International Journal of Quantum Information

We study the ground-state entanglement properties of an XX spin 1/2 chain in transverse field, in its quasi-long-ranged ordered phase, with a magnetic impurity, represented in terms of an additional transverse magnetic field located at one precise site. For such a system, we show that a control of the ground state entanglement can be achieved by acting on the impurity field. To demonstrate this possibility, we evaluate exactly the nearest neighbor and next-nearest neighbor concurrence in the presence of the impurity. It turns out that either an enhancement or a quenching of entanglement between selected spin pairs can be obtained by acting on the intensity of the impurity. For specific values of the magnetic field a spatial modulation of concurrence along the chain is also obtained.

It is shown that errors due to spatially correlated noises can be corrected by the quantum error-correction code and error-correction procedure prepared for those for independent noises. A model of noisy-channel which is under the influence of spatially correlated quantum Brownian motion is investigated within the framework of non-equilibrium thermo field dynamics that is a canonical operator formalism for dissipative quantum systems.

Quantum trajectory theory is the best mathematical set up to model continual observations of a quantum system and feedback based on the observed output. Inside this framework, we study how to enhance the squeezing of the fluorescence light emitted by a two-level atom, stimulated by a coherent monochromatic laser. In the presence of a Wiseman-Milburn feedback scheme, based on the homodyne detection of a fraction of the emitted light, we analyze the squeezing dependence on the various control parameters.

We show that a suitably engineered external non-Gaussian noise can entangle a class of initially separable, polarized two-photon coherent states.

We give a brief introduction to the algebraic formulation of error correction in quantum computing called operator algebra quantum error correction (OAQEC). Then we extend one of the basic results for subsystem codes in operator quantum error correction (OQEC) to the OAQEC setting: Every hybrid classical-quantum code is shown to be unitarily recoverable in an appropriate sense. The algebraic approach of the proof yields a new, less technical proof for the OQEC case.

We explore some basic entanglement features of multiqubit systems that are relevant for the development of algorithms for searching highly entangled states. In particular, we compare the behaviours of multiqubit entanglement measures based (i) on the von Neumann entropy of marginal density matrices and (ii) on the linear entropy of those matrices.

A quantum measurement process, when non-trivial, is not a closed evolution: the appearance of classical outcomes is usually interpreted as the evidence of some decoherence-like mechanism causing quantum superpositions to degrade into classical mixtures. Such mechanism is due to a net flow of information from the input system (measurement object), through the physical apparatus interacting with the object (measurement probe), into some environment, the latter representing all those degrees of freedom which are not directly accessible by the experimenter. For this reason, the phenomenon of state reduction induced by the measurement process generally entails an irreversible state change. The aim of our contribution is to answer the following questions : how much information a measurement is able to extract? "How much" irreversible is the state reduction due to a particular measurement process? In which way information gain and irreversibility are related?

We analyze qubit channels by exploiting the possibility of representing two-level quantum systems in terms of characteristic functions. To do so, we use functions of non-commuting variables (Grassmann variables), defined in terms of generalized displacement operators, following an approach which resemble the one adopted for continuous–variable (Bosonic) systems. It allows us to introduce the notion of qubit Gaussian channels and to show that they share similar properties with the corresponding continuous–variable counterpart. Some examples of qubit channels are investigated using this approach.

We construct a large class of quantum d ⊗ d states which are positive under partial transposition (so called PPT states). The construction is based on certain direct sum decomposition of the total Hilbert space displaying characteristic circular structure — that is way we call them circulant states. It turns out that partial transposition maps any such decomposition into another one and hence both original density matrix and its partially transposed partner share similar cyclic properties. This class contains many well known examples of PPT states from the literature and gives rise to a huge family of completely new states.

The realization of quantum logic gates with neutral atoms on atom chips is investigated, including realistic features, such as noise and actual experimental setups.

In this work, we have studied the post-measurement dynamics of several electrons in a double quantum dot system using a new method of calculation. We have solved the effective-mass non-linear Schrödinger equation for two electron wave packets in a double quantum well taking into account the different number of projected electrons in each quantum well after an observation. It is found the existence of a critical density that reduces strongly the tunneling dynamics between both quantum wells. In addition, we have shown the possibility of having a new kind of electromagnetic radiation emerging from a semiconductor device after a quantum observation.

We discuss the effect of low-frequency noise on interacting superconducting qubits in a fixed coupling scheme. By properly choosing operating conditions, within the adiabatic framework the systems develops two decoupled subspaces. The subspace where a SWAP operation takes place turns out to be resilient to low frequency fluctuations. The possibility to encode a single qubit in a protected two-physical-qubit system subspace is briefly discussed.

We study a dephasing channel with memory, modelled by a Markov chain. We show that even weak memory effects have a detrimental impact on the performance of quantum error correcting schemes designed for uncorrelated errors. We also discuss an alternative scheme that takes advantage of memory effects to protect quantum information.

We use the recently introduced concept of information flux in a many-body register in order to give an alternative viewpoint on quantum state transfer in linear chains of many spins.

In the article we analyse how noisiness of quantum channels can influence the magic squares quantum pseudo-telepathy game. We show that the probability of success can be used to determine characteristics of quantum channels. Therefore the game deserves more careful study aiming at its implementation.

Entangling and disentangling capacities are the key manifestation of the nonlocal content of a quantum operation. A lot of effort has been put recently into investigating (dis)entangling capacities of unitary operations, but very little is known about capacities of non-unitary operations. Here we investigate (dis)entangling capacities of unital CPTP maps acting on two qubits.

We study decoherence of a three-qubit array coupled to substrate phonons. Assuming an initial three-qubit entangled state that would be decoherence-free for identical qubit positions, allows us to focus on non-Markovian effects of the inevitable spatial qubit separation. It turns out that the coherence is most affected when the qubits are regularly spaced. Moreover, we find that up to a constant scaling factor, two-qubit entanglement is not influenced by the presence of the third qubit, even though all qubits interact via the phonon field.

In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we solve in the asymptotic long-time regime the master equation for two independent harmonic oscillators interacting with an environment. We give a description of the continuous-variable asymptotic entanglement in terms of the covariance matrix of the considered subsystem for an arbitrary Gaussian input state. Using Peres–Simon necessary and sufficient condition for separability of two-mode Gaussian states, we show that for certain classes of environments the initial state evolves asymptotically to an entangled equilibrium bipartite state, while for other values of the coefficients describing the environment, the asymptotic state is separable. We calculate also the logarithmic negativity characterizing the degree of entanglement of the asymptotic state.

Complex chaos is specified by an iterated mapping on complex numbers. It has recently been found in the dynamics of qubits where each time step is conditioned on a measurement result on part of the system. We analyse the simplest case of one qubit dynamics with one complex parameter in some detail. We point out that two attractive cycles can exist and provide examples how the fractal like Julia set divides the areas of corresponding initial states. We show how to determine the set of parameters for which one, two or no stable fixed cycles exists and provide the numerically calculated images of the sets. The results can be relevant for the quantum state purification protocol based on the similar dynamics of two or more qubits and in general for any protocol based on conditioned nonlinear dynamics where truly chaotic behavior may occur.

A quantum gate is implemented by control interactions between qubits and their ancilla system. It has been shown that the control interactions have possibilities to induce the dynamical decoherence on the qubits if an additive conservation law is assumed in the interactions and the ancilla system is finite. This decoherece put the precision limit on the gate, which cannot be removed from the qubit by optimizing the interaction and the initialization of the ancilla system. In this paper, we give the outline of investigating the precision limit which is formulated by the lower bound of the gate infidelity, one minus the squared fidelity, for an arbitrary self-adjoint gate on a single qubit. We show rigorous lower bounds in terms of the variance of the conserved quantity and a simple geometrical relation between the conservation law to be assumed and the gates to be implemented. We also comment on another approach to provide the precision limit for an arbitrary single qubit gate under a conservation law.

We calculate the geometric phase for different open systems (spin-boson and spin-spin models). We study not only how they are corrected by the presence of the different type of environments but also discuss the appearence of decoherence effects. These should be taken into account when planning experimental setups to study the geometric phase in the nonunitary regime. We propose a model with slow decoherence rate in which the geometric phase is still modified and might be measured.

The notion of distance in Hilbert space is relevant in many scenarios. In particular, "distances" between quantum states play a central role in quantum information theory. An appropriate measure of distance is the quantum Jensen Shannon divergence (QJSD) between quantum states. Here we study this distance as a geometrical measure of entanglement and apply it to different families of states.

We have recently shown that the output field in the Braunstein–Kimble protocol of teleportation is a superposition of two fields: the input one and a field created by Alice's measurement and by displacement of the state at Bob's station by using the classical information provided by Alice. We study here the noise added by teleportation and compare its influence in the Gaussian and non-Gaussian settings.

We study patterns of temporal evolution, creation and transport, of entanglement in quantum spin chains. The model used is an isotropic Heisenberg chain with periodic boundary conditions, and we obtain in analytic form the time dependence of concurrence and negativity of various pairs of spins in the system. The objective of the present study is to assess the usefulness of various averaged entanglement measures in the characterization of entangling properties of quantum evolutions.

We show a memory model of an imperative concurrent quantum programming language LanQ. The memory model is used to specify the shape of semantical structure upon which the language operational semantics is defined. We also outline the language abilities in the area of formal verification on an example implementation of teleportation protocol.

We study a way of establishing a pure entangled state between two segments of a 1D ring using impenetrable bosons. The two bosons are initially simply placed at two positions on the ring which is an unentangled state. After some time evolution, we project the segments to a pure state through coarse grained measurements which ascertain whether there is a particle present in a given segment without revealing any information about its position within the segment. Subject to finding a particle in each segment, we quantify the entanglement established between the segments through the von Neumann entropy of a subsystem. We also investigate whether this entanglement increases with the number of particles and compare the entanglement in dynamical and ground states.

We obtain a maximizer for the quantum mutual information for classical information sent over the quantum amplitude damping channel. This is achieved by limiting the ensemble of input states to antipodal states, in the calculation of the product state capacity for the channel. We also consider the product state capacity of a convex combination of two memoryless channels and demonstrate in particular that it is in general not given by the minimum of the capacities of the respective memoryless channels.

To understand multi-partite entanglement of the thermal state in the 1D spin 1/2 XY model with a transverse magnetic field, we investigate the temperature below which the thermal state is certainly entangled. We refer to such a temperature as a threshold temperature. We show that two characteristic lines in the phase diagram at zero temperature of the XY model can be clearly emphasized by the threshold temperature.

We have recently presented a protocol for extracting the singlet state of two non-interacting high-dimensional spins through post-selection of the internal state of interaction mediators sent in succession [F. Ciccarello et al., arXiv:0710.3855v1]. The scheme requires each mediator's wavevector to obey appropriate resonance conditions. Here we show the robustness of the scheme in the realistic case where such conditions are not sharply fulfilled.

We consider the collective eavesdropping of the BB84 and six-state protocols. Since these protocols are symmetric in the eigenstates of conjugate bases, we consider collective attacks having the same kind of symmetry. We then show how these symmetric collective attacks are sufficiently strong in order to minimize the Devetak–Winter rates. In fact, it is quite easy to construct simple examples able to reach the unconditionally secure key rates of these protocols.

We construct a quantum algorithm to approximate efficiently the colored Jones polynomial of the plat presentation of any oriented link L at a fixed root of unity q. The construction exploits the q-deformed spin network as computational background. The complexity of such algorithm is bounded above linearly by the number of crossings of the link, and polynomially by the number of link strands.

It is shown that quantum coherence is conserved in a principal system in the case that the system is coupled to a fast dissipating environment [arXiv:0709.0562]. The phenomenon is called the quantum wipe effect. Here, this effect is reviewed and the analytical proof for a model system consisting of a one-qubit system coupled to a fast dissipating environment is extended to an environment at a thermal equilibrium.

We introduce and evaluate measures of nonclassical correlation defined on the basis of a paradigm claiming that a multipartite system represented by a density matrix having no product eigenbasis possesses nonclassical correlation.

Evolution of animals with multiple organs is considered. We report computer-aided modeling and simulation of evolution in biological systems with living organisms as effect of extremum properties of classical statistical entropy of Gibbs–Boltzmann type or its associates, e.g. Tsallis q-entropy. A variational problem searches for the maximum entropy subject to the geometric constraint of constant thermodynamic distance in a non-Euclidean space of independent probabilities p_i, plus possibly other constraints. Tensor form of dynamics is obtained. Some developmental processes progress in a relatively undisturbed way, whereas others may terminate rapidly due to inherent instabilities. The results show that a discrete gradient dynamics (governed by the entropy) can be predicted from variational principles for shortest paths and suitable transversality conditions.

We investigate the transient dynamics of a short overdamped Josephson junction with a periodic driving signal in the presence of colored noise. We analyze noise induced phenomena, specifically resonant activation and noise enhanced stability. We find that the positions both of the minimum of RA and maximum of NES depend on the value of the noise correlation time τ_c. Moreover, in the range where RA is observed, we find a non-monotonic behavior of the mean switching time as a function of τ_c.

In an interacting continuous time quantum walk, while the walker (the cursor) is moving on a graph, computational primitives (unitary operators associated to the edges) are applied to ancillary qubits (the register). The model with one walker was originally proposed by R. Feynman, who thus anticipated many features of the Continuous Time Quantum Walk (CTWQ) computing paradigm. In this note we examine the behaviour of an interacting CTQW with two walkers and examine the interaction of the walkers with noncommuting primitives. We endow such a walk with a notion of trajectory, in the sense of sample path of an associated Markov process, in order to use such notions as sojourn time and first passage time as heuristic tools for gaining intuition about its behaviour.