Non-Markovian decoherence: complete positivity and decomposition

In this work, the non-Markovian decoherence is considered in two ways. Firstly, an effective Hamiltonian approach is demonstrated to investigate the decoherence of a quantum system in a non-Markovian environment, in which complete positivity of the reduced dynamics is achieved. This method uses the notion of an effective environment, that is a subsystem of the environment that causes the decoherence. Secondly, the evolution of the system and environment is decomposed, thus partially illuminating how they would interact given that memory effects are allowed. It should be noted that beam splitters and rotators are sufficient to explain this decomposition.

Completely positive non-Markovian decoherence

We propose an effective Hamiltonian approach to investigate decoherence of a quantum system in a non-Markovian reservoir, naturally imposing the complete positivity on the reduced dynamics of the system. The formalism is based on the notion of an effective reservoir, i.e., certain collective degrees of freedom in the reservoir that are responsible for the decoherence. As examples for completely positive decoherence, we present three typical decoherence processes for a qubit such as dephasing, depolarizing, and amplitude damping. The effects of the non-Markovian decoherence are compared to the Markovian decoherence.

Many-body entanglement in decoherence processes

A pure state decoheres into a mixed state as it entangles with an environment. When an entangled two-mode system is embedded in a thermal environment, however, each mode may not be entangled with its environment by their simple linear interaction. We consider an exactly solvable model to study the dynamics of a total system, which is composed of an entangled two-mode system and a thermal environment. The Markovian interaction with the environment is concerned with an array of infinite number of beam splitters. It is shown that many-body entanglement of the system and the environment may play a crucial role in the process of disentangling the system.

Experimental demonstration of decoherence-free one-way information transfer

We report the experimental demonstration of a one-way quantum protocol reliably operating in the presence of decoherence. Information is protected by designing an appropriate decoherence-free subspace for a cluster state resource. We demonstrate our scheme in an all-optical setup, encoding the information into the polarization states of four photons. A measurement-based one-way information-transfer protocol is performed with the photons exposed to severe symmetric phase-damping noise. Remarkable protection of information is accomplished, delivering nearly ideal outcomes.

One-way quantum computing in a decoherence-free subspace

We introduce a novel scheme for one-way quantum computing (QC) based on the use of information encoded qubits in an effective cluster state resource. With the correct encoding structure, we show that it is possible to protect the entangled resource from phase damping decoherence, where the effective cluster state can be described as residing in a decoherence-free subspace (DFS) of its supporting quantum system. One-way QC then requires either single or two-qubit adaptive measurements. As an example where this proposal can be realized, we describe an optical lattice set-up where the scheme provides robust quantum information processing. We also outline how one can adapt the model to provide protection from other types of decoherence.

Decoherence-based exploration of d-dimensional one-way quantum computation: Information transfer and basic gates

We study the effects of amplitude and phase damping decoherence in d-dimensional one-way quantum computation. We focus our attention on low dimensions and elementary unidimensional cluster state resources. Our investigation shows how information transfer and entangling gate simulations are affected for d >= 2. To understand motivations for extending the one-way model to higher dimensions, we describe how basic qudit cluster states deteriorate under environmental noise of experimental interest. In order to protect quantum information from the environment, we consider encoding logical qubits into qudits and compare entangled pairs of linear qubit-cluster states to single qudit clusters of equal length and total dimension. A significant reduction in the performance of cluster state resources for d > 2 is found when Markovian-type decoherence models are present.

Unusual decoherence in qubit measurements with a Bose-Einstein condensate

We consider an electrostatic qubit located near a Bose-Einstein condensate (BEC) of noninteracting bosons in a double-well potential, which is used for qubit measurements. Tracing out the BEC variables we obtain a simple analytical expression for the qubit's density matrix. The qubit's evolution exhibits a slow (proportional to 1/root t) damping of the qubit's coherence term, which however turns to be a Gaussian one in the case of static qubit. This is in contrast to the exponential damping produced by most classical detectors. The decoherence is, in general, incomplete and strongly depends on the initial state of the qubit.

Collective decoherence of cold atoms coupled to a Bose-Einstein condensate

We examine the time evolution of cold atoms (impurities) interacting with an environment consisting of a degenerate bosonic quantum gas. The impurity atoms differ from the environment atoms, being of a different species. This allows one to superimpose two independent trapping potentials, each being effective only on one atomic kind, while transparent to the other. When the environment is homogeneous and the impurities are confined in a potential consisting of a set of double wells, the system can be described in terms of an effective spin-boson model, where the occupation of the left or right well of each site represents the two (pseudo)-spin states. The irreversible dynamics of such system is here studied exactly, i.e. not in terms of a Markovian master equation. The dynamics of one and two impurities is remarkably different in respect of the standard decoherence of the spin-boson system. In particular, we show: (i) the appearance of coherence oscillations, (ii) the presence of super and subdecoherent states that differ from the standard ones of the spin-boson model, and (iii) the persistence of coherence in the system at long times. We show that this behaviour is due to the fact that the pseudospins have an internal spatial structure. We argue that collective decoherence also prompts information about the correlation length of the environment. In a one-dimensional (1D) configuration, one can change even more strongly the qualitative behaviour of the dephasing just by tuning the interaction of the bath.

Sudden Transition between Classical and Quantum Decoherence

We study the dynamics of quantum and classical correlations in the presence of nondissipative decoherence. We discover a class of initial states for which the quantum correlations, quantified by the quantum discord, are not destroyed by decoherence for times t < <(t)over bar>. In this initial time interval classical correlations decay. For t > (t) over bar, on the other hand, classical correlations do not change in time and only quantum correlations are lost due to the interaction with the environment. Therefore, at the transition time (t) over bar the open system dynamics exhibits a sudden transition from classical to quantum decoherence regime.

Competition between memory-keeping and memory-erasing decoherence channels

We study the competing effects of simultaneous Markovian and non-Markovian decoherence mechanisms acting on a single spin. We show the existence of a threshold in the relative strength of such mechanisms above which the spin dynamics becomes fully Markovian, as revealed by the use of several non-Markovianity measures. We identify a measure-dependent nested structure of such thresholds, hinting at a causality relationship among the various non-Markovianity witnesses used in our analysis. Our considerations are then used to argue the unavoidably non-Markovian evolution of a single-electron quantum dot exposed to both intrinsic and Markovian technical noise, the latter of arbitrary strength. 

Self-consistent non-Markovian theory of a quantum-state evolution for quantum-information processing

We study non-Markovian decoherence phenomena by employing projection-operator formalism when a quantum system (a quantum bit or a register of quantum bits) is coupled to a reservoir. By projecting out the degree of freedom of the reservoir, we derive a non-Markovian master equation for the system, which is reduced to a Lindblad master equation in Markovian limit, and obtain the operator sum representation for the time evolution. It is found that the system is decohered slower in the non- Markovian reservoir than the Markovian because the quantum information of the system is memorized in the non-Markovian reservoir. We discuss the potential importance of non-Markovian reservoirs for quantum-information processing.

Simulation of quantum random walks using the interference of a classical field

We suggest a theoretical scheme for the simulation of quantum random walks on a line using beam splitters, phase shifters, and photodetectors. Our model enables us to simulate a quantum random walk using of the wave nature of classical light fields. Furthermore, the proposed setup allows the analysis of the effects of decoherence. The transition from a pure mean-photon-number distribution to a classical one is studied varying the decoherence parameters.

Asymmetric quantum channel for quantum teleportation

We propose an optimal strategy for continuous-variable teleportation in a realistic situation. We show that the typical imperfect quantum operation can be described as a combination of an asymmetrically decohered quantum channel and perfect apparatuses for other operations. For the asymmetrically decohered quantum channel, we find some counterintuitive results: teleportation does not necessarily get better as the channel is initially squeezed more. We show that decoherence-assisted measurement and transformation may enhance fidelity for an asymmetrically mixed quantum channel.

Entanglement induced by a single-mode heat environment

A thermal field, which frequently appears in problems of decoherence, provides us with minimal information about the field. We study the interaction of the thermal field and a quantum system composed of two qubits and find that such a chaotic field with minimal information can nevertheless entangle qubits that are prepared initially in a separable state. This simple model of a quantum register interacting with a noisy environment allows us to understand how memory of the environment affects the state of a quantum register.

Characterization of the entanglement of two squeezed states

We study a continuous-variable entangled state composed of two states which are squeezed in two opposite quadratures in phase space. Various entanglement conditions are tested for the entangled squeezed state and we study decoherence models for noise, producing a mixed entangled squeezed state. We briefly describe a probabilistic protocol for entanglement swapping based on the use of this class of entangled states and the main features of a general generation scheme.