Open-system dynamics of entanglement: a key issues review

Entanglement Entropy of Free Fermions with a Random Matrix as a One-Body Hamiltonian

We consider a quantum system of large size N and its subsystem of size L, assuming that N is much larger than L, which can also be sufficiently large, i.e., 1≪L≲N. A widely accepted mathematical version of this inequality is the asymptotic regime of successive limits: first the macroscopic limit N→∞, then an asymptotic analysis of the entanglement entropy as L→∞. In this paper, we consider another version of the above inequality: the regime of asymptotically proportional L and N, i.e., the simultaneous limits L→∞,N→∞,L/N→λ>0. Specifically, we consider a system of free fermions that is in its ground state, and such that its one-body Hamiltonian is a large random matrix, which is often used to model long-range hopping. By using random matrix theory, we show that in this case, the entanglement entropy obeys the volume law known for systems with short-range hopping but described either by a mixed state or a pure strongly excited state of the Hamiltonian. We also give streamlined proof of Page's formula for the entanglement entropy of black hole radiation for a wide class of typical ground states, thereby proving the universality and the typicality of the formula.

Dilaton-induced open quantum dynamics

In modern cosmology, scalar fields with screening mechanisms are often used as explanations for phenomena like dark energy or dark matter. Amongst a zoo of models, the environment dependent dilaton, screened by the Polyakov-Damour mechanism, is one of the least constrained ones. Using recently developed path integral tools for directly computing reduced density matrices, we study the open quantum dynamics of a probe, modelled by another real scalar field, induced by interactions with an environment comprising fluctuations of a dilaton. As the leading effect, we extract a correction to the probe's unitary evolution, which can be observed as a frequency shift. Assuming the scalar probe to roughly approximate a cold atom in matter wave interferometry, we show that comparing the predicted frequency shifts in two experimentally distinct setups has the potential to exclude large parts of the dilaton parameter space.

The efficiency of quantum teleportation with three-qubit entangled state in a noisy environment

Quantum teleportation plays a significant role in the field of quantum communication. This paper investigates quantum teleportation through a noisy environment by using GHZ state and non-standard W state as quantum channels. We analyze the efficiency of quantum teleportation by solving analytically a master equation in Lindblad form. Following the quantum teleportation protocol, we obtain the fidelity of quantum teleportation as a function of evolution time. The calculation results show that the teleportation fidelity using non-standard W is higher in comparison to GHZ state at the same evolution time. Moreover, we consider the efficiency of teleportation with weak measurements and reverse quantum measurement under amplitude damping noise. Our analysis suggests that the teleportation fidelity using non-standard W is also more robust to noise than GHZ state in the same conditions. Interestingly, we found that weak measurement and its reverse operation have no positive effect on the efficiency of quantum teleportation by using GHZ and non-standard W state in the amplitude damping noise environment. In addition, we also demonstrate the efficiency of quantum teleportation can be improved by making minor modifications to the protocol.

Suppressing Decoherence in Quantum State Transfer with Unitary Operations

Decoherence is the fundamental obstacle limiting the performance of quantum information processing devices. The problem of transmitting a quantum state (known or unknown) from one place to another is of great interest in this context. In this work, by following the recent theoretical proposal, we study an application of quantum state-dependent pre- and post-processing unitary operations for protecting the given (multi-qubit) quantum state against the effect of decoherence acting on all qubits. We observe the increase in the fidelity of the output quantum state both in a quantum emulation experiment, where all protecting unitaries are perfect, and in a real experiment with a cloud-accessible quantum processor, where protecting unitaries themselves are affected by the noise. We expect the considered approach to be useful for analyzing capabilities of quantum information processing devices in transmitting known quantum states. We also demonstrate the applicability of the developed approach for suppressing decoherence in the process of distributing a two-qubit state over remote physical qubits of a quantum processor.

Analysis of Quantum Correlations Obtained Using Local Optimal Universal Asymmetric Cloners

We apply the local optimal universal asymmetric cloning machine on an initially pure entangled state of two qubits. As output, we obtain two final states which present quantum correlations. We analyze three types of quantum correlations among the final states, namely, concurrence, quantum discord, and consonance. A detailed comparison between concurrence, quantum discord, and consonance is made, and we find that consonance is greater than quantum discord, which is in turn greater than concurrence.

Speed of Evolution and Correlations in Multi-Mode Bosonic Systems

We employ an exact solution of the thermal bath Lindblad master equation with the Liouvillian superoperator that takes into account both dynamic and environment-induced intermode couplings to study the speed of evolution and quantum speed limit (QSL) times of a open multi-mode bosonic system. The time-dependent QSL times are defined from quantum speed limits, giving upper bounds on the rate of change of two different measures of distinguishability: the fidelity of evolution and the Hilbert-Schmidt distance. For Gaussian states, we derive explicit expressions for the evolution speed and the QSL times. General analytical results are applied to the special case of a two-mode system where the intermode couplings can be characterized by two intermode coupling vectors: the frequency vector and the relaxation rate vector. For the system initially prepared in a two-mode squeezed state, dynamical regimes are generally determined by the intermode coupling vectors, the squeezing parameter and temperature. When the vectors are parallel, different regimes may be associated with the disentanglement time, which is found to be an increasing (a decreasing) function of the length of the relaxation vector when the squeezing parameter is below (above) its temperature-dependent critical value. Alternatively, we study dynamical regimes related to the long-time asymptotic behavior of the QSL times, which is characterized by linear time dependence with the proportionality coefficients defined as the long-time asymptotic ratios. These coefficients are evaluated as a function of the squeezing parameter at varying temperatures and relaxation vector lengths. We also discuss how the magnitude and orientation of the intermode coupling vectors influence the maximum speed of evolution and dynamics of the entropy and the mutual information.

Unified master equation for molecules in phonon and radiation baths

We have developed a unified quantum optical master equation that includes the dissipative mechanisms of an impurity molecule in crystals. Our theory applies generally to polyatomic molecules where several vibrational modes give rise to intramolecular vibrational redistributions. The usual assumption on identical shapes of the nuclear potentials in ground and excited electronic states and the rotating wave approximation have been relaxed, i.e. the vibrational coordinates are different in the ground and excited states, with counter-rotating terms included for generality. Linear vibrational coupling to the lattice phonons accounts for dissipations via non-radiative transitions. The interaction of a molecule with photons includes Herzberg–Teller coupling as the first order non-Condon interaction where the transition dipole matrix elements depend linearly on vibrational coordinates. We obtain new cross terms as the result of mixing the terms from the zeroth-order (Condon) and first-order (non-Condon) approximations. The corresponding Lamb shifts for all Liouvilleans are derived explicitly including the contributions of counter-rotating terms. The computed absorption and emission spectra for carbon monoxide is in good agreement with experimental data. We use our unified model to obtain the spectra for nitrogen dioxide, demonstrating the capability of our theory to incorporate all typical dissipative relaxation and decoherence mechanisms for polyatomic molecules. The molecular quantum master equation is a promising theory for studying molecular quantum memory.

Optomechanical Quantum Entanglement Mediated by Acoustic Phonon Fields

We present exact solutions for the quantum time evolution of two spatially separated, local inductor-capacitor (LC) oscillators that are coupled optomechanically to a long elastic strip that functions as a quantum thermal acoustic field environment. We show that the optomechanical coupling to the acoustic environment gives rise to causal entanglement dynamics between the two LC oscillators in the absence of resonant photon exchange between them, and that significant entanglement develops regardless of the environment temperature. Such a process establishes that distributed entanglement may be generated between superconducting qubits via a connected phonon bus bar, without the need for resonant phonon release and capture.

Quantum Information Scrambling in Non-Markovian Open Quantum System

In this paper, we investigate the dynamics of a spin chain whose two end spins interact with two independent non-Markovian baths by using the non-Markovian quantum state diffusion (QSD) equation approach. Specifically, two issues about information scrambling in an open quantum system are addressed. The first issue is that tripartite mutual information (TMI) can quantify information scrambling properly via its negative value in a closed system, whether it is still suitable to indicate information scrambling in an open quantum system. We find that negative TMI is not a suitable quantifier of information scrambling in an open quantum system in some cases, while negative tripartite logarithmic negativity (TLN) is an appropriate one. The second one is that up to now almost all information scrambling in open quantum systems reported were focus on a Markovian environment, while the effect of a non-Markovian environment on information scrambling is still elusive. Our results show that the memory effect of an environment will be beneficial to information scrambling. Moreover, it is found that the environment is generally detrimental for information scrambling in the long-term, while in some cases it will be helpful for information scrambling in the short-term.

Coupled Harmonic Oscillator in a System of Free Particles

The coupled quantum harmonic oscillator is one of the most researched and important model systems in quantum optics and quantum informatics. This system is often investigated for quantum entanglement in the environment. As a result, such studies are complex and can only be carried out using numerical methods that do not reveal the general pattern of such systems. In this work, the external environment is considered to be two independent particles interacting with coupled harmonic oscillators. It is shown that such a system has an exact analytical solution to the dynamic Schrödinger equation. The analysis of this solution is carried out, and the main parameters of this system are revealed. The solutions obtained can be used to study more complex systems and their quantum entanglement.

Lindblad Dynamics and Disentanglement in Multi-Mode Bosonic Systems

In this paper, we consider the thermal bath Lindblad master equation to describe the quantum nonunitary dynamics of quantum states in a multi-mode bosonic system. For the two-mode bosonic system interacting with an environment, we analyse how both the coupling between the modes and the coupling with the environment characterised by the frequency and the relaxation rate vectors affect dynamics of the entanglement. We discuss how the revivals of entanglement can be induced by the dynamic coupling between the different modes. For the system, initially prepared in a two-mode squeezed state, we find the logarithmic negativity as defined by the magnitude and orientation of the frequency and the relaxation rate vectors. We show that, in the regime of finite-time disentanglement, reorientation of the relaxation rate vector may significantly increase the time of disentanglement.

Dynamics of quantum entanglement in a zigzag graphene nanoribbon

We study the dynamics of entanglement between two edge spins in a zigzag graphene nanoribbon (ZGNR) which is thermalized with a reservoir at temperatureT. The results show that the entanglement evolution displays oscillating behaviors in the presence of an external magnetic field. Such oscillating behaviors of entanglement strongly depend on the field frequency and relative location between two inter-edge coupled spins. At some critical field frequencies, the entanglement exhibits a periodic structure. When the temperature is low, the oscillating patterns of entanglement are quite regular and symmetrical. When the temperature is high, the patterns of entanglement evolution occur irregular distortions due to the thermal fluctuations. However, the entanglement between two inter-edge coupled spins in ZGNR still exists a nontrivial value even at room temperature.

Entanglement Robustness via Spatial Deformation of Identical Particle Wave Functions

We address the problem of entanglement protection against surrounding noise by a procedure suitably exploiting spatial indistinguishability of identical subsystems. To this purpose, we take two initially separated and entangled identical qubits interacting with two independent noisy environments. Three typical models of environments are considered: amplitude damping channel, phase damping channel and depolarizing channel. After the interaction, we deform the wave functions of the two qubits to make them spatially overlap before performing spatially localized operations and classical communication (sLOCC) and eventually computing the entanglement of the resulting state. This way, we show that spatial indistinguishability of identical qubits can be utilized within the sLOCC operational framework to partially recover the quantum correlations spoiled by the environment. A general behavior emerges: the higher the spatial indistinguishability achieved via deformation, the larger the amount of recovered entanglement.

Dephasing-assisted entanglement in a system of strongly coupled qubits

Creation of entangled states of quantum systems with low decoherence rates is a cornerstone in practical implementation of quantum computations. Processes of separate dephasing in each qubit in experimentally feasible systems is commonly accepted to destroy entanglement. In this work, we consider a system of two strongly coupled qubits that interact with dephasing reservoirs. We demonstrate that interaction with dephasing reservoirs can contribute to the formation of a long-lived mixed entangled state with nonzero concurrence. The weight of the subradiant state in this mixed state tends toward unity if the dephasing rate is much larger than the radiative rate and less than the coupling constant between qubits. The lifetime of this state is proportional to the exponent of the ratio of the coupling constant to environmental temperature and can be, by orders of magnitude, larger than the system's characteristic dephasing and dissipation times. Therefore, high dephasing, along with strong coupling, contributes to the creation of an entangled state with a long lifetime. This result paves the way for creation of long-lived entangled states.

Nonlinear Dynamics of a Cavity Containing a Two-Mode Coherent Field Interacting with Two-Level Atomic Systems

This study analytically explored two coupled two-level atomic systems (TLAS) as two qubits interacting with two modes of an electromagnetic field (EMF) cavity via two-photon transitions in the presence of dipole–dipole interactions between the atoms and intrinsic damping. Using special unitary su(1,1) Lie algebra, the general solution of an intrinsic noise model is obtained when an EMF is initially in a generalized coherent state. We investigated the population inversion of two TLAS and the generated quantum coherence of some partitions (including the EMF, two TLAS, and TLAS–EMF). It is possible to generate quantum coherence (mixedness and entanglement) from the initial pure state. The robustness of the quantum coherence produced and the sudden appearance and disappearance of coherence depended not only on dipole–dipole coupling but also on the intrinsic noise rate. The growth of mixedness and entanglement may be enhanced by increasing dipole–dipole coupling, leading to more robustness against intrinsic noise.

Counting Classical Nodes in Quantum Networks

Quantum networks illustrate the use of connected nodes of quantum systems as the backbone of distributed quantum information processing. When the network nodes are entangled in graph states, such a quantum platform is indispensable to almost all the existing distributed quantum tasks. Unfortunately, real networks unavoidably suffer from noise and technical restrictions, making nodes transit from quantum to classical at worst. Here, we introduce a figure of merit in terms of the number of classical nodes for quantum networks in arbitrary graph states. Such a network property is revealed by exploiting a novel Einstein-Podolsky-Rosen steerability. Experimentally, we demonstrate photonic quantum networks of n_{q} quantum nodes and n_{c} classical nodes with n_{q} up to 6 and n_{c} up to 18 using spontaneous parametric down-conversion entanglement sources. We show that the proposed method is faithful in quantifying the classical defects in prepared multiphoton quantum networks. Our results provide novel identification of generic quantum networks and nonclassical correlations in graph states.

Multipartite Entanglement Generation in a Structured Environment

In this paper, we investigate the entanglement generation of n-qubit states in a model consisting of n independent qubits, each coupled to a harmonic oscillator which is in turn coupled to a bath of N additional harmonic oscillators with nearest-neighbor coupling. With analysis, we can find that the steady multipartite entanglement with different values can be generated after a long-time evolution for different sizes of the quantum system. Under weak coupling between the system and the harmonic oscillator, multipartite entanglement can monotonically increase from zero to a stable value. Under strong coupling, multipartite entanglement generation shows a speed-up increase accompanied by some oscillations as non-Markovian behavior. Our results imply that the strong coupling between the harmonic oscillator and the N additional harmonic oscillators, and the large size of the additional oscillators will enhance non-Markovian dynamics and make it take a very long time for the entanglement to reach a stable value. Meanwhile, the couplings between the additional harmonic oscillators and the decay rate of additional harmonic oscillators have almost no effect on the multipartite entanglement generation. Finally, the entanglement generation of the additional harmonic oscillators is also discussed.

Non-locality Correlation in Two Driven Qubits Inside an Open Coherent Cavity: Trace Norm Distance and Maximum Bell Function

We analytically investigate two separated qubits inside an open cavity field. The cavity is initially prepared in a superposition coherent state. The non-locality correlations [including trace norm measurement induced non-locality, maximal Bell-correlation, and concurrence entanglement] of the two qubits are explored. It is shown that, the generated non-locality correlations crucially depend on the decay and the initial coherence intensity of the cavity field. The enhancement of the initial coherence intensity and its superposition leads to increasing the generated non-locality correlations. The phenomena of sudden birth and death entanglement are found.

Enhanced Multiqubit Phase Estimation in Noisy Environments by Local Encoding

The first generation of multiqubit quantum technologies will consist of noisy, intermediate-scale devices for which active error correction remains out of reach. To exploit such devices, it is thus imperative to use passive error protection that meets a careful trade-off between noise protection and resource overhead. Here, we experimentally demonstrate that single-qubit encoding can significantly enhance the robustness of entanglement and coherence of four-qubit graph states against local noise with a preferred direction. In particular, we explicitly show that local encoding provides a significant practical advantage for phase estimation in noisy environments. This demonstrates the efficacy of local unitary encoding under realistic conditions, with potential applications in multiqubit quantum technologies for metrology, multipartite secrecy, and error correction.

Heralded Bell State of Dissipative Qubits Using Classical Light in a Waveguide

Maximally entangled two-qubit states (Bell states) are of central importance in quantum technologies. We show that heralded generation of a maximally entangled state of two intrinsically open qubits can be realized in a one-dimensional (1D) system through strong coherent driving and continuous monitoring. In contrast to the natural idea that dissipation leads to decoherence and so destroys quantum effects, continuous measurement and strong interference in our 1D system generate a pure state with perfect quantum correlation between the two open qubits. Though the steady state is a trivial product state that has zero coherence or concurrence, we show that, with carefully tuned parameters, a Bell state can be generated in the system's quantum jump trajectories, heralded by a reflected photon. Surprisingly, this maximally entangled state survives the strong coherent state input-a classical state that overwhelms the system. This simple method to generate maximally entangled states using classical coherent light and photon detection may, since our qubits are in a 1D continuum, find application as a building block of quantum networks.

Non-Markovianity of qubit evolution under the action of spin environment

The question, whether an open system dynamics is Markovian or non-Markovian can be answered by studying the direction of the information flow in the dynamics. In Markovian dynamics, information must always flow from the system to the environment. If the environment is interacting with only one of the subsystems of a bipartite system, the dynamics of the entanglement in the bipartite system can be used to identify the direction of information flow. Here we study the dynamics of a two-level system interacting with an environment, which is also a heat bath, and consists of a large number of two-level quantum systems. Our model can be seen as a close approximation to the ‘spin bath’ model at low temperatures. We analyze the Markovian nature of the dynamics, as we change the coupling between the system and the environment. We find the Kraus operators of the dynamics for certain classes of couplings. We show that any form of time-independent or time-polynomial coupling gives rise to non-Markovianity. Also, we witness non-Markovianity for certain parameter values of time-exponential coupling. Moreover, we study the transition from non-Markovian to Markovian dynamics as we change the value of coupling strength.

Improving the Robustness of Entangled States by Basis Transformation

In the practical application of quantum entanglement, entangled particles usually need to be distributed to many distant parties or stored in different quantum memories. In these processes, entangled particles unavoidably interact with their surrounding environments, respectively. We here systematically investigate the entanglement-decay laws of cat-like states under independent Pauli noises with unbalanced probability distribution of three kinds of errors. We show that the robustness of cat-like entangled states is not only related to the overall noise strength and error distribution parameters, but also to the basis of qubits. Moreover, we find that whether a multi-qubit state is more robust in the computational basis or transversal basis depends on the initial entanglement and number of qubits of the state as well as the overall noise strength and error distribution parameters of the environment. However, which qubit basis is conductive to enhancing the robustness of two-qubit states is only dependent on the error distribution parameters. These results imply that one could improve the intrinsic robustness of entangled states by simply transforming the qubit basis at the right moment. This robustness-improving method does not introduce extra particles and works in a deterministic manner.

Supremum of block entanglement for symmetric Gaussian states

For a system composed of permutationally symmetric Gaussian modes, by identifying the boundary of valid states and making necessary change of variables, the existence and exact value of the supremum of logarithmic negativity (and negativity likewise) between any two blocks can be shown analytically. Involving only the total number of interchangeable modes and the sizes of respective blocks, this result is general and easy to be applied for such a class of states.

Protecting quantum resources via frequency modulation of qubits in leaky cavities

Finding strategies to preserve quantum resources in open systems is nowadays a main requirement for reliable quantum-enhanced technologies. We address this issue by considering structured cavities embedding qubits driven by a control technique known as frequency modulation. We first study a single qubit in a lossy cavity to determine optimal modulation parameters and qubit-cavity coupling regime allowing a gain of four orders of magnitude concerning coherence lifetimes. We relate this behavior to the inhibition of the qubit effective decay rate rather than to stronger memory effects (non-Markovianity) of the system. We then exploit these findings in a system of noninteracting qubits embedded in separated cavities to gain basic information about scalability of the procedure. We show that the determined modulation parameters enable lifetimes of quantum resources, such as entanglement, discord and coherence, three orders of magnitude longer than their natural (uncontrolled) decay times. We discuss the feasibility of the system within the circuit-QED scenario, typically employed in the current quantum computer prototypes. These results provide new insights towards efficient experimental strategies against decoherence.

Parametrization and Optimization of Gaussian Non-Markovian Unravelings for Open Quantum Dynamics

We derive a family of Gaussian non-Markovian stochastic Schrödinger equations for the dynamics of open quantum systems. The different unravelings correspond to different choices of squeezed coherent states, reflecting different measurement schemes on the environment. Consequently, we are able to give a single shot measurement interpretation for the stochastic states and microscopic expressions for the noise correlations of the Gaussian process. By construction, the reduced dynamics of the open system does not depend on the squeezing parameters. They determine the non-Hermitian Gaussian correlation, a wide range of which are compatible with the Markov limit. We demonstrate the versatility of our results for quantum information tasks in the non-Markovian regime. In particular, by optimizing the squeezing parameters, we can tailor unravelings for improving entanglement bounds or for environment-assisted entanglement protection.

Environmental noise spectroscopy with qubits subjected to dynamical decoupling

A qubit subjected to pure dephasing due to classical Gaussian noise can be turned into a spectrometer of this noise by utilizing its readout under properly chosen dynamical decoupling (DD) sequences to reconstruct the power spectral density of the noise. We review the theory behind this DD-based noise spectroscopy technique, paying special attention to issues that arise when the environmental noise is non-Gaussian and/or it has truly quantum properties. While we focus on the theoretical basis of the method, we connect the discussed concepts with specific experiments, and provide an overview of environmental noise models relevant for solid-state based qubits, including quantum-dot based spin qubits, superconducting qubits, and NV centers in diamond.

Relationship between quantum speed limit time and memory time in a photonic-band-gap environment

Non-Markovian effect is found to be able to decrease the quantum speed limit (QSL) time, and hence to enhance the intrinsic speed of quantum evolution. Although a reservoir with larger degree of non-Markovianity may seem like it should cause smaller QSL times, this seemingly intuitive thinking may not always be true. We illustrate this by investigating the QSL time of a qubit that is coupled to a two-band photonic-band-gap (PBG) environment. We show how the QSL time is influenced by the coherent property of the reservoir and the band-gap width. In particular, we find that the decrease of the QSL time is not attributed to the increasing non-Markovianity, while the memory time of the environment can be seen as an essential reflection to the QSL time. So, the QSL time provides a further insight and sharper identification of memory time in a PBG environment. We also discuss a feasible experimental realization of our prediction.

Experimental observation of weak non-Markovianity

Non-Markovianity has recently attracted large interest due to significant advances in its characterization and its exploitation for quantum information processing. However, up to now, only non-Markovian regimes featuring environment to system backflow of information (strong non-Markovianity) have been experimentally simulated. In this work, using an all-optical setup we simulate and observe the so-called weak non-Markovian dynamics. Through full process tomography, we experimentally demonstrate that the dynamics of a qubit can be non-Markovian despite an always increasing correlation between the system and its environment which, in our case, denotes no information backflow. We also show the transition from the weak to the strong regime by changing a single parameter in the environmental state, leading us to a better understanding of the fundamental features of non-Markovianity.

Dissipative Quantum Control of a Spin Chain

A protocol is discussed for preparing a spin chain in a generic many-body state in the asymptotic limit of tailored nonunitary dynamics. The dynamics require the spectral resolution of the target state, optimized coherent pulses, engineered dissipation, and feedback. As an example, we discuss the preparation of an entangled antiferromagnetic state, and argue that the procedure can be applied to chains of trapped ions or Rydberg atoms.

Cavity-based architecture to preserve quantum coherence and entanglement

Quantum technology relies on the utilization of resources, like quantum coherence and entanglement, which allow quantum information and computation processing. This achievement is however jeopardized by the detrimental effects of the environment surrounding any quantum system, so that finding strategies to protect quantum resources is essential. Non-Markovian and structured environments are useful tools to this aim. Here we show how a simple environmental architecture made of two coupled lossy cavities enables a switch between Markovian and non-Markovian regimes for the dynamics of a qubit embedded in one of the cavity. Furthermore, qubit coherence can be indefinitely preserved if the cavity without qubit is perfect. We then focus on entanglement control of two independent qubits locally subject to such an engineered environment and discuss its feasibility in the framework of circuit quantum electrodynamics. With up-to-date experimental parameters, we show that our architecture allows entanglement lifetimes orders of magnitude longer than the spontaneous lifetime without local cavity couplings. This cavity-based architecture is straightforwardly extendable to many qubits for scalability.

Transient and steady-state entanglement mediated by three-dimensional plasmonic waveguides

Entanglement between two qubits (two level atoms) mediated by surface plasmons in three-dimensional plasmonic waveguides is studied using a quantum master equation formalism. Two types of waveguides, a nanowire and a V-shaped channel cut in a flat metal plane, are considered. The Green functions for the waveguides, which rigorously describes the dissipative qubit environment, are calculated numerically using a direct finite-difference time-domain (FDTD) solution of Maxwell's equations. Finite-length effects are shown to play a crucial role in enhancing entanglement, and resonant-length plasmonic waveguides can provide higher entanglement between qubits than infinite-length waveguides. It is also shown that coupling slots can improve entanglement via stronger qubit-waveguide coupling, for both the infinite- and finite-waveguide cases. The formalism used in the paper can be applied to a wide range of plasmonic waveguides.

Quantum correlations and energy currents across three dissipative oscillators

We present a study that addresses both the stationary properties of the energy current and quantum correlations in a three-mode chain subjected to Ohmic and super-Ohmic dissipations. An extensive numerical analysis shows that the mean value and the fluctuations of the energy current remain insensitive to the emergence of a rich variety of quantum correlations, such as two-mode discord and entanglement and bipartite three-mode and genuine tripartite entanglement. The discussion of the numerical results is based on the derived expressions for the stationary properties in terms of the two-time correlation functions of the oscillator operators, which carry the quantum correlations. Interestingly, we show that quantum discord can be enhanced by considering both initially squeezed thermal bath states and imposing temperature gradients.