so that Tr[W ρ]< 0 indicates entanglement in quantum state ρ). In the bipartite case, it is known that by a modification of the local no-signaling measurements by spacelike separated parties A and B, the supra-correlations exhibited by any W can be modeled as derivable from a physically realizable quantum state ρ. However, this result does not generalize to the n-partite case for n>2. Supracorrelations can also be exhibited in 2- and 3-qubit systems by explicitly constructing "states" Ο (not necessarily positive quantum states) that exhibit PR correlations for a fixed, but arbitrary number, of measurements available to each party. In this paper we examine the structure of "states" that exhibit supra-correlations. In addition, we examine the affect upon the distribution of the correlations amongst the parties involved when constraints of positivity and purity are imposed. We investigate circumstances in which such "states" do and do not represent valid quantum states.

This paper expands upon prior work on an entangled photon source generating six pairs of photons via spontaneous parametric down-conversion in a single pass configuration. Experimental results measuring entangled photons at 810 nm are shown and other wavelength regimes will be discussed. The design and fabrication considerations for a group velocity matched (GVM) superlattice photon source are discussed. An application of this source enables various multiqubit cluster states to be generated in a compact unidirectional configuration. This configuration simplifies the interferometric stability for any associated feed-forward methods required in photon-based quantum logic circuitry.

Methods of generating N00N, M&N, linear combinations of M&N states as well as more complicated quantum entangled and quantum hyper-entangled states will be considered. Quantum hyper-entanglement refers to quantum entanglement in more than one degree of freedom, e.g. energy-time, polarization, orbital angular momentum, etc. Internal noise and loss within the entanglement or hyper-entanglement generators and external noise and loss due to atmospheric effects and detectors are modeled. Analysis related to the devices that generate these entangled or hyperentangled states will be provided. The following will be derived: closed form expressions for wave function normalization, wave function, density operator, reduced density operator, phase error bound, the symmetrized logarithmic derivative, the quantum Fisher information, the quantum Cramer-Rao lower bound, the relevant projection operators and the related probability of detection expressions. Generation and detection of the entangled or hyperentangled states will be considered. The entanglement generators will use linear and nonlinear optical devices. Optimization criteria for the quantum states, generation and detection schemes and designs optimal with respect to the criteria will be discussed. Applications of the generated states for producing super sensitivity and super resolution will be discussed. The fundamental role of coincidence measurement for generating entanglement is included. Hyperentanglement offers N times classical resolution, where N is a quantum number associated with the system.

Experimental measurements of entangled photons have enabled effective probing of foundational principles of physical law, Quantum Mechanics (QM) in particular. When it was noted that QM is non-local and precludes certain real properties, change in the description of basic phenomena was required. Bell's Inequality work clarified this conflict with Local-Realistic descriptions but left open whether locality, realism, or both should be abandoned. More recent investigations consider models that maintain forms of non-local realism as alternatives to QM. Problems with those are illustrated here, and support a non-local QM description of entangled photons having non-determinate properties.

Quantum memory is regarded as one of the essential components in the fields of quantum computing and quantum communication. Warm atomic vapor cells for quantum memory, as originally described in DLCZ (for Duan, Lukin, Cirac, and Zoller) protocol, are appealing due to the perceived reduction in experimental complexity and commercial availability. However, published studies on quantum memory using warm vapor cells were performed under widely dissimilar experimental conditions and reported ambiguous results. In order for the memory to exhibit non-classical behavior to a high degree of certainty, the cross-correlation value between the Stokes and anti-Stokes photons needs to be greater than two. In this work we demonstrate quantum memory with cross-correlation value between the Stokes and anti-Stokes photons greater than two lasting for 4 μs using warm Rb vapor with buffer gas for nearly co-propagating write and read beams.

We propose an experiment in Linear Optical Quantum Computing (LOQC) in the style rst suggested by Knill, La amme, and Milburn. This experiment is intended to test the theories proposed in the authors' previous work on imperfect LOQC gates using number-resolving photon-detectors. We develop a simple physical apparatus capable of producing controllable delity less than 1 and success rates higher than the current theoretical maximum (S=2/27) for perfect delity. This experimental setup is within the reach of many experimental groups and would provide an interesting experiment in photon-based quantum computing.