Disentanglement and decoherence from classical non-Markovian noise: random telegraph noise

We calculate the two-qubit disentanglement due to classical random telegraph noise using the quasi-Hamiltonian method. This allows us to obtain analytical results even for strong coupling and mixed noise, important when the qubits have tunable working point. We determine when entanglement sudden death and revival occur as functions of qubit working point, noise coupling strength and initial state entanglement. For extended Werner states, we show that the concurrence is related to the difference of two functions: one is related to dephasing and the other longitudinal relaxation. A physical interpretation based on the generalized Bloch vector is given: revival only occurs for strongly-coupled noise and comes from the angular motion of the vector.     

Entanglement dynamics of a two-qutrit system under DM interaction and the relevance of the initial state

Using concurrence as a measure of entanglement, we present analytical and numerical study of entanglement dynamics in a two-qutrit system in the presence of the Dzyaloshinskii–Moriya interaction, as a function of the parameters involved. Three distinct initial states: a superposition of the ground and the first excited state, the Bell-type state and a superposition of qutrit coherent states will be considered in this investigation.     

Generating and using truly random quantum states in Mathematica

The problem of generating random quantum states is of a great interest from the quantum information theory point of view. In this paper we present a package for Mathematica computing system harnessing a specific piece of hardware, namely Quantis quantum random number generator (QRNG), for investigating statistical properties of quantum states. The described package implements a number of functions for generating random states, which use Quantis QRNG as a source of randomness. It also provides procedures which can be used in simulations not related directly to quantum information processing.Program summaryProgram title: TRQSCatalogue identifier: AEKA_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEKA_v1_0.htmlProgram obtainable from: CPC Program Library, Queen?s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 7924No. of bytes in distributed program, including test data, etc.: 88 651Distribution format: tar.gzProgramming language: Mathematica, CComputer: Requires a Quantis quantum random number generator (QRNG, http://www.idquantique.com/true-random-number-generator/products-overview.html) and supporting a recent version of MathematicaOperating system: Any platform supporting Mathematica; tested with GNU/Linux (32 and 64 bit)RAM: Case dependentClassification: 4.15Nature of problem: Generation of random density matrices.Solution method: Use of a physical quantum random number generator.Running time: Generating 100 random numbers takes about 1 second, generating 1000 random density matrices takes more than a minute.     

Quantum biology: explore quantum dynamics in biological systems

In recent years, people have been extending the concepts developed in quantum information science to explore quantum dynamics in biological systems. The existence of quantum coherence in certain biological processes has been identified in a number of experiments. The role of quantum coherence and quantum entanglement has been carefully investigated, which suggests that quantum effect is important in these processes although in a more complicated way. In the mean time, these findings urge the development of new experiment methodology to reveal more biological scenarios in which quantum effect exists and plays a non-trivial role. In this article, we review the latest progress in the field of quantum biology and discuss the key challenges in further development of quantum biology.     

QuTiP: An open-source Python framework for the dynamics of open quantum systems

We present an object-oriented open-source framework for solving the dynamics of open quantum systems written in Python. Arbitrary Hamiltonians, including time-dependent systems, may be built up from operators and states defined by a quantum object class, and then passed on to a choice of master equation or Monte Carlo solvers. We give an overview of the basic structure for the framework before detailing the numerical simulation of open system dynamics. Several examples are given to illustrate the build up to a complete calculation. Finally, we measure the performance of our library against that of current implementations. The framework described here is particularly well suited to the fields of quantum optics, superconducting circuit devices, nanomechanics, and trapped ions, while also being ideal for use in classroom instruction.Program summaryProgram title: QuTiP: The Quantum Toolbox in PythonCatalogue identifier: AEMB_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEMB_v1_0.htmlProgram obtainable from: CPC Program Library, Queen?s University, Belfast, N. IrelandLicensing provisions: GNU General Public License, version 3No. of lines in distributed program, including test data, etc.: 16 482No. of bytes in distributed program, including test data, etc.: 213 438Distribution format: tar.gzProgramming language: PythonComputer: i386, x86-64Operating system: Linux, Mac OSX, WindowsRAM: 2+ GigabytesClassification: 7External routines: NumPy (http://numpy.scipy.org/), SciPy (http://www.scipy.org/), Matplotlib (http://matplotlib.sourceforge.net/)Nature of problem: Dynamics of open quantum systems.Solution method: Numerical solutions to Lindblad master equation or Monte Carlo wave function method.Restrictions: Problems must meet the criteria for using the master equation in Lindblad form.Running time: A few seconds up to several tens of minutes, depending on size of underlying Hilbert space.     

Static and output-feedback of discrete-time LTI systems with state multiplicative noise

A parameter dependent approach for designing static output-feedback controller for linear time-invariant systems with state-multiplicative noise is introduced which achieves a minimum bound on either the stochastic H₂ or the H_∞ performance levels. A solution is obtained also for the case where, in addition to the stochastic parameters, the system matrices reside in a given polytope. In this case, a parameter dependent Lyapunov function is described which enables the derivation of the required constant feedback gain via a solution of a set of linear matrix inequalities that correspond to the vertices of the uncertainty polytope.The stochastic parameters appear in both the dynamics and the input matrices of the state space model of the system. The problems are solved using the expected value of the standard performance indices over the stochastic parameters. The theory developed is demonstrated by a simple example.     

Application of the Feynman-Kac path integral method in finding excited states of quantum systems

Group theory considerations and properties of a continuous path are used to define a failure tree procedure for finding eigenvalues of the Schrödinger equation using stochastic methods. The procedure is used to calculate the lowest excited state eigenvalues of eigenfunctions possessing anti-symmetric nodal regions in configuration space using the Feynman-Kac path integral method. Within this method the solution of the imaginary time Schrödinger equation is approximated by random walk simulations on a discrete grid constrained only by symmetry considerations of the Hamiltonian. The required symmetry constraints on random walk simulations are associated with a given irreducible representation and are found by identifying the eigenvalues for the irreducible representation corresponding to symmetric or antisymmetric eigenfunctions for each group operator. The method provides exact eigenvalues of excited states in the limit of infinitesimal step size and infinite time. The numerical method is applied to compute the eigenvalues of the lowest excited states of the hydrogenic atom that transform as Γ² and Γ⁴ irreducible representations. Numerical results are compared with exact analytical results.     

Root-mean-square filtering of the state of polynomial stochastic systems with multiplicative noise

Some results obtained by the present author in the field of designing the finitedimensional root-mean-square filters for stochastic systems with polynomial equations of state and multiplicative noise from the linear observations were overviewed. A procedure to derive the finite-dimensional system of approximate filtering equations for a polynomial arbitrary-order equation of state was presented. The closed system of filtering equations for the root-mean-square estimate and covariance matrix error was deduced explicitly for special cases of linear and quadratic coefficients of drift and diffusion in the equation of state. For linear stochastic systems with unknown parameters, the problem of joint root-mean-square state filtering and identification of the parameters from linear observations was considered in the Appendix.     

On the design of regulator systems using bounding optimal initial state manifolds

This paper presents a discussion of techniques for designing optimal linear time-invariant regulator systems, which have inaccessible states, and which are based on a quadratic performance functional for the definition of optimality. A definition is given of a suboptimal control vectorhat{k}, which hasmnonzero, constant elements andn - melements defined as zero, and which will provide optimal performance from anm-dimensional linear manifold of initial states. An algorithm is given for determininghat{k}for a linear manifold lying between two optimal manifolds and an example illustrates the superiority of these routines for initial-state sets about an optimal manifold.     

Deterministic generation of singlet states for N-atoms in coupled cavities via quantum Zeno dynamics

We propose an efficient scheme to drive two atoms in two coupled cavities into a two-atom singlet state via quantum Zeno dynamics and virtual excitations by one step. Then, we convert the two-atom singlet state into a three-atom singlet state in three coupled bimodal cavities with the same principle. We also discuss the influence of decoherence induced by cavity decay and atomic spontaneous emission by numerical calculation. This scheme is robust against both the cavity decay and atomic spontaneous emission since there are no excited cavity fields involved during the operation process, and the atoms are only virtually excited. Actually, if multi-level atoms and multi-mode cavities are applicable, we can convert the ( \(n-1\) )-atom ( \(n\ge 3\) ) singlet state into a \(n\) -atom singlet state in coupled cavity arrays with the same principle in theory.     

Generation of three-atom singlet state in a bimodal cavity via quantum Zeno dynamics

We propose an efficient scheme for generation of three-atom singlet state in a bimodal cavity based on quantum Zeno dynamics and the large detuning condition. The influence of decoherence induced by cavity decay and atomic spontaneous emission is also discussed by numerical calculation. The advantages of the scheme are that the initial input states of atoms are not entangled and the fidelity is insensitive to cavity decay and atomic spontaneous emission due to no exciting the cavity fields during the whole evolution and the large detuning condition.     

A new approach to fuzzy modeling of nonlinear dynamic systems with noise: relevance vector learning mechanism

This paper presents a new fuzzy inference system for modeling of nonlinear dynamic systems based on input and output data with measurement noise. The proposed fuzzy system has a number of fuzzy rules and parameter values of membership functions which are automatically generated using the extended relevance vector machine (RVM). The RVM has a probabilistic Bayesian learning framework and has good generalization capability. The RVM consists of the sum of product of weight and kernel function which projects input space into high dimensional feature space. The structure of proposed fuzzy system is same as that of the Takagi-Sugeno fuzzy model. However, in the proposed method, the number of fuzzy rules can be reduced under the process of optimizing a marginal likelihood by adjusting parameter values of kernel functions using the gradient ascent method. After a fuzzy system is determined, coefficients in consequent part are found by the least square method. Examples illustrate effectiveness of the proposed new fuzzy inference system.     

Estimations of the errors between the evolving states generated by two Hamiltonians with the same initial state

Time evolution of a quantum system is described by Schrödinger equation with initial pure state, or von Neumann equation with initial mixed state. In this paper, we estimate the error between the evolving states generated by two Hamiltonians with the same initial pure state. Secondly, according to the method of operator–vector correspondence, we give a relation of the Schrödinger equation and von Neumann equation and then estimate the error between the evolving states generated by two Hamiltonians with the same initial mixed state.     

Adaptive ILC for a class of discrete-time systems with iteration-varying trajectory and random initial condition

In this work we present a discrete-time adaptive iterative learning control (AILC) scheme to deal with systems with time-varying parametric uncertainties. Using the analogy between the discrete-time axis and the iterative learning axis, the new adaptive ILC can incorporate a Recursive Least Squares (RLS) algorithm, hence the learning gain can be tuned iteratively along the learning axis and pointwisely along the time axis. When the initial states are random and the reference trajectory is iteration-varying, the new AILC can achieve the pointwise convergence over a finite time interval asymptotically along the iterative learning axis.     

Identification and validation of the statistics of the initial states of linear dynamic systems based on cross-sectional data

This note examines the problem of statistical inference of the initial states of a linear discrete dynamic system based on a set of cross-sectional data. Several compressed data structures are proposed to reduce the amount of the cross-sectional data obtained from multiple independent experiments. It is shown that these data structures are sufficient statistics for estimating the mean and the covariance of the initial states, given the entire raw data from multiple experiments. Thus, the identification and the validation of these parameters can be performed with reduced data structures without referring back to the entire raw data and the original dynamics. For the identification of these parameters, theE-Mprocedure presented in [1] can be applied to this case. For the validation of these parameters having specified values, simple tests of "significance" type are proposed. The major advantage of these tests over the generalized likelihood ratio test is that their probability distributions are known and computable under both the null and the alternative hypotheses even for the finite sample case, i.e., the asymptotic assumption is not necessary.     

Dynamics of tripartite quantum correlations and decoherence in flux qubit systems under local and non-local static noise

We investigate the dynamics of entanglement, decoherence and quantum discord in a system of three non-interacting superconducting flux qubits (fqubits) initially prepared in a Greenberger–Horne–Zeilinger (GHZ) state and subject to static noise in different, bipartite and common environments, since it is recognized that different noise configurations generally lead to completely different dynamical behavior of physical systems. The noise is modeled by randomizing the single fqubit transition amplitude. Decoherence and quantum correlations dynamics are strongly affected by the purity of the initial state, type of system–environment interaction and the system–environment coupling strength. Specifically, quantum correlations can persist when the fqubits are commonly coupled to a noise source, and reaches a saturation value respective to the purity of the initial state. As the number of decoherence channels increases (bipartite and different environments), decoherence becomes stronger against quantum correlations that decay faster, exhibiting sudden death and revival phenomena. The residual entanglement can be successfully detected by means of suitable entanglement witness, and we derive a necessary condition for entanglement detection related to the tunable and non-degenerated energy levels of fqubits. In accordance with the current literature, our results further suggest the efficiency of fqubits over ordinary ones, as far as the preservation of quantum correlations needed for quantum processing purposes is concerned.     

On the optimum timing of observations for linear control systems with unknown initial state

A linear system with a cost function that is quadratic in the control and terminal position error is given. The initial state is unknown and noise-corrupted observations are taken. Due to the cost of taking the observations, they are limited to a given number. Using the tools of optimum stochastic control theory, the optimum timing of the available observations is determined (minimizing the expected value of the loss function). For the cases considered, the locations can be determined a priori, and do not depend on the values of previous observations. Graphs of the optimum observation locations for several scalar cases are given. Graphs of the true cost, as a function of the locations of the observations, are also given for several scalar cases. The change in cost for small variations from the optimum location is usually not significant.     

SLOCC orbit of rank-deficient two-qubit states: quantum entanglement,quantum discord and EPR steering

We study selected aspects of non-classical correlations of arbitrary states from the stochastic local operations and classical communication orbit of rank-deficient two-qubit states. In particular, we find explicitly entanglement of formation and quantum discord for these states. Moreover, we determine and analyze the Einstein–Podolsky–Rosen steering ellipsoids corresponding to these states.     

Multi-letter quantum finite automata: decidability of the equivalence and minimization of states

Multi-letter quantum finite automata (QFAs) can be thought of quantum variants of the one-way multi-head finite automata (Hromkovi?, Acta Informatica 19:377?C384, 1983). It has been shown that this new one-way QFAs (multi-letter QFAs) can accept with no error some regular languages, for example (a?+?b)*b, that are not acceptable by QFAs of Moore and Crutchfield (Theor Comput Sci 237:275?C306, 2000) as well as Kondacs and Watrous (66?C75, 1997; Observe that 1-letter QFAs are exactly measure-once QFAs (MO-1QFAs) of Moore and Crutchfield (Theor Comput Sci 237:275?C306, 2000)). In this paper, we study the decidability of the equivalence and minimization problems of multi-letter QFAs. Three new results presented in this paper are the following ones: (1) Given a k ₁-letter QFA ${{\mathcal A}_1}$ and a k ₂-letter QFA ${{\mathcal A}_2}$ over the same input alphabet ??, they are equivalent if and only if they are (n ² m ^k-1?m ^k-1?+?k)-equivalent, where m =?|??| is the cardinality of ??, k =?max(k ₁,k ₂), and n =?n ₁?+?n ₂, with n ₁ and n ₂ being numbers of states of ${{\mathcal A}_{1}}$ and ${{\mathcal A}_{2}}$ , respectively. When k =?1, this result implies the decidability of equivalence of measure-once QFAs (Moore and Crutchfield in Theor Comput Sci 237:275?C306, 2000). (It is worth mentioning that our technical method is essentially different from the previous ones used in the literature.) (2) A polynomial-time O(m ^2k-1 n ⁸?+?km ^k n ⁶) algorithm is designed to determine the equivalence of any two multi-letter QFAs (see Theorems 2 and 3; Observe that if a brute force algorithm to determine equivalence would be used, as suggested by the decidability outcome of the point (1), the worst case time complexity would be exponential). Observe also that time complexity is expressed here in terms of the number of states of the multi-letter QFAs and k can be seen as a constant. (3) It is shown that the states minimization problem of multi-letter QFAs is solvable in EXPSPACE. This implies also that the state minimization problem of MO-1QFAs (see Moore and Crutchfield in Theor Comput Sci 237:275?C306, 2000, page 304, Problem 5), an open problem stated in that paper, is also solvable in EXPSPACE.     

Quantum coherence as indicators of quantum phase transitions,factorization and thermal phase transitions in the anisotropic XY model

Quantifying quantum coherence has attracted considerable interests. In the present work, we employ two measures of quantum coherence recently proposed in terms of the skew information and the trace norm, respectively, to investigate the quantum phase transitions (QPTs), factorization in the XY model and the thermal phase transitions (TPTs) in the transverse field Ising model. Two quantifications of quantum nonlocality via the same distance measure of the quantum coherence are also studied for reference. It is shown that two types of quantum coherence are reliable in identifying QPTs and TPTs. However, only the quantum coherence based on the skew information can detect factorization. In addition, the quantum coherence and nonlocality measured via the same distance space have similar finite temperature scaling law, while the quantum coherence based on skew information and trace norm has different finite temperature scaling law. Moreover, the skew-information-based quantum coherence at finite temperature suggests that factorization vanishes when temperature exceeds 0.02 (Boltzmann constant \(k_{B} = 1\)), which is in agreement with the results of the fidelity for states with different distances of spin-pairs.