The destruction of quantum interference, decoherence, and the destruction of entanglement both appear to occur under the same circumstances. To address the connection between these two phenomena, we consider the evolution of arbitrary initial states of a two-particle system under open system dynamics described by a class of master equations which produce decoherence of each particle. We show that all initial states become separable after a finite time, and we produce the explicit form of the separated state. The result extends and amplifies an earlier result of Diósi. We illustrate the general result by considering the case in which the initial state is an EPR state (in which both the positions and momenta of a particle pair are perfectly correlated). This example clearly illustrates how the spreading out in phase space produced by the environment leads to certain disentanglement conditions becoming satisfied.
Decoherence is well understood, in contrast to disentanglement. According to common lore, irreversible coupling to a dissipative environment is the mechanism for loss of entanglement. Here, we show that, on the contrary, disentanglement can in fact occur at large enough temperatures $T$ even for vanishingly small dissipation (as we have shown previously for decoherence). However, whereas the effect of $T$ on decoherence increases exponentially with time, the effect of $T$ on disentanglement is constant for all times, reflecting a fundamental difference between the two phenomena. Also, the poss…
We study the relation between the sudden death and revival of the entanglement of two qubits in a common squeezed reservoir, and the normal decoherence, by getting closer to the Decoherence Free Subspace and calculating the effect on the death and revival times.
We compare disentanglement and decoherence rates within two-spin and three-spin entangled systems subjected to all possible combinations of local and collective pure dephasing noise combinations. In all cases, the bipartite entanglement decay rate is found to be greater than or equal to the dephasing-decoherence rates and often significantly greater. This sharpens previous results for two-spin systems [T. Yu and J. H. Eberly Phys. Rev. B 68, 165322 (2003)] and extends them to the three-spin context.
The simple stationary decoherence of a two-state quantum system is discussed from a new viewpoint of environmental entanglement. My work emphasizes that an unconditional local state must totally be disentangled from the rest of the universe. It has been known for long that the loss of coherence within the given local system is gradual. Also the quantum correlations between the local system and the rest of the universe are being destroyed gradually. I show that, differently from local decoherence, the process of environmental disentanglement may terminate in finite time. The time of perfect dis…
We study the non-Markovian decoherence and disentanglement dynamics of dissipative quantum systems with special emphasis on non-Gaussian continuous variable systems. The dynamics are described by the Hu-Paz-Zhang master equation of quantum Brownian motion. The time evolution of the decoherence function of a single-mode superposition is compared to the concurrence of a two-mode entangled state. It is verified that moderate non-Markovian influences slow down the decay of interference fringes and quantum correlations, while strong non-Markovian effects resulting from an out-of-resonance bath can …
We relate disentanglement and decoherence rates in a pair of three-level atoms subjected to multi-local and collective pure dephasing noise acting in a preferred basis. The bipartite entanglement decay rate, as bounded from above by the negativity, is found to be greater than or equal to the dephasing-decoherence rates characterized by the decay of off-diagonal elements in the corresponding full density matrix describing the system or the reduced density matrix describing either qutrit, extending previous results for qubit pairs subject to such 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 inte…
We examine the influence of environmental interactions on simple quantum systems by obtaining the exact reduced dynamics of a qubit coupled to a one-dimensional spin bath. In contrast to previous studies, both the qubit-bath coupling and the nearest neighbor intrabath couplings are taken as the spin-flip XX-type. We first study the Rabi oscillations of a single qubit with the spin bath prepared in a spin coherent state, finding that nonresonance and finite intrabath interactions have significant effects on the qubit dynamics. Next, we discuss the bath-induced decoherence of the qubit when the …
We consider whether quantum coherence in the form of mutual entanglement between a pair of qubits is susceptible to decay that may be more rapid than the decay of the coherence of either qubit individually. An instance of potential importance for solid state quantum computing arises if embedded qubits (spins, quantum dots, Cooper pair boxes, etc.) are exposed to global and local noise at the same time. Here we allow separate phase-noisy channels to affect local and non-local measures of system coherence. We find that the time for decay of the qubit entanglement can be significantly shorter tha…
The decoherence of two initially entangled qubits in a squeezed vacuum cavity has been investigated exactly. The results show that, first, in principle, the disentanglement time decreases with the increasing of squeeze parameter r, due to the augmenting of average photon number of every mode in squeezed vacuum cavity. Second, there are entanglement revivals after complete disentanglement for the case of even parity initial Bell state, while there are entanglement decrease and revival before complete disentanglement for the case of odd parity initial Bell state. The results are quite different …
This article studies the decoherence induced on a system of two qubits by local interactions with a spin chain with nontrivial internal dynamics (governed by an XY Hamiltonian). Special attention is payed to the transition between two limits: one in which both qubits interact with the same site of the chain and another one where they interact with distant sites. The two cases exhibit different behaviours in the weak and strong coupling regimes: when the coupling is weak it is found that decoherence tends to decrease with distance, while for strong coupling the result is the opposite. Also, in …
We study the non-Markovian entanglement dynamics of two qubits in a common squeezed bath. We see remarkable difference between the non-Markovian entanglement dynamics with its Markovian counterpart. We show that a non-Markovian decoherence free state is also decoherence free in the Markovian regime, but all the Markovian decoherence free states are not necessarily decoherence free in the non-Markovian domain. We extend our calculation from squeezed vacuum bath to squeezed thermal bath, where we see the effect of finite bath temperatures on the entanglement dynamics.
An entangled multipartite system coupled to a zero-temperature bath undergoes rapid disentanglement in many realistic scenarios, due to local, symmetry-breaking, differences in the particle-bath couplings. We show that locally controlled perturbations, addressing each particle individually, can impose a symmetry, and thus allow the existence of decoherence-free multipartite entangled systems in zero-temperature environments.
We consider Unruh-Wald qubit detector model adopted for the far future region of an exactly solvable 1+1 dimensional scalar field theory in a Robertson-Walker expanding spacetime. It is shown that the expansion of the universe in its history enhances the decoherence of the qubit coupled with a scalar field. Moreover, we consider two entangled qubits, each locally coupled a scalar field. The expansion of the universe in its history degrades the entanglement between the qubits, and can lead to entanglement sudden death if the initial entanglement is small enough. The details depend on the parame…
We study competition between the dissipative and coherent effects in the entanglement dynamics of two qubits. The coherent interactions are needed for designing logic gate operations with systems like ion traps, semicondutor quantum dots and atoms. We show that the interactions lead to a phenomenon of periodic disentanglement and entanglement between the qubits. The disentanglement is primarily caused by environmental perturbations. The qubits are seen to remain disentangled for a finite time before getting entangled again. We find that the phenomenon is generic and occurs for wide variety of …
We investigate the quantum decoherence of frequency and polarization variables of photons via polarization mode dispersion in optical fibers. By observing the analogy between the propagation equation of the field and the Schrödinger equation, we develop a master equation under Markovian approximation and analytically solve for the field density matrix. We identify distinct decay behaviors for the polarization and frequency variables for single-photon and two-photon states. For the single photon case, purity functions indicate that complete decoherence for each variable is possible only for inf…
Entangled qubit pairs can serve as a quantum memory or as a resource for quantum communication. The utility of such pairs is measured by how long they take to disentangle or decohere. To answer the question of whether qubit-qubit interactions can prolong entanglement, we calculate the dissipative dynamics of a pair of qubits coupled via the exchange interaction in the presence of random telegraph noise and $1/f$ noise. We show that for maximally entangled (Bell) states, the exchange interaction generally suppresses decoherence and disentanglement. This suppression is more apparent for random t…
We outline an exact approach to decoherence and entanglement problems for continuous variable systems. The method is based on a construction of quantum distribution functions introduced by Ford and Lewis \cite{ford86} in which a system in thermal equilibrium is placed in an initial state by a measurement and then sampled by subsequent measurements. With the Langevin equation describing quantum Brownian motion, this method has proved to be a powerful tool for discussing such problems. After reviewing our previous work on decoherence and our recent work on disentanglement, we apply the method to…
We study the dynamical process of disentanglement of two qubits and two qutrits coupled to an Ising spin chain in a transverse field, which exhibits a quantum phase transition. We use the concurrence and negativity to quantify entanglement of two qubits and two qutrits, respectively. Explicit connections between the concurrence (negativity) and the decoherence factors are given for two initial states, the pure maximally entangled state and the mixed Werner state. We find that the concurrence and negativity decay exponentially with fourth power of time in the vicinity of critical point of the e…
We study the dynamics of disentanglement of two qubits initially prepared in a Bell state and coupled at different sites to an Ising transverse field spin chain (ITF) playing the role of a dynamic spin environment. The initial state of the whole system is prepared into a tensor product state $ρ_{Bell}\otimes ρ_{chain}$ where the state of the chain is taken to be given by the ground state $|G(λ_i)\rangle$ of the ITF Hamiltonian $H_E(λ_i)$ with an initial field $λ_i$. At time $t=0^+$, the strength of the transverse field is suddenly quenched to a new value $λ_f$ and the whole system (chain $+$ q…
We study the spatial decoherence dynamics for the relative position of two atoms in a singlemode ring cavity. We find that the spatial decoherence of the two atoms depends strongly on their relative position. Taking into account the spatial degrees of freedom, we investigate the entanglement dynamics of the internal states of the two atoms. It is shown that the entanglement decays to almost zero in a finite time, and the disentanglement time depends on the width of the wave packets describing the atomic spatial distribution.
The thesis is contributed to the study of the decoherence dynamics of dissipative qubit systems. We reveal the profound impact of the formation of a bound state between the qubit and its local environment on the decoherence dynamics of qubit system in non-Markovian regime. We find that the decoherence can be suppressed greatly under the non-Markovian dynamics when the bound state is formed. Consequently, the entanglement can be partially preserved in the steady state. A criterion on this decoherence/disentanglement suppression is given explicitly. It can give a useful guideline on the decohere…
We theoretically study the non-Markovian dynamics of qubit systems coupled to nonequilibrium environments with nonstationary and non-Markovian statistical properties. The reduced density matrix of the single qubit system satisfies a closed third-order differential equation with all the higher-order environmental correlations taken into account and the reduced density matrix of the two qubit system can be expressed as the Kraus representation in terms of the tensor products of the single qubit Kraus operators. We derive the relation between the entanglement and nonlocality of the two qubit syst…
We investigate disentanglement dynamics of two coupled qubits and qutrits which interact uniformly to a general XY spin-chain environment with the Dzyaloshinsky-Moriya (DM) interaction. We obtained exact expression of the time evolution operator and analyzed the dynamical process of the decoherence factors. Through explicitly calculating the concurrence and the negativity, we examined disentanglement behaviors of two coupled central spins evolve from different initial pure states, which are found to be nontrivially different from those of the uncorrelated ones, in particular, the enhanced deca…
We study a dynamic process of disentanglement by considering the time evolution of bound entanglement for a quantum open system, two qutrits coupling to a common environment. Here, the initial quantum correlations of the two qutrits are characterized by the bound entanglement. In order to show the universality of the role of environment on bound entanglement, both bosonic and spin environments are considered. We found that the bound entanglement displays collapses and revivals, and it can be stable against small temperature and time change. The thermal fluctuation effects on bound entanglement…
Control of electron spin decoherence in contact with a mesoscopic bath of many interacting nuclear spins in an InAs quantum dot is studied by solving the coupled quantum dynamics. The nuclear spin bath, because of its bifurcated evolution predicated on the electron spin up or down state, measures the which-state information of the electron spin and hence diminishes its coherence. The many-body dynamics of nuclear spin bath is solved with a pair-correlation approximation. In the relevant timescale, nuclear pair-wise flip-flops, as elementary excitations in the mesoscopic bath, can be mapped int…
We microscopically model the decoherence dynamics of entangled coherent states under the influence of vacuum fluctuation. We derive an exact master equation with time-dependent coefficients reflecting the memory effect of the environment, by using the Feynman-Vernon influence functional theory in the coherent-state representation. Under the Markovian approximation, our master equation recovers the widely used Lindblad equation in quantum optics. We then investigate the non-Markovian entanglement dynamics of the quantum channel in terms of the entangled coherent states under noise. Compared wit…
This paper investigates disentanglement as a result of evolution according to a class of master equations which include dissipation and interparticle interactions. Generalizing an earlier result of Diósi, the time taken for complete disentanglement is calculated (i.e. for disentanglement from any other system). The dynamics of two harmonically coupled oscillators is solved in order to study the competing effects of environmental noise and interparticle coupling on disentanglement. An argument based on separability conditions for gaussian states is used to arrive at a set of conditions on the c…
We study the disentanglement of two spin qubits which interact with a general XY spin-chain environment. The dynamical process of the disentanglement is numerically and analytically investigated in the vicinity of quantum phase transition (QPT) of the spin chain in both weak and strong coupling cases. We find that the disentanglement of the two qubits is in general enhanced greatly when the environmental spin chain is exposed to QPT. We give a detailed analysis to facilitate the understanding of the QPT-enhanced decaying behavior of the disentanglement factor. Furthermore, the scaling behavior…
Entanglement evolution in high dimensional bipartite systems under dissipation is studied. Discontinuities for the time derivative of the lower bound of entanglement of formation is found depending on the initial conditions for entangled states. This abrupt changes along the evolution appears as precursors of entanglement sudden death.
We study the disentanglement dynamics of two giant atoms coupled to a common one-dimensional waveguide. We focus on the non-Markovian retarded effect in the disentanglement of the two giant atoms by taking the photon transmission time into account. By solving the time-delayed equations of motion for the probability amplitudes, we obtain the evolution of the entanglement of the two giant atoms, which are initially in the maximally entangled states in the single-excitation space. It is found that the retardation-induced non-Markovianity leads to non-exponential decay and revivals of entanglement…
We analyze rigorously the dynamics of the entanglement between two qubits which interact only through collective and local environments. Our approach is based on the resonance perturbation theory which assumes a small interaction between the qubits and the environments. The main advantage of our approach is that the expressions for (i) characteristic time-scales, such as decoherence, disentanglement, and relaxation, and (ii) observables are not limited by finite times. We introduce a new classification of decoherence times based on clustering of the reduced density matrix elements. The charact…
The dynamics of entanglement between three - level atoms coupled to the common vacuum is investigated. We show that the collective effects such as collective damping, dipole - dipole interaction and the cross coupling between orthogonal dipoles, play a crucial role in the process of creation of entanglement. In particular, the additional cross coupling enhances the production of entanglement. For the specific initial states we find that the effect of delayed sudden birth of entanglement, recently invented by Ficek and Tanas [Phys. Rev. A 77, o54301(2008)] in the case of two - level atoms, can …
We propose experimental methods to engineer reservoirs at arbitrary temperature which are feasible with current technology. Our results generalize to mixed states the possibility of quantum state engineering through controlled decoherence. Finite temperature engineered reservoirs can lead to the experimental observation of thermal entanglement --the appearance and increase of entanglement with temperature-- to the study of the dependence of finite time disentanglement and revival with temperature, quantum thermodynamical effects, among many other applications, enlarging the comprehension of te…
The reduced dynamics of a single or two qubits coupled to an interacting quantum spin bath modeled by a XXZ spin chain is investigated. By using the method of time-dependent density matrix renormalization group (t-DMRG), we go beyond the uniform coupling central spin model and evaluate nonperturbatively the induced decoherence and entanglement. It is shown that both decoherence and entanglement strongly depend on the phase of the underlying spin bath. We show that in general, spin baths can induce entanglement for an initially disentangled pair of qubits. Furthermore, when the spin bath is in …
In this paper we investigate how common is the phenomenon of Finite Time Disentanglement (FTD) with respect to the set of quantum dynamics of bipartite quantum states with finite dimensional Hilbert spaces. Considering a quantum dynamics from a general sense, as just a continuous family of Completely Positive Trace Preserving maps (parametrized by the time variable) acting on the space of the bipartite systems, we conjecture that FTD happens for all dynamics but those when all maps of the family are induced by local unitary operations. We prove this conjecture valid for two important cases: i)…
We propose a method for directly probing the dynamics of disentanglement of an initial two-qubit entangled state, under the action of a reservoir. We show that it is possible to detect disentanglement, for experimentally realizable examples of decaying systems, through the measurement of a single observable, which is invariant throughout the decay. The systems under consideration may lead to either finite-time or asymptotic disentanglement. A general prescription for measuring this observable, which yields an operational meaning to entanglement measures, is proposed, and exemplified for cavity…
In this paper we derive an exact master equation for two coupled quantum harmonic oscillators interacting via bilinear coupling with a common environment at arbitrary temperature made up of many harmonic oscillators with a general spectral density function. We first show a simple derivation based on the observation that the two-harmonic oscillator model can be effectively mapped into that of a single harmonic oscillator in a general environment plus a free harmonic oscillator. Since the exact one harmonic oscillator master equation is available [Hu, Paz and Zhang, Phys. Rev. D \textbf{45}, 284…
The entanglement dynamics of a pair of donor-based charge qubits is obtained in analytical form. The disentanglement is induced by off resonant scattering of acoustical phonons in the semiconductor host. According to our results a rather unusual recovery of entanglement occurs that depends on the geometrical configuration of the qubits. In addition, for large times a non-vanishing stationary entanglement is predicted. For the cases of one and two initial excitations a simple kinetic interpretation allows for an adequate analysis of the observed dynamics. Our results also reveal a direct relati…
Models of quantum disentanglement are developed for nanometer-scale molecular charge qubits (MCQs). Two MCQs, $A$ and $B$, are prepared in a Bell state and separated for negligible $A$-$B$ interactions. Interactions between the local environment and each MCQ unravels $A$-$B$ entanglement during coherent system+environment evolution. Three models are used for dynamics: (1) a previously-developed, numerical model, in which both $AB$ and environment $\mathcal{E}$ are modeled explicitly; (2) an exact, semi-analytic model, in which only the dynamics of $AB$ are calculated, and (3) an approximate mo…
Dynamics of disentanglement as measured by the tripartite negativity and Bell nonlocality as measured by the extent of violation of the multipartite Bell-type inequalities are investigated in this work. It is shown definitively that for the initial three-qubit Greenberger-Horne-Zeilinger (GHZ) or {\it W} class state preparation the Bell nonlocality suffers sudden death under the influence of thermal reservoirs. Moreover, all the Bell-nonlocal states are useful for nonclassical teleportation, while there are entangled states that do not violate any Bell-type inequalities, but still yield noncla…
A direct classical analog of the quantum dynamics of intrinsic decoherence in Hamiltonian systems, characterized by the time dependence of the linear entropy of the reduced density operator, is introduced. The similarities and differences between the classical and quantum decoherence dynamics of an initial quantum state are exposed using both analytical and computational results. In particular, the classicality of early-time intrinsic decoherence dynamics is explored analytically using a second-order perturbative treatment, and an interesting connection between decoherence rates and the stabil…
An effective force induced by spatially depending decoherence is predicted. The phenomenon is illustrated by a simple model of a 1/2-spin particle subjected to distributed unselective measurement of noncommuting spin components.
A direct classical analog of quantum decoherence is introduced. Similarities and differences between decoherence dynamics examined quantum mechanically and classically are exposed via a second-order perturbative treatment and via a strong decoherence theory, showing a strong dependence on the nature of the system-environment coupling. For example, for the traditionally assumed linear coupling, the classical and quantum results are shown to be in exact agreement.
We investigate the dynamics of global entanglement, the Meyer-Wallach measure, under decoherence, analytically. We study two important class of multi-partite entangled states, the Greenberger-Horne-Zeilinger and the W state. We obtain exact results for various models of system-environment interactions (decoherence). Our results shows distinctly different scaling behavior for these initially entangled states indicating a relative robustness of the W state, consistent with previous studies.
We study decoherence in a circuit QED system consisting of a charge qubit and two superconducting transmission line resonators (TLRs). We show that in the dispersive regime of the circuit QED system one TLR can be used as an auxiliary subsystem to realize decoherence-free quantum dynamics of the bipartite target system consisting of the charge qubit and the other TLR conditioned on the auxiliary TLR initially being a proper number state. Our study gives new insight into control and manipulation of decoherence in quantum systems.
We study the dynamics of a Bose-Einstein condensate in a double-well potential in the mean-field approximation. Decoherence effects are considered by analyzing the couplings of the condensate to environments. Two kinds of coupling are taken into account. With the first kind of coupling dominated, the decoherence can enhance the self-trapping by increasing the damping of the oscillations in the dynamics, while the decoherence from the second kind of condensate-environment coupling leads to spoiling of the quantum tunneling and self-trapping.
The possible effect of environment on the efficiency of a quantum algorithm is considered explicitely. It is illustrated through the example of Shor's prime factorization algorithm that this effect may be disastrous. The influence of environment on quantum computation is probed on the basis of its analogy to the problem of wave function collapse in quantum measurement.Techniques from the Hepp-Colemen approach and its generalization are used to deal with decoherence problems in quantum computation including dynamic mechanism of decoherence, quantum error avoiding tricks and calculation of decoh…
We report on the application of a dynamic decoherence control pulse sequence on a nuclear quadrupole transition in $Pr^{3+}:Y_2SiO_5$ . Process tomography is used to analyse the effect of the pulse sequence. The pulse sequence was found to increase the decoherence time of the transition to over 30 seconds. Although the decoherence time was significantly increased, the population terms were found to rapidly decay on the application of the pulse sequence. The increase of this decay rate is attributed to inhomogeneity in the ensemble. Methods to circumvent this limit are discussed.
In orthodox quantum theory, decoherence is presumed to be caused by observation. In this paper, the idea of replacing observation, as the cause of decoherence, with rules derived from the dynamics of the system is addressed. Such rules determine the timing of decoherence and the states in the mixture afterward. For instance, energy conservation during decohenence, for each possible transition, leads to a timing rule. Exponetial decay and ergodic behavior follow directly from the dynamic rules as do Boltzman's postulate of equally probable micro-states and the Pauli rate equations. Ergodic beha…
This paper explores the use of laboratory closed-loop learning control to either fight or cooperate with decoherence in the optimal manipulation of quantum dynamics. Simulations of the processes are performed in a Lindblad formulation on multilevel quantum systems strongly interacting with the environment without spontaneous emission. When seeking a high control yield it is possible to find fields that successfully fight with decoherence while attaining a good quality yield. When seeking modest control yields, fields can be found which are optimally shaped to cooperate with decoherence and the…
We summarize our results on decoherence for short- to intermediate-time dynamics of an externally controlled two-state quantum system - a qubit - interacting with thermal bosonic environment. The developed approximation schemes are illustrated for an adiabatic model with time-dependent gate control, and for a model with rotating-wave gate function.
We investigate the decoherence dynamics of continuous variable entanglement as the system-environment coupling strength varies from the weak-coupling to the strong-coupling regimes. Due to the existence of localized modes in the strong-coupling regime, the system cannot approach equilibrium with its environment, which induces a nonequilibrium quantum phase transition. We analytically solve the entanglement decoherence dynamics for an arbitrary spectral density. The nonequilibrium quantum phase transition is demonstrated as the system-environment coupling strength varies for all the Ohmic-type …
We investigate the time evolution of entanglement for bipartite systems of arbitrary dimensions under the influence of decoherence. For qubits, we determine the precise entanglement decay rates under different system-environment couplings, including finite temperature effects. For qudits, we show how to obtain upper bounds for the decay rates and also present exact solutions for various classes of states.
