Controlled Cyclic Remote State Preparation of Arbitrary Qubit States

Quantum secure communications could securely transmit quantum information by using quantum resource. Recently, novel applications such as bidirectional and asymmetric quantum protocols have been developed. In this paper, we propose a new method for generating entanglement which is highly useful for multiparty quantum communications such as teleportation and Remote State Preparation (RSP). As one of its applications, we propose a new type of quantum secure communications, i.e. cyclic RSP protocols. Starting from a four-party controlled cyclic RSP protocol of one-qubit states, we show that this cyclic protocol can be generalized to a multiparty controlled cyclic RSP protocol for preparation of arbitrary qubit states. We point out that previous bidirectional and asymmetric protocols can be regarded as a simpler form of our cyclic RSP protocols.     

The one-way quantum computer--a non-network model of quantum computation

A one-way quantum computer (QC _C ) works by performing a sequence of one-qubit measurements on a particular entangled multi-qubit state, the cluster state. No non-local operations are required in the process of computation. Any quantum logic network can be simulated on the QC _C . On the other hand, the network model of quantum computation cannot explain all ways of processing quantum information possible with the QC _C . In this paper, two examples of the non-network character of the QC _C are given. First, circuits in the Clifford group can be performed in a single time step. Second, the QC _C -realization of a particular circuit—the bit-reversal gate—has no network interpretation.     

Geometric aspects of composite pulses

Unitary operations acting on a quantum system must be robust against systematic errors in control parameters for reliable quantum computing. Composite pulse technique in nuclear magnetic resonance realizes such a robust operation by employing a sequence of possibly poor-quality pulses. In this study, we demonstrate that two kinds of composite pulses-one compensates for a pulse length error in a one-qubit system and the other compensates for a J-coupling error in a two-qubit system-have a vanishing dynamical phase and thereby can be seen as geometric quantum gates, which implement unitary gates by the holonomy associated with dynamics of cyclic vectors defined in the text.     

Implementation of the Deutsch-Jozsa algorithm with Josephson charge qubits

We investigate the realization of a simple solid-state quantum computer by implementing the Deutsch-Jozsa algorithm in a system of Josephson charge qubits. Starting from a procedure to carry out the one-qubit Deutsch-Jozsa algorithm we show how the N -qubit version of the Bernstein-Vazirani algorithm can be realized. For the implementation of the three-qubit Deutsch-Jozsa algorithm we study in detail a set-up which allows us to produce entangled states.     

The Rashba Effect Within the Coherent Scattering Formalism with Applications to Electron Quantum Optics

The influence of spin–orbit coupling in electron quantum optics experiments is investigated within the framework of the Landauer–Büttiker coherent scattering formalism. We begin with a brief review of our electron quantum optics toolbox: an electron intensity interferometer (Hanbury Brown and Twiss-type experiment), an electron collision analyzer (Hong–Ou–Mandel-type experiment), and a proposed Bell state analyzer. These experiments are performed or proposed in two-dimensional electron gas systems and, therefore, may be influenced by the Rashba spin–orbit coupling. To quantify this effect, we define the creation/annihilation operators for the stationary states of the Rashba spin–orbit coupling Hamiltonian and use them to derive the current operator within the Landauer–Büttiker formalism. The current is expressed as it is in the standard spin-independent case, but with the spin label replaced by a new label that we call the spin–orbit coupling label. The spin–orbit coupling effects can then be represented in a scattering matrix that relates the spin–orbit coupling stationary states in different leads. We apply this new formalism to the case of a four-port beamsplitter, and it is shown to mix states with different spin–orbit coupling labels in a manner that depends on the angle between the leads. A noise measurement after the collision of spin-polarized electrons at an electron beamsplitter provides a new experimental means to measure the Rashba parameter . It is also shown that the degree of electron bunching in an entangled-electron collision experiment is reduced by the spin–orbit coupling according the beamsplitter lead angle.     

Polymorphic Spin,Charge, and Lattice Waves in Vanadium Ditelluride

Lattice distortion, spin interaction, and dimensional crossover in transition metal dichalcogenides (TMDs) have led to intriguing quantum phases such as charge density waves (CDWs) and 2D magnetism. However, the combined effect of many factors in TMDs, such as spin–orbit, electron–phonon, and electron–electron interactions, stabilizes a single quantum phase at a given temperature and pressure, which restricts original device operations with various quantum phases. Here, nontrivial polymorphic quantum states, CDW phases, are reported in vanadium ditelluride (VTe₂) at room temperature, which is unique among various CDW systems; the doping concentration determines the formation of either of the two CDW phases in VTe₂ at ambient conditions. The two CDW polymorphs show different antiferromagnetic spin orderings in which the vanadium atoms create two different stripe-patterned spin waves. First-principles calculations demonstrate that the magnetic ordering is critically coupled with the corresponding CDW in VTe₂, which suggests a rich phase diagram with polymorphic spin, charge, and lattice waves all coexisting in a solid for new conceptual quantum state-switching device applications.     

Quantum properties and dynamics of X states

X states are a broad class of two-qubit density matrices that generalize many states of interest in the literature. In this work, we give a comprehensive account of various quantum properties of these states, such as entanglement, negativity, quantum discord and other related quantities. Moreover, we discuss the transformations that preserve their structure both in terms of continuous time evolution and discrete quantum processes.     

Having It Both Ways: Distinguishable Yet Phase-Coherent Mixtures of Bose-Einstein Condensates

We have begun a series of experiments on mixed bosonic quantum fluids. Our system is mixed Bose-Einstein condensates in dilute Rb-87. By simultaneously trapping the atoms in two different hyperfine states, we are able to study the dynamics of component separation and of the relative quantum phase of two interpenetrating condensates. Population can be converted from one state to the other at a rate that is sensitive to the relative quantum phase.     

Dynamics of surface diffeomorphisms relative to homoclinic and heteroclinic orbits

We show how to obtain information about the dynamics of a two-dimensional discrete-time system from its homoclinic and heteroclinic orbits. The results obtained are based on the theory of 'trellises', which comprise finite-length subsets of the stable and unstable manifolds of a collection of saddle periodic orbits. For any collection of homoclinic or heteroclinic orbits, we show how to associate a canonical 'trellis type' which describes the orbits. Given a trellis type, we show how to compute a 'graph representative' which gives a combinatorial invariant of the trellis type. The orbits of the graph give the dynamics forced by the homoclinic/heteroclinic orbits in the sense that every orbit of the graph representative is 'globally shadowed' by some orbit of the system, and periodic, homoclinic/heteroclinic orbits of the graph representative are shadowed by similar orbits.     

Quantum correlations,local interactions and error correction

Abstract

We consider the effects of local interactions upon quantum mechanically entangled systems. In particular we demonstrate that non-local correlations cannot increase through local operations on any of the subsystems, but that through the use of quantum error correction methods, correlations can be maintained. We provide two mathematical proofs that local general measurements cannot increase correlations, and also derive general conditions for quantum error correcting codes. Using these we show that local quantum error correction can preserve non-local features of entangled quantum systems. We also demonstrate these results by use of specific examples employing correlated optical cavities interacting locally with resonant atoms. By way of counter example, we also describe a mechanism by which correlations can be increased, which demonstrates the need for non-local interactions.     

Numerical simulation of coherent transport in quantum wires for quantum computing

A solid-state implementation of a universal set of gates for quantum computation is proposed and analysed using a time-dependent 2D Schrödinger solver. The qubit is defined as the state of an electron propagating along a couple of quantum wires. The wires are suitably coupled through a potential barrier with variable height and/or width. It is shown how a proper design of the system allows the implementation of any one-qubit transformation. The two-qubit gate is realized through a Coulomb coupler able to entangle the quantum states of two electrons running in two wires of two different qubits. The simulated devices are GaAs—AlGaAs heterostructures that should be on the borderline of present semiconductor technology. An estimate of decoherence effects due to phonon scattering is also presented.     

Rashba Spin–Orbit Interaction and Its Applications to Spin-Interference Effect and Spin-Filter Device

The Rashba spin–orbit interaction in InGaAs quantum wells (QW) is studied using the weak antilocalization analysis as a function of the structural inversion asymmetry (SIA). We have observed a clear cross-over from positive to negative magnetoresistance near zero-magnetic field by controlling the degree of the SIA in the QWs. This is a strong evidence of a zero-field spin splitting that is induced by the Rashba effect. The spin-interference effect in a gate-controlled mesoscopic Aharonov–Bohm ring structure is investigated in the presence of Rashba spin–orbit interaction. The oscillatory behavior appearing in ensemble averaged Fourier spectrum of h/2e oscillations as a function of gate voltage is possibly because of the Aharonov–Casher type interference. We propose a spin-filter device based on the Rashba effect using a nonmagnetic resonant tunneling diode structure. Detailed calculation using InAIAs/InGaAs heterostructures shows that the spin-filtering efficiency exceeds 99.9%.     

Engineering Dirac electrons emergent on the surface of a topological insulator

Abstract

The concept of the topological insulator (TI) has introduced a new point of view to condensed-matter physics, relating a priori unrelated subfields such as quantum (spin, anomalous) Hall effects, spin–orbit coupled materials, some classes of nodal superconductors, superfluid ³He, etc. From a technological point of view, TIs are expected to serve as platforms for realizing dissipationless transport in a non-superconducting context. The TI exhibits a gapless surface state with a characteristic conic dispersion (a surface Dirac cone). Here, we review peculiar finite-size effects applicable to such surface states in TI nanostructures. We highlight the specific electronic properties of TI nanowires and nanoparticles, and in this context we contrast the cases of weak and strong TIs. We study the robustness of the surface and the bulk of TIs against disorder, addressing the physics of Dirac and Weyl semimetals as a new research perspective in the field.     

A new rescheduling method for computer based scheduling systems

Providing a powerful interactive tool for the scheduler to quickly and easily react to the inevitable rescheduling changes is mandatory in today's complex and flexible manufacturing environment. The conventional approaches either employ the regeneration method, which results in unsatisfactory response times, or use. methods that require too much manual intervention for editing operations to be changed. A new rescheduling method is proposed in this paper which addresses these problems. The fundamental scheme of this rescheduling method is based on a scheduling graph as well as concepts of time effect and relationship effect. The scheduling graph is an alternative representation structure of a schedule Gantt chart. The time effect and relationship effect provide functions of (1) identifying those operations that require revision, (2) revising those identified affected operations (via a partial change of the scheduling graph structure) and (3) updating starting and ending times of those revised operations. The rescheduling method both reduces manual intervention of rescheduling to a minimum and permits net change (opposite to regeneration) rescheduling to be achievable. This rescheduling method can be embedded in current computer assistance scheduling systems so as to enhance their effectiveness.     

On the quantization of the electromagnetic field in conducting media

In this work we investigate the quantization of electromagnetic waves propagating through homogeneous conducting linear media with no charge density. We use Coulomb's gauge to reduce the problem to that of a time-dependent harmonic oscillator, which is described by the Caldirola–Kanai Hamiltonian. Furthermore, we obtain the corresponding exact wave functions with the help of quadratic invariants and of the dynamic invariant method. These wave functions are written in terms of a particular solution of the Milne–Pinney equation. We also construct coherent and squeezed states for the quantized electromagnetic waves and evaluate the quantum fluctuations in coordinates and momentum as well as the uncertainty product for each mode of the electromagnetic field.     

Quantum information processing in localized modes of light within a photonic band-gap material

Abstract

The single photon occupation of a localized field mode within an engineered network of defects in a photonic band-gap (PBG) material is proposed as a unit of quantum information (qubit). Qubit operations are mediated by optically-excited atoms interacting with these localized states of light as the atoms traverse the connected void network of the PBG structure. We describe conditions under which this system can have independent qubits with controllable interactions and very low decoherence, as required for quantum computation.     

Transitive sets for quasi-periodically forced monotone maps

There has been considerable interest in recent years in quasi-periodically forced systems, partly due to the fact that these commonly exhibit strange non-chaotic attractors. Relatively little is known rigorously about such systems. In this paper we concentrate on investigating the structure of the simplest possible invariant sets for a particular class of quasi-periodically forced maps, namely those that are monotone in each fibre. Due to the quasi-periodic nature of the forcing, periodic orbits cannot occur, and their role is played by various types of invariant graph. Any compact invariant set is bounded by two invariant graphs, which are respectively upper and lower semi-continuous. If the set is minimal, these two graphs intersect on a residual set, on which both are continuous. Any transitive set Ω contains either one or two minimal sets, which must be the closure of one or the other of the boundaries of Ω. If Ω contains only one minimal set, then again its upper and lower boundaries intersect on a residual set. This case contains the original example of Grebogi et al. and its generalizations by Keller and by Glendinning. If Ω contains two minimal sets, then its upper and lower boundaries cannot intersect, though as far as we are aware, there is no known example where the existence of such a transitive set has been proven rigorously.     

Two‐Photon Up‐Conversion Photoluminescence Realized through Spatially Extended Gap States in Quasi‐2D Perovskite Films

A new approach to generate a two‐photon up‐conversion photoluminescence (PL) by directly exciting the gap states with continuous‐wave (CW) infrared photoexcitation in solution‐processing quasi‐2D perovskite films [(PEA)₂(MA)₄Pb₅Br₁₆ with n = 5] is reported. Specifically, a visible PL peaked at 520 nm is observed with the quadratic power dependence by exciting the gap states with CW 980 nm laser excitation, indicating a two‐photon up‐conversion PL occurring in quasi‐2D perovskite films. Decreasing the gap states by reducing the n value leads to a dramatic decrease in the two‐photon up‐conversion PL signal. This confirms that the gap states are indeed responsible for generating the two‐photon up‐conversion PL in quasi‐2D perovskites. Furthermore, mechanical scratching indicates that the different‐n‐value nanoplates are essentially uniformly formed in the quasi‐2D perovskite films toward generating multi‐photon up‐conversion light emission. More importantly, the two‐photon up‐conversion PL is found to be sensitive to an external magnetic field, indicating that the gap states are essentially formed as spatially extended states ready for multi‐photon excitation. Polarization‐dependent up‐conversion PL studies reveal that the gap states experience the orbit–orbit interaction through Coulomb polarization to form spatially extended states toward developing multi‐photon up‐conversion light emission in quasi‐2D perovskites.     

Quantum information processing by nuclear magnetic resonance on quadrupolar nuclei

Nuclear magnetic resonance is viewed as an important technique for the implementation of many quantum information algorithms and protocols. Although the most straightforward approach is to use the two-level system composed of spin 1/2 nuclei as qubits, quadrupolar nuclei, which possess a spin greater than 1/2, are being used as an alternative. In this study, we show some unique features of quadrupolar systems for quantum information processing, with an emphasis on the ability to execute efficient quantum state tomography (QST) using only global rotations of the spin system, whose performance is shown in detail. By preparing suitable states and implementing logical operations by numerically optimized pulses together with the QST method, we follow the stepwise execution of Grover's algorithm. We also review some work in the literature concerning the relaxation of pseudo-pure states in spin 3/2 systems as well as its modelling in both the Redfield and Kraus formalisms. These data are used to discuss differences in the behaviour of the quantum correlations observed for two-qubit systems implemented by spin 1/2 and quadrupolar spin 3/2 systems, also presented in the literature. The possibilities and advantages of using nuclear quadrupole resonance experiments for quantum information processing are also discussed.