This PDF file contains the front matter associated with SPIE Proceedings Volume 8749 including the Title Page, Copyright information, Table of Contents, Introduction, and Conference Committee listing.

Energy teleportation with no energy carrier between two physically separated sites was demonstrated in principle by M. Hotta in 2008. His demonstration used a three-step protocol applied to a Heisenberg spin particle pair initially in its fully entangled ground state. We apply the Hotta protocol to the same Heisenberg pair but now suppose the pair is, more generally, in a thermal state, introducing temperature as an explicit parameter. These thermal states show a degree of quantum correlation (thermal discord) at all temperatures. We find that at any temperature energy teleportation is possible with the Hotta protocol, even at temperatures beyond the threshold where the particles’ entanglement vanishes. This shows that entanglement is not fundamentally necessary for energy teleportation; quantum discord generally can suffice. It is also a new instance in which quantum dissonance (discord without entanglement) is seen to act as a quantum resource.

We have formulated a theory for investigating the conditions which are required to achieve entangled states of electrons on graphene and three-dimensional (3D) topological insulators (TIs). We consider the quantum entanglement of spins by calculating the exchange energy. A gap is opened up at the Fermi level between the valence and conduction bands in the absence of doping when graphene as well as 3D TIs are irradiated with circularly-polarized light. This energy band gap is dependent on the intensity and frequency of the applied electromagnetic field. The electron-photon coupling also gives rise to a unique energy dispersion of the dressed states which is different from either graphene or the conventional two-dimensional electron gas (2DEG). In our calculations, we obtained the dynamical polarization function for imaginary frequencies which is then employed to determine the exchange energy. The polarization function is obtained with the use of both the energy eigenstates and the overlap of pseudo-spin wave functions. We have concluded that while doping has a significant influence on the exchange energy and consequently on the entanglement, the gap of the energy dispersions affects the exchange slightly, which could be used as a good technique to tune and control entanglement for quantum information purposes.

Transmission of quantum entanglement will play a crucial role in future networks and long-distance quantum communications. Quantum Key Distribution, the working mechanism of quantum repeaters and the various quantum communication protocols are all based on quantum entanglement. To share entanglement between distant points, high fidelity quantum channels are needed. In practice, these communication links are noisy, which makes it impossible or extremely difficult and expensive to distribute entanglement. In this work we first show that quantum entanglement can be generated by a new idea, exploiting the most natural effect of the communication channels: the noise itself of the link. We prove that the noise transformation of quantum channels that are not able to transmit quantum entanglement can be used to generate distillable (useable) entanglement from classically correlated input. We call this new phenomenon the Correlation Conversion property (CC-property) of quantum channels. The proposed solution does not require any nonlocal operation or local measurement by the parties, only the use of standard quantum channels. Our results have implications and consequences for the future of quantum communications, and for global-scale quantum communication networks. The discovery also revealed that entanglement generation by local operations is possible.

The space of separable states of a quantum system is a hyperbolic surface in a high dimensional linear space, which we call the separation surface, within the exponentially high dimensional linear space containing the quantum states of an n component multipartite quantum system. A vector in the linear space is representable as an n-dimensional hypermatrix with respect to bases of the component linear spaces. A vector will be on the separation surface iff every determinant of every 2-dimensional, 2-by-2 submatrix of the hypermatrix vanishes. This highly rigid constraint can be tested merely in time asymptotically proportional to d, where d is the dimension of the state space of the system due to the extreme interdependence of the 2-by-2 submatrices. The constraint on 2-by-2 determinants entails an elementary closed formformula for a parametric characterization of the entire separation surface with d-1 parameters in the char- acterization. The state of a factor of a partially separable state can be calculated in time asymptotically proportional to the dimension of the state space of the component. If all components of the system have approximately the same dimension, the time complexity of calculating a component state as a function of the parameters is asymptotically pro- portional to the time required to sort the basis. Metric-based entanglement measures of pure states are characterized in terms of the separation hypersurface.

Considerations of non-locality and correlation measures provide insights to Quantum Mechanics. Nonphysical states are shown to exceed limits of QM in both respects and yet conform to relativity’s ‘nosignaling’ constraint. Recent work has shown that the Uncertainty Principle limits non-locality to distinguish models that exceed those of QM. Accordingly, the Uncertainty Principle is shown to limit correlation strength independently of non-locality, extending interpretation of the prior work, and to underlie the security of Quantum Key Distribution. The established Ekert protocol[6] is compared with more secure variations, in particular H. Yuen's Keyed Communication in Quantum Noise (KCQ) [7] and a new Time-Gating protocol which minimizes authentication and susceptibility to active eavesdropping.

We present the quantum key distribution (QKD) secure key ratio expression in a form that exposes the parameters that affect the Reconciliation (error correction) stage. Reconciliation is the least well understood in practical terms and is typically described through a model that provides little guidance when it comes to efficient implementation, although it requires significant resources and is required to achieve a performance level commensurate with the other stages of the QKD protocol implementation. We addresses the issue of practical QKD error correction, questions of performance based on our data and data that have been published, and addresses the issue of platforms capable of handling rates of Gb/s.

This paper gives an account of topological quantum computing based on unitary solutions to the Yang-Baxter Equation. We show how quantum computing with Majorana Fermions fits into this context.

I claim that for macroscopic objects consisting of more than Avo- gadro’s number of atoms, any supposed quantum state is negligibly small, so that for all practical purposes the object is best described by classical mechanics. I argue that this follows from a reasonable upper bound on physically possible proper acceleration.

Effects of local availability of mathematics (LAM) and space time dependent number scaling on physics and, especially, geometry are described. LAM assumes separate mathematical systems as structures at each space time point. Extension of gauge theories to include freedom of choice of scaling for number structures, and other structures based on numbers, results in a space time dependent scaling factor based on a scalar boson field. Scaling has no effect on comparison of experimental results with one another or with theory computations. With LAM all theory expressions are elements of mathematics at some reference point. Changing the reference point introduces (external) scaling. Theory expressions with integrals or derivatives over space or time include scaling factors (internal scaling) that cannot be removed by reference point change. Line elements and path lengths, as integrals over space and/or time, show the effect of scaling on geometry. In one example, the scaling factor goes to 0 as the time goes to 0, the big bang time. All path lengths, and values of physical quantities, are crushed to 0 as t goes to 0. Other examples have spherically symmetric scaling factors about some point, x. In one type, a black scaling hole, the scaling factor goes to infinity as the distance, d, between any point y and x goes to 0. For scaling white holes, the scaling factor goes to 0 as d goes to 0. For black scaling holes, path lengths from a reference point, z, to y become infinite as y approaches x. For white holes, path lengths approach a value much less than the unscaled distance from z to x.

There exists a fundamental dimensional mismatch between the Hong-Ou-Mandel (HOM) interferometer and two-photon states: while the latter are represented using two temporal (or spectral) dimensions, the HOM interferometer allows access to only one temporal dimension owing to its single delay element. We introduce a linear two-photon interferometer containing two independent delays spanning the two-photon state. By unlocking the fixed phase relationship between the interfering two-photon probability amplitudes in a HOM interferometer, one of these probability amplitudes now serves as a delay-free two-photon reference against which the other beats, thereby resolving ambiguities in two-photon state identification typical of HOM interferometry. We discuss the operation of this phase-unlocked HOM on a variety of input states focusing on instances where this new interferometer outperforms a traditional HOM interferometer: frequency-correlated states and states produced by a pulse doublet pump. Additionally, this interferometer affords the opportunity to synchronize two-photon states in a manner analogous to an HOM interferometer; moreover, it extends that capability to the aforementioned class of states.

This paper provides some examples about quantum games simulated in Python’s programming language. The quantum games have been developed with the Sympy Python library, which permits solving quantum problems in a symbolic form. The application of these methods of quantum mechanics to game theory gives us more possibility to achieve results not possible before. To illustrate the results of these methods, in particular, there have been simulated the quantum battle of the sexes, the prisoner’s dilemma and card games. These solutions are able to exceed the classic bottle neck and obtain optimal quantum strategies. In this form, python demonstrated that is possible to do more advanced and complicated quantum games algorithms.

Galois fields are constantly gaining importance in quantum computing due to their wide usage in quantum error correction algorithms, and so it becomes relevant to define the QFT over Galois fields because of its main role in many of the most important quantum algorithms. The present article illustrates how to generalize the QFT so it can be applied over Galois fields and explains several examples of the application of the QFT over the simplest Galois fields. In particular the QFT will be defined for the Galois fields F2, F4 and GF(9), also the application of the QFT and the operations involved will be made using the Maple mathematical software.

Recently the celebrated Khovanov Homology was introduced as a target for Topological Quantum Computation given that the Khovanov Homology provides a generalization of the Jones polynomal and then it is possible to think about of a generalization of the Aharonov.-Jones-Landau algorithm. Recently, Lipshitz and Sarkar introduced a space-level refinement of Khovanov homology. which is called Khovanov Homotopy. This refinement induces a Steenrod square operation Sq² on Khovanov homology which they describe explicitly and then some computations of Sq² were presented. Particularly, examples of links with identical integral Khovanov homology but with distinct Khovanov homotopy types were showed. In the presente work we will introduce possible quantum algorithms for the Lipshitz- Sarkar-Steenrod square for Khovanov Homolog and their possible simulations using computer algebra.

In order to carry out different quantum algorithms on the same quantum circuit, we have to start the next algorithm from the qubit arrangement at the end of the previous one. The arrangement of trapped ions after some algorithm execution is generally not optimal for the following algorithm in an ion-trap quantum computer. We simulated the sequences in the Grover's quantum circuits for searching an unsorted database in order to obtain sequence error rates under a random initial arrangement of qubits. When the sequence error rate for the circuit with QEC is less than that for the circuit without QEC, it is worth introducing the QEC circuit. From the condition, we obtained the quantum error correction criteria that depends on two parameters: concentrations flip of qubits and error rates. If we can know the flip error rate in an ion-trap quantum computer and determine the concentration, the criteria help us to realize a quantum circuit execution with less error rates in an ion-trap quantum computer.

The Search Based Software Engineering (SBSE) is widely used in software engineering for identifying optimal solutions. However, there is no polynomial-time complexity solution used in the traditional algorithms for SBSE, and that causes the cost very high. In this paper, we analyze and compare several quantum search algorithms that could be applied for SBSE: quantum adiabatic evolution searching algorithm, fixed-point quantum search (FPQS), quantum walks, and a rapid modified Grover quantum searching method. The Grover’s algorithm is thought as the best choice for a large-scaled unstructured data searching and theoretically it can be applicable to any search-space structure and any type of searching problems.

We examine a dc SQUID phase qubit with an on-chip low-pass resonant LC filter that transforms the line impedance, improving the qubit lifetime. Unusual features in the spectroscopy suggest dynamics more complicated than a simple two-level system. To model this behavior, we consider a lumped-element circuit model of the SQUID that includes the filter as part of the quantum system to be modeled. We show this model reduces to an effective Jaynes-Cummings Hamiltonian, in analogy with circuit QED.

Atomic clocks exchanging signals serve as a background against which to measure the motion of objects on or near the Earth. The background of clocks and signals requires feedback involving computation, both internal to each clock and for regulating relations between clocks. Feedback within a clock responds to a flow of measured outcomes which, by quantum theory, are unpredictable. The steering of atomic clocks in response to unpredictable occurrences of outcomes depends on a wave function, and the choice of this wave function requires an assumption underivable in any logic consistent with quantum theory—another form of unpredictability. Currently backgrounds for motion, for example used in the Global Positioning System, consist of one or another (physical) reference frame as a realization of a (mathematical) reference system that consists of a spacetime coordinate chart with a specified metric tensor field—a structure that expresses neither the unpredictability inherent in atomic clocks nor the feedback by which one deals with this unpredictability. Without requiring the assumption of a metric tensor or even a spacetime, here we introduce a novel type of reference system consisting of the records and criteria resident in real-time computers that mediate feedback, a reference system that, by expressing feedback, structures the unpredictables in a background of motion. The criteria for clock adjustment are discussed. Trade-offs involved in these criteria call for adjusting a background in response to the motion of the objects tracked.

Here we present a fully quantum mechanical transfer function model for travelling wave whispering gallery mode resonators. Micro-resonators, such as ring and disk resonators, have been key to the development of high performance chip-scale photonic systems due to their compact footprint, sensitivity and low power operation. In this work we present the first understanding of these resonators to any arbitrary multi-photon state. This was achieved by developing a model that utilizes an efficient scheme for determining the quantum electrodynamic transfer functions relating the Bosonic input/output mode operators in the resonator. This approach has been applied to the understanding of both single photon and two-photon states. In this work we will present a key result on a resonant Hong-Ou-Mandel effect that is inherently realized for any resonator-waveguide coupling constants and can operate over a wide range of resonance conditions. Furthermore, the transfer function approach allows for the straightforward understanding of any resonator-waveguide network with arbitrary modes. This will directly enable the application of quantum resonators to the realization of robust, scalable and efficient Linear Optical Quantum Computing (LOQC) gates. Consequently, it is expected that resonators can be used for both Nonlinear Sign Shift and CNOT gates. And these gates can robustly controlled and efficiently tuned using standard electro-optic effects available in a variety of material systems, such as, Silicon.

Conventional ghost imaging can only obtain two dimensional image because it only uses spatial correlation characteristics of light source. We describe a three dimensional arrangement using only a single-pixel detector based on computational ghost imaging. The three dimensional image of the object can be divided into gray-scale image and digital elevation model, where the gray-scale image can be obtained relying spatial correlation, and the digital elevation model can be obtained relying temporal correlation. In the further, this technology maybe find application in remote sense domain.

There is a measurements principle that ensures the increase of accuracy of measurements based on redundant measurements. Main properties of the solution are: a discrete method with a surge of probability within the parent entity and comparison of the graph of the probability distribution for the diffraction grids with the graph of probability density function. Method based on the analog of Pauli equation solution. The method of electronic reference measurements with quantum computing applied to mathematical data processing allows to greatly increase the credibility and accuracy of measurements at low cost, which is confirmed by simulation.

Efficient coupling between a localized quantum emitter and a well defined optical channel represents a powerful route to realize single-photon sources and spin-photon interfaces. The tailored fiber-like photonic nanowire embedding a single quantum dot has recently demonstrated an appealing potential. However, the device requires a delicate, sharp needle-like taper with performance sensitive to minute geometrical details. To overcome this limitation we demonstrate the photonic trumpet, exploiting an opposite tapering strategy. The trumpet features a strongly Gaussian far-field emission. A first implementation of this strategy has lead to an ultra-bright single-photon source with a first-lens external efficiency of 0.75 ± 0.1 and a predicted coupling to a Gaussian beam of 0.61 ± 0.08.

Some new filters for image processing are obtained from the wave functions of the two-dimensional quantum oscillator. Such filters are gaussians multiplied by Hermite polynomials and for this reason they will be called Gaussian- Hermite filters. These new quantum filters can be used as smoothing filters and they show good performance when elimination of noise is concerned. Besides of this the new quantum filters can be used to define blurred derivatives and blurred Laplacians for images and in this case the quantum filters are excellent edge detectors. Finally the quantum filters and their derivatives are used to define quantum curvature filters as the Ricci-scalar-curvature filter and the Gaussian-curvature filter. In this last case the quantum filters perform well as curvature detectors and contrast enhancement operators. Our experimental results show that the quantum filters are more efficient than the classical filters and we claim that the quantum image processing will be a very important trend in the near future sensing technology.

A hyper-entanglement based atmospheric imaging/detection system involving only a signal and an ancilla photon will be considered for optical and infrared frequencies. Only the signal photon will propagate in the atmosphere and its loss will be classical. The ancilla photon will remain within the sensor experiencing low loss. Closed form expressions for the wave function, normalization, density operator, reduced density operator, symmetrized logarithmic derivative, quantum Fisher information, quantum Cramer-Rao lower bound, coincidence probabilities, probability of detection, probability of false alarm, probability of error after M measurements, signal to noise ratio, quantum Chernoff bound, time-on-target expressions related to probability of error and resolution will be provided. The effect of noise in every mode will be included as well as loss. The system will provide the basic design for an imaging/detection systems functioning at optical or infrared frequencies that offer better than classical angular and range resolution. Optimization for enhanced resolution will be included. The signal to noise ratio will be increased by a factor equal to the number of modes employed during the hyper-entanglement process. Likewise, the measurement time can be reduced by the same factor. The hyper-entanglement generator will typically make use of entanglement in polarization, energy-time, orbital angular momentum, etc. Mathematical results will be provided describing the system’s performance as a function of loss mechanisms and noise.