Quantum walks: Decoherence and coin-flipping games

We investigate the global chirality distribution of the quantum walk on the line when decoherence is introduced either through simultaneous measurements of the chirality and particle position, or as a result of broken links. The first mechanism drives the system towards a classical diffusive behavior. This is used to build new quantum games, similar to the spin-flip game. The second mechanism involves two different possibilities: (a) All the quantum walk links have the same probability of being broken. (b) Only the quantum walk links on a half-line are affected by random breakage. In case (a) the decoherence drives the system to a classical Markov process, whose master equation is equivalent to the dynamical equation of the quantum density matrix. This is not the case in (b) where the asymptotic global chirality distribution unexpectedly maintains some dependence with the initial condition. Explicit analytical equations are obtained for all cases.     

Classical random walk with memory versus quantum walk on a one-dimensional infinite chain

Quantum walk is a very useful tool for building quantum algorithms due to the faster spreading of probability distributions as compared to a classical random walk. Comparing the spreading of the probability distributions of a quantum walk with that of a mnemonic classical random walk on a one-dimensional infinite chain, we find that the classical random walk could have a faster spreading than that of the quantum walk conditioned on a finite number of walking steps. Quantum walk surpasses classical random walk with memory in spreading speed when the number of steps is large enough. However, in such a situation, quantum walk would seriously suffer from decoherence. Therefore, classical walk with memory may have some advantages in practical applications.     

Decoherence in quantum mechanics

We study decoherence in a simple quantum mechanical model using two approaches. Firstly, we follow the conventional approach to decoherence where one is interested in solving the reduced density matrix from the perturbative master equation. Secondly, we consider our novel correlator approach to decoherence where entropy is generated by neglecting observationally inaccessible correlators. We show that both methods can accurately predict decoherence time scales. However, the perturbative master equation generically suffers from instabilities which prevents us to reliably calculate the system’s total entropy increase. We also discuss the relevance of the results in our quantum mechanical model for interacting field theories.     

Improved frequency standard via weighted graph states

We study the spin squeezing property of weighted graph states,which can be used to improve sensitivity in interferometry.We study the time evolution of spin squeezing under local decoherence acting independently on each qubit.Based on the analysis,the spin squeezing of the weighted graph states is somehow robust in the presence of decoherence and the decoherence limit in the improvement of the interferometric sensitivity is still achievable.Furthermore,one can obtain the optimal improvement of sensitivity by tuning the weighted of each edges of the weighted graph state.     

Brun-Type Formalism for Decoherence in Two-Dimensional Quantum Walks

We study decoherence in the quantum walk on the xy-plane.We generalize the method of decoherent coin quantum walk,introduced by [T.A.Brun,et al.,Phys.Rev.A 67(2003) 032304],which could be applicable to all sorts of decoherence in two-dimensional quantum walks,irrespective of the unitary transformation governing the walk.As an application we study decoherence in the presence of broken line noise in which the quantum walk is governed by the two-dimensional Hadamard operator.     

Transport Efficiency of Continuous-Time Quantum Walks on Graphs

Continuous-time quantum walk describes the propagation of a quantum particle (or an excitation) evolving continuously in time on a graph. As such, it provides a natural framework for modeling transport processes, e.g., in light-harvesting systems. In particular, the transport properties strongly depend on the initial state and specific features of the graph under investigation. In this paper, we address the role of graph topology, and investigate the transport properties of graphs with different regularity, symmetry, and connectivity. We neglect disorder and decoherence, and assume a single trap vertex that is accountable for the loss processes. In particular, for each graph, we analytically determine the subspace of states having maximum transport efficiency. Our results provide a set of benchmarks for environment-assisted quantum transport, and suggest that connectivity is a poor indicator for transport efficiency. Indeed, we observe some specific correlations between transport efficiency and connectivity for certain graphs, but, in general, they are uncorrelated.     

Quantum to classical transition for random walks

We look at two possible routes to classical behavior for the discrete quantum random walk on the integers: decoherence in the quantum "coin" which drives the walk, or the use of higher-dimensional (or multiple) coins to dilute the effects of interference. We use the position variance as an indicator of classical behavior and find analytical expressions for this in the long-time limit; we see that the multicoin walk retains the "quantum" quadratic growth of the variance except in the limit of a new coin for every step, while the walk with decoherence exhibits "classical" linear growth of the variance even for weak decoherence.     

Non-Markovian decoherent quantum walks

Quantum walks act in obviously different ways from their classical counterparts, but decoherence will lessen and close this gap between them. To understand this process, it is necessary to investigate the evolution of quantum walks under different decoherence situations. In this article, we study a non-Markovian decoherent quantum walk on a line. In a short time regime, the behavior of the walk deviates from both ideal quantum walks and classical random walks. The position variance as a measure of the quantum walk collapses and revives for a short time, and tends to have a linear relation with time. That is, the walker's behavior shows a diffusive spread over a long time limit, which is caused by non-Markovian dephasing affecting the quantum correlations between the quantum walker and his coin. We also study both quantum discord and measurement-induced disturbance as measures of the quantum correlations, and observe both collapse and revival in the short time regime, and the tendency to be zero in the long time limit. Therefore, quantum walks with non-Markovian decoherence tend to have diffusive spreading behavior over long time limits, while in the short time regime they oscillate between ballistic and diffusive spreading behavior, and the quantum correlation collapses and revives due to the memory effect.     

Semi-Classical Limit and Minimum Decoherence in the Conditional Probability Interpretation of Quantum Mechanics

The Conditional Probability Interpretation of Quantum Mechanics replaces the abstract notion of time used in standard Quantum Mechanics by the time that can be read off from a physical clock. The use of physical clocks leads to apparent non-unitary and decoherence. Here we show that a close approximation to standard Quantum Mechanics can be recovered from conditional Quantum Mechanics for semi-classical clocks, and we use these clocks to compute the minimum decoherence predicted by the Conditional Probability Interpretation.     

Indirect decoherence in optical lattices and cold gases

The interaction of two–level atoms with a common heat bath leads to an effective interaction between the atoms, such that with time the internal degrees of the atoms become correlated or even entangled. If part of the atoms remain unobserved this creates additional indirect decoherence for the selected atoms, on top of the direct decoherence due to the interaction with the heat bath. I show that indirect decoherence can drastically increase and even dominate the decoherence for sufficiently large times. I investigate indirect decoherence through thermal black body radiation quantitatively for atoms trapped at regular positions in an optical lattice as well as for atoms at random positions in a cold gas, and show how indirect decoherence can be controlled or even suppressed through experimentally accessible parameters.     

三量子位系统的消相干和退纠缠

基于多谐振子热库环境模型,采用求解非马尔可夫近似主方程方法,研究了三量子位系统由于相对位相变化引起的消相干和退纠缠.计算得到了初始态为GHZ-class态、W-class态和WGHZ-class态在演化过程中的消相干和退纠缠时间尺度.结果表明,对初始GHZ-class态,相干性全部丧失,退纠缠完全发生,纠缠度变为0;对初始W-class态,相干性和纠缠度被保持;对初始WGHZ-class态,消相干部分发生,纠缠首先随时间变化最后达到一个渐近值.     

Remanent quantum correlations in dissipative qubits

Starting from the exact evolution of a Markovian dissipative quantum walk, a non-Markovian decoherence of two qubits interacting with a phonon thermal bath has been investigated analytically using quantum information tools. Concurrence and quantum discord are affected in a complex way, showing that entanglement decreases with dissipation. At the limit where dissipation dominates, quantum correlations survive in time as ∝t^−1/2$\propto t^{-1/2}$. Thus, even under the influence of dissipation, two qubits retain their quantumness for a long time. Quantum correlations could be therefore observed for a long time in related photonic experiments.     

Decoherence of quantum Brownian motion in noncommutative space

The decoherence of a harmonic oscillator under two-dimensional quantum Brownian motion on a noncommutative plane is investigated. The interaction with the environment is considered by two separate models so-called coupled and uncoupled. The two-dimensional master equation and its noncommutative counterpart are derived for both employed models. The rate of the linear entropy (predictability sieve) is chosen as a criterion to investigate the purity in the presence of the space noncommutativity. Besides, a two-dimensional charged harmonic oscillator on a plane which is imposed by a perpendicular magnetic field is introduced as a realization of our model. Therefore, our approach provides a formalism to investigate the influence of the magnetic field on the decoherence of the pure states. We show that in the high magnetic field limit the rate of the decoherence will be decreased.     

Decoherence and disorder in quantum walks: from ballistic spread to localization

We investigate the impact of decoherence and static disorder on the dynamics of quantum particles moving in a periodic lattice. Our experiment relies on the photonic implementation of a one-dimensional quantum walk. The pure quantum evolution is characterized by a ballistic spread of a photon's wave packet along 28 steps. By applying controlled time-dependent operations we simulate three different environmental influences on the system, resulting in a fast ballistic spread, a diffusive classical walk, and the first Anderson localization in a discrete quantum walk architecture.     

Adaptive random walks on the class of Web graphs

We study random walk with adaptive move strategies on a class of directed graphs with variable wiring diagram. The graphs are grown from the evolution rules compatible with the dynamics of the world-wide Web [B. Tadić, Physica A 293, 273 (2001)], and are characterized by a pair of power-law distributions of out- and in-degree for each value of the parameter β, which measures the degree of rewiring in the graph. The walker adapts its move strategy according to locally available information both on out-degree of the visited node and in-degree of target node. A standard random walk, on the other hand, uses the out-degree only. We compute the distribution of connected subgraphs visited by an ensemble of walkers, the average access time and survival probability of the walks. We discuss these properties of the walk dynamics relative to the changes in the global graph structure when the control parameter β is varied. For β≥ 3, corresponding to the world-wide Web, the access time of the walk to a given level of hierarchy on the graph is much shorter compared to the standard random walk on the same graph. By reducing the amount of rewiring towards rigidity limit β↦β_c≲ 0.1, corresponding to the range of naturally occurring biochemical networks, the survival probability of adaptive and standard random walk become increasingly similar. The adaptive random walk can be used as an efficient message-passing algorithm on this class of graphs for large degree of rewiring.     

Implementation of a one-dimensional quantum walk in both position and phase spaces

Quantum walks have been investigated as they have remarkably different features in contrast to classical random walks. We present a quantum walk in a one-dimensional architecture, consisting of two coins and a walker whose evolution is in both position and phase spaces alternately controlled by the two coins respectively. By analyzing the dynamics evolution of the walker in both the position and phase spaces, we observe an influence on the quantum walk in one space from that in the other space, which behaves like decoherence. We propose an implementation of the two-coin quantum walk in both position and phase spaces via cavity quantum electrodynamics(QED).     

Noise effect on Grover algorithm

The decoherence effect on Grover algorithm has been studied numerically through a noise modelled by a depolarizing channel. Two types of error are introduced characterizing the qubit time evolution and gate application, so the noise is directly related to the quantum network construction. The numerical simulation concludes an exponential damping law for the successive probability of the maxima as time increases. We have obtained an allowed-error law for the algorithm: the error threshold for the allowed noise behaves as ε_th(N) ∼1/N^1.1 (N being the size of the data set). As the power of N is almost one, we consider the Grover algorithm as robust to a certain extent against decoherence. This law also provides an absolute threshold: if the free evolution error is greater than 0.043, Grover algorithm does not work for any number of qubits affected by the present error model. The improvement in the probability of success, in the case of two qubits has been illustrated by using a fault-tolerant encoding of the initial state by means of the [[7,1,3]] quantum code.