Phase Flip Research Articles

Mutual Information of Pauli Channels with Correlated Noise

A general formula for the mutual information of the Pauli channels with memory modelled by correlated noise is derived. It is shown that the mutual information depends on the channel shrinking factor, the input state parameter and the channel memory coefficient. The analyses based on the general formula reveal that the entanglement is always a useful resource to enhance the mutual information of some Pauli channels, such as the bit flip channel and the bit-phase flip channel. Our analyses also show that the entanglement is not advantageous to the reliable transmission of classical information for some Pauli channels at any time, such as the phase flip channel and the phase damping channel.

Dynamical Localization and Environmental Noise: a Quantum Trajectory Approach

Using the quantum trajectory approach, we study the eects of environmental noise on dynamical localization in a quantum algorithm simulating the kicked rotator. We apply two models that generalize single qubit noisy channels, like phase flip and amplitude damping, to the many-qubit situation. Our numerical results show that the quantum trajectory approach is suitable for simulating the quantum kicked rotator in realistic environments.

Symmetries and noise in quantum walk

We study some discrete symmetries of unbiased (Hadamard) and biased quantum walk on a line, which are shown to hold even when the quantum walker is subjected to environmental effects. The noise models considered in order to account for these effects are the phase flip, bit flip and generalized amplitude damping channels. The numerical solutions are obtained by evolving the density matrix, but the persistence of the symmetries in the presence of noise is proved using the quantum trajectories approach. We also briefly extend these studies to quantum walk on a cycle. These investigations can be relevant to the implementation of quantum walks in various known physical systems. We discuss the implementation in the case of NMR quantum information processor and ultra cold atoms.

Representing sound energy, phase, and interference using three-dimensional signals

As graphic representations of vibrations/waves, sound signals capture only selected attributes of the phenomenon they represent. Assuming equivalence between signals and sound waves obscures the fact that 2-D signals are unfit to a) represent wave-energy quantities consistently across frequencies, b) account for the phase flip and alternating positive/negative amplitude values in modulated waves with AM-depth >100%, and c) represent the energy content of interference. The proposed sound-signal representation is based on the complex equation of motion describing a wave. It results in spiral sine signals and twisted-spiral complex signals, similar to complex analytic signals, with the imaginary component of the complex equation of motion representing the signal envelope’s argument (phase). Spiral sine signals offer a consistent measure of sine-wave energy across frequencies, while twisted-spiral complex signals account for the negative amplitudes observed in modulated signals, mapping the modulation parameters onto the twisting parameters. In terms of interference, 3-D signals illustrate that amplitude fluctuations and the signal envelopes that describe them are not just boundary curves but waves that trace changes in the total instantaneous energy of a signal over time, representing the oscillation between potential and kinetic energies within a wave. Examples of 3-D animations illustrating the proposed signals are presented.

Códigos Concatenados Corretores de Erros Quânticos

In this article, we make a review of quantum error-correcting codes (QECCs) constructed from the concatenation of a phase flip code with a bit flip code. In particular, two examples are reviewed in details: the rate-1/9 quantum block code (QBC) proposed by Shor, and the rate 1/4 quantum convolutional code (QCC) proposed by Almeida and Palazzo. The purpose of this article is to introduce the study of QECCs to the community of telecommunication engineers.

Superdense coding in noisy environments: A quantum trajectory approach

Using the theory of quantum trajectories, we study the classical capacity C of noisy quantum channels in the superdense coding protocol. We apply the two models that generalize single-qubit noisy channels, such as amplitude damping and phase flip, to the many-qubit situation. Our numerical results show that the quantum trajectory approach is suitable for modeling the superdense coding protocol in realistic environments.

One-step implementation of a multiqubit controlled-phase-flip gate

We propose a scheme for implementing quantum computation with $N$ atoms trapped in a single-sided cavity. In our scheme, a multiqubit controlled-phase-flip (MCPF) gate as well as a quantum controlled phase flip gate is performed by only one step. The numerical simulations show that the protocol is robust to practical noise. In addition, the scheme can also be extended to achieve other multiqubit controlled unitary gates, and implement MCPF gate on atoms trapped in different cavities.

Publisher's Note: Higher-order perturbation theory for decoherence in Grover’s algorithm [Phys. Rev. A72, 042305 (2005)

In this paper, we study decoherence in Grover's quantum search algorithm using a perturbative method. We assume that each two-state system (qubit) that belongs to a register suffers a phase flip error (\sigma_{z} error) with probability p independently at every step in the algorithm, where $0\leq p\leq 1$. Considering an n-qubit density operator to which Grover's iterative operation is applied M times, we expand it in powers of 2Mnp and derive its matrix element order by order under the large-n limit. [In this large-n limit, we assume p is small enough, so that 2Mnp can take any real positive value or zero. We regard $x\equiv 2Mnp(\geq 0)$ as a perturbative parameter.] We obtain recurrence relations between terms in the perturbative expansion. By these relations, we compute higher orders of the perturbation efficiently, so that we extend the range of the perturbative parameter that provides a reliable analysis. Calculating the matrix element numerically by this method, we derive the maximum value of the perturbative parameter x at which the algorithm finds a correct item with a given threshold of probability P_{th} or more. (We refer to this maximum value of x as x_{c}, a critical point of x.) We obtain a curve of x_{c} as a function of P_{th} by repeating this numerical calculation for many points of P_{th} and find the following facts: a tangent of the obtained curve at P_{th}=1 is given by x=(8/5)(1-P_{th}), and we have x_{c}>-(8/5)\log_{e}P_{th} near P_{th}=0.

Realizing quantum controlled phase flip through cavity QED

We propose a scheme to realize quantum controlled phase flip (CPF) between two rare-earth ions embedded in the respective microsphere cavity via interacting with a single-photon pulse in sequence. The numerical simulations illuminate that the CPF gate between ions is robust and scalable with extremely high fidelity and low error rate. Our scheme is more applicable than other schemes presented before based on current laboratory cavity-QED technology, and it is possible to be used as an applied unit gate in future quantum computation and quantum communication.

Quantum CPF gates between rare earth ions through measurement

We propose a method to realize quantum controlled phase flip (CPF) through interaction between a single-photon pulse and two microsphere cavities with a single three-level ion respectively and final photonic measurement. Our CPF gates are scalable with extremely high fidelity and low error rate, and are more applicable based on current laboratory cavity-QED technology.

Simulating noisy quantum protocols with quantum trajectories

The theory of quantum trajectories is applied to simulate the effects of quantum noise sources induced by the environment on quantum information protocols. We study two models that generalize single qubit noise channels like amplitude damping and phase flip to the many-qubit situation. We calculate the fidelity of quantum information transmission through a chaotic channel using the teleportation scheme with different environments. In this example, we analyze the role played by the kind of collective noise suffered by the quantum processor during its operation. We also investigate the stability of a quantum algorithm simulating the quantum dynamics of a paradigmatic model of chaos, the baker's map. Our results demonstrate that, using the quantum trajectories approach, we are able to simulate quantum protocols in the presence of noise and with large system sizes of more than 20 qubits.

Observing Bragg-like diffraction via multiple coupled nuclear spins

Using intermolecular multiple-quantum coherence (iMQC) we report the first observation of Bragg-like diffraction via multiple distantly coupled nuclear spins. A compact quantum-mechanical formalism has been developed for analytically calculating iMQCs. The diffraction of iMQCs of various orders has been studied in a two-dimensional array structure. It indicates that phase cycling and flip angle selection are crucial for accurately measuring iMQC and the specific iMQCs measured in previous studies were likely contaminated by undesired coherences. We have also examined the capability and the current limitation of applying iMQCs for structural studies. The observation of iMQC diffraction introduces a new method for studying collective dynamics.

Observing Bragg-like diffraction via multiple coupled nuclear spins

Using intermolecular multiple-quantum coherence (iMQC) we report the first observation of Bragg-like diffraction via multiple distantly coupled nuclear spins. A compact quantum-mechanical formalism has been developed for analytically calculating iMQCs. The diffraction of iMQCs of various orders has been studied in a two-dimensional array structure. It indicates that phase cycling and flip angle selection are crucial for accurately measuring iMQC and the specific iMQCs measured in previous studies were likely contaminated by undesired coherences. We have also examined the capability and the current limitation of applying iMQCs for structural studies. The observation of iMQC diffraction introduces a new method for studying collective dynamics.

Generation of a phase-flipped Gaussian mode for optical measurements

We propose optical techniques for the generation of a TEM00 Gaussian beam which has a π phase flip in the electric field amplitudes between the two halves of the beam profile. The methods make use of a special waveplate and a masked Sagnac interferometer. The produced phase-flipped mode is the ideal light mode for optical measurements requiring high precision in one spatial dimension. Two examples of such applications are discussed.

ENTANGLEMENT-ASSISTED CLASSICAL CAPACITIES OF SOME SINGLE QUBIT QUANTUM NOISY CHANNELS

In this paper, we calculate the entanglement-assisted classical capacities of the depolarizing channel, the phase damping channel, the phase flip channel, the bit flip channel, the bit-phase flip channel, the two-Pauli channel and the amplitude channel, and discuss the analytical results obtained. The Stokes papametrization representation of a qubit and the characteristic of unitary covariance of some quantum noisy channels are used in the calculations.

Dispersion of theπresonance in the superconducting state of the cuprates

We study the dispersion of $\ensuremath{\pi}$ resonance in the superconducting state within the projected SO(5) model [S.C. Zhang et al., Phys. Rev. B 60, 13 070 (1999)]. Away from the commensurate momentum, the propagation of the $\ensuremath{\pi}$ resonance creates phase flips in the superconducting order parameter. This frustration effect leads to a strong dressing of the $\ensuremath{\pi}$ resonance and a downward dispersion away from the commensurate wave vector. Based on these results, we argue that the commensurate resonance and incommensurate magnetic fluctuations in the cuprates are continuously connected.

Conductance oscillations in mesoscopic rings: Microscopic versus global phase

The phase of Aharonov-Bohm oscillations in mesoscopic diffusive metal rings in the presence of a magnetic field, can be modulated by the application of a dc-bias current ${I}_{\mathrm{dc}}.$ We address the question of how a variation of ${I}_{\mathrm{dc}}$ and hence of the microscopic phases of the electronic wave functions results in the observable ``global'' phase of the conductance oscillations. Whereas the first one can be varied continuously, the latter has to be quantized for a ring in a two-wire configuration by virtue of the Onsager symmetry relations. We observe a correlation between a phase flip by $\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}$ and the amplitude of the oscillations.

Pattern formation in a surface chemical reaction with global delayed feedback.

We consider effects of global delayed feedback on anharmonic oscillations in the reaction-diffusion model of the CO oxidation reaction on a Pt(110) single-crystal surface. Depending on the feedback intensity and the delay time, we find that various spatiotemporal patterns can be induced. These patterns are characterized using a transformation to phase and amplitude variables designed for anharmonic oscillations. Typical feedback-induced patterns represent traveling phase flips, asynchronous oscillations, and dynamical clustering. Three different types of cluster patterns are identified: amplitude clusters, phase clusters, and cluster turbulence. For phase clusters, two different front instabilities are possible. A pitchfork bifurcation leads to propagation of cluster fronts. An instability of the state of phase balance results in spatial front oscillations.

Chaotic regime of Alfvén Eigenmode wave-particle interaction.

The chaotic regime in Alfvén eigenmode wave-particle interaction is identified for the first time in the tokamak plasma of the Joint European Torus. The Alfvén modes are driven by energetic hydrogen minority ions produced by ion cyclotron resonance heating. The experimental signatures of the chaotic regime include spectral broadening, phase flips, and nonperiodic amplitude variations. These phenomena are found to be consistent with a general nonlinear theory of kinetic instabilities near stability threshold developed by Berk, Breizman, and Pekker.

Investigations of Coherent Vibrational Oscillations in Myoglobin

The technique of femtosecond coherence spectroscopy (FCS) is applied to the heme protein myoglobin. Photostable samples of deoxy myoglobin (Mb) and photochemically active samples of the nitric oxide adduct (MbNO) are investigated. The pump-induced change in the probe transmittance for both samples displays coherent oscillations that, when transformed into the frequency domain, are in agreement with the resonance Raman spectrum of deoxy Mb. This indicates that the coherences associated with the photoreactive sample (MbNO) arise from the rapidly changing forces appearing in the crossing region(s) between the reactant and product state potential energy surfaces. The relative phase and amplitude of the Fe−His vibration, associated with the sole covalent linkage between the heme and the protein, are analyzed as a function of sample state and pump/probe carrier frequency. The dependence of the phase on carrier frequency is found to be significantly different for the “field driven” coherence in Mb and the “reaction driven” coherence in MbNO. In MbNO we observe a dip in amplitude and a phase flip near 439 nm for the Fe−His mode, whereas in deoxy Mb we observe a nearly constant phase and amplitude for this mode across the Soret absorption band. These observations are shown to be in good agreement with a simple theoretical model of the pump−probe experiment. Finally, we present recent observations of strong low-frequency oscillations, occurring near 40 cm-1 in both species and near 80 cm-1 for MbNO.