Stefano Mancini
We present a model to realize quantum feedback control of continuous variable entanglement. It consists of two interacting bosonic modes subject to amplitude damping and achieving entangled Gaussian steady state. The possibility to greatly improve the degree of entanglement by means of Markovian (direct) feedback is then shown.
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On the analytic ground we examine a physical mechanism how particle velocity can protect an entanglement when quantum system is embedded in Markovian or non-Markovian environment. In particular the effect of particle velocity is examined in the entanglement sudden death (ESD) and revival of entanglement (ROE) phenomena. Even though particles move fast, the ESD phenomenon does not disappear if it occurs at zero velocity. However the time domain $0 \leq t \leq t_*$ for nonvanishing entanglement becomes larger and larger with increasing velocity. When ROE phenomenon occurs at zero velocity, even …
The dynamics of two spins coupled to bosonic baths at different temperatures is studied. The analytical solution for the reduced density matrix of the system in the Markovian and Post-Markovian case with exponential memory kernel is found. The dynamics and temperature dependence of spin-spin entanglement is analyzed.
We consider two qubits interacting with a common bosonic bath, but not directly between themselves. We derive the (bipartite) entanglement generation conditions for Gaussian non-Markovian dynamical maps and show that they are similar as in the Markovian regime; however, they depend on different physical coefficients and hold on different time scales. Indeed, for small times, in the non-Markovian regime entanglement is possibly generated on a shorter time scale ($\propto t^2$) than in the Markovian one ($\propto t$). Moreover, although the singular coupling limit of non-Markovian dynamics yield…
We investigate the entanglement dynamics of two initially entangled qubits interacting independently with two uncorrelated reservoirs beyond the Markovian approximation. Quite different from the Markovian reservoirs [C. E. Lopez et al., Phys. Rev. Lett. 101 (2008) 080503], we find that entanglement sudden birth (ESB) of the two reservoirs occurs without certain symmetry with respect to the entanglement sudden death (ESD) of the two qubits. A phenomenological interpretation of entanglement revival is also given.
The fully quantized model of double qubits coupled to a common bath is solved using the quantum state diffusion (QSD) approach in the non-Markovian regime. We have established the explicit time-local non-Markovian QSD equations for the two-qubit dissipative and dephasing models. Diffusive quantum trajectories are applied to the entanglement estimation of two-qubit systems in a non-Markovian regime. In both cases, non-Markovian features of entanglement evolution are revealed through quantum diffusive unravellings in the system state space.
Non-Markovianity and entanglement detection
本文提出基于结构物理近似检测非马尔可夫不可分量子信道的新方法，并利用永恒非马尔可夫性设计量子纠缠检测协议。
We show that two, non interacting 2-level systems, immersed in a common bath, can become mutually entangled when evolving according to a Markovian, completely positive reduced dynamics.
We provide an analytical investigation of the pairwise entanglement dynamics for a system, consisting an arbitrary number of qubits dissipating into a common and non-Markovian environment for both weak and strong coupling regimes. In the latter case, a revival of pairwise entanglement due to the memory depth of the environment is observed. The leakage of photons into a continuum state is assumed to be the source of dissipation. We show that for an initially Werner state, the environment washes out the pairwise entanglement, but a series of non-selective measurements can protect the relevant en…
We devise a novel protocol to detect genuinely multipartite entangled states by harnessing quantum non-Markovian operations. We utilize a particular type of non-Markovianity known as the eternal non-Markovianity to construct a non-complete positive map to filter out the bi-separable states and detect genuine multipartite entanglement. We further propose a witness operator to detect genuinely multipartite entangled states experimentally based on this theory. Our study sheds light on a hitherto unexplored connection between entanglement theory and quantum non-Markovianity.
In this paper, we investigate preservation of quantum coherence of a single-qubit interacting with a zero-temperature thermal reservoir through the addition of noninteracting qubits in the reservoir. Moreover, we extend this scheme to preserve quantum entanglement between two and three distant qubits, each of which interacts with a dissipative reservoir independently. At the long time limit, we obtained analytical expressions for the coherence measure and the concurrence of two and three qubits in terms of the number of additional qubits. It is observed that, by increasing the number of additi…
The non-Markovia dynamics of quantum evolution plays an important role in open quantum sytem. However, how to quantify non-Markovian behavior and what can be obtained from non- Markovianity are still open questions, especially in complex solid systems. Here we address the problem of quantifying non-Markovianity with entanglement in a genuine noisy solid state system at room temperature. We observed the non-Markovianity of quantum evolution with entanglement. By prolonging entanglement with dynamical decoupling, we can reveal the non-Markovianity usually concealed in the environment and obtain …
We study dynamics of genuine entanglement for quantum states of three and four qubits under non-Markovian dephasing. Using a computable entanglement monotone for multipartite systems, we find that GHZ state is quite resilient state whereas the W state is the most fragile. We compare dynamics of chosen quantum states with dynamics of random pure states and weighted graph states.
Entanglement assisted probe of the non-Markovian to Markovian transition in open quantum system dynamics
本研究利用超导量子比特处理器，通过纠缠辅助探测开放量子系统的非马尔可夫动力学，观测到纠缠坍缩复苏的记忆效应，并通过热光子调控实现非马尔可夫到马尔可夫的转变，最终借量子芝诺效应的无退相干子空间稳定纠缠。
The dynamics evolutions of discord and entanglement of two atoms in two independent Lorentzian reservoirs at zero or finite temperature have been investigated by using the time-convolutionless master-equation method. Our results show that, when both the non-Markovian effect and the detuning are present simultaneously, due to the memory and feedback effect of the non-Markovian reservoirs, the discord and the entanglement can be effectively protected even at nonzero temperature by increasing the non-Markovian effect and the detuning. The discord and the entanglement have different robustness for…
A maximal steady-state fermionic entanglement of a nanoelectronic system is generated in finite temperature non-Markovian environments. The fermionic entanglement dynamics is presented by connecting the exact solution of the system with an appropriate definition of fermionic entanglement. We prove that the two understandings of the dissipationless non-Markovian dynamics, namely the bound state and the modified Laplace transformation are completely equivalent. For comparison, the steady-state entanglement is also studied in the wide-band limit and Born-Markovian approximation. When the environm…
We analyze the dynamics of the entanglement in two independent non-Markovian channels. In particular, we focus on the entanglement dynamics as a function of the initial states and the channel parameters like the temperature and the ratio $r$ between $ω_0$ the characteristic frequency of the quantum system of interest, and $ω_c$ the cut-off frequency of Ohmic reservoir. We give a stationary analysis of the concurrence and find that the dynamic of non-markovian entanglement concurrence $\mathcal{C}_ρ(t)$ at temperature $k_BT=0$ is different from the $k_BT>0$ case. We find that "entanglement sudd…
We investigate dynamics of an optomechanical system under the Non-Markovian environment. In the weak optomechanical single-photon coupling regime, we provide an analytical approach fully taking into account the non-Markovian memory effects. When the cavity-bath coupling strength crosses a certain threshold, an oscillating memory state for the classical cavity field (called bound state) is formed. Due to the existence of the non-decay optical bound state, a nonequilibrium optomechanical thermal entanglement is preserved even without external driving laser. Our results provide a potential usage …
The quantum entropic uncertainty relation and entanglement witness in the two-atom system coupling with the non-Markovian environments are studied by the time-convolutionless master-equation approach. The influence of non-Markovian effect and detuning on the lower bound of the quantum entropic uncertainty relation and entanglement witness is discussed in detail. The results show that, only if the two non-Markovian reservoirs are identical, increasing detuning and non-Markovian effect can reduce the lower bound of the entropic uncertainty relation, lengthen the time region during which the enta…
We study the time behavior of entanglement between two noninteracting qubits each immersed in its own environment for two different non-Markovian conditions: a high-$Q$ cavity slightly off-resonant with the qubit transition frequency and a nonperfect photonic band-gap, respectively. We find that revivals and retardation of entanglement loss may occur by adjusting the cavity-qubit detuning, in the first case, while partial entanglement trapping occurs in non-ideal photonic-band gap.
Analytical solution and entanglement swapping of a double Jaynes-Cummings model in non-Markovian environments are investigated by the timeconvolutionless master equation method. We obtain the analytical solution of this model and discuss in detail the influence of atom-cavity coupling, non-Markovian effect and initial state purity on entanglement dynamics. The results show that, in the non-Markovian environments, the entanglement between two cavities can be swapped to other bipartite subsystems by interaction between an atom and its own cavity. Due to the dissipation of environment, the entang…
We extend recent theoretical studies of entanglement dynamics in the presence of environmental noise, following the long-time interest of Krzysztof Wodkiewicz in the effects of stochastic models of noise on quantum optical coherences. We investigate the quantum entanglement dynamics of two spins in the presence of classical Ornstein-Uhlenbeck noise, obtaining exact solutions for evolution dynamics. We consider how entanglement can be affected by non-Markovian noise, and discuss several limiting cases.
Entanglement Degradation in the Presence of Markovian Noise: a Statistical Analysis
本文采用统计方法研究量子系统在随机分布的马尔可夫噪声作用下的纠缠退化问题，并应用于刻画由 $n$ 个 qudits 组成的量子存储器在局部均匀噪声下的纠缠退化统计特性。
We present a detailed study of the entanglement dynamics of a two-qubit system coupled to independent non-Markovian environments, employing hierarchy equations. This recently developed theoretical treatment can conveniently solve non-Markovian problems and take into consideration the correlation between the system and bath in an initial state. We concentrate on calculating the death and rebirth time points of the entanglement to obtain a general view of the concurrence curve and explore the behavior of entanglement dynamics with respect to the coupling strength, the characteristic frequency of…
We identify a set of dynamical maps of open quantum system, and refer to them as "$ ε$-Markovian" maps. It is constituted of maps which, in a higher dimensional system-environment Hilbert space, possibly violate Born approximation but only a "little". We characterize the "$ε$-nonmarkovianity" of a general dynamical map by the minimum distance of that map from the set of $ε$-Markovian maps. We analytically derive an inequality which gives a bound on the $ ε$-nonmarkovianity of the dynamical map, in terms of an entanglement-like resource generated between the system and its "immediate" environme…
The entanglement survival time is defined as the maximum time a system which is evolving under the action of local Markovian, homogenous in time noise, is capable to preserve the entanglement it had at the beginning of the temporal evolution. In this paper we study how this quantity is affected by the interplay between the coherent preserving and dissipative contributions of the corresponding dynamical generator. We report the presence of a counterintuitive, non-monotonic behaviour in such functional, capable of inducing sudden death of entanglement in models which, in the absence of unitary d…
We study the entanglement dynamics of two non-interacting, spatially separated qubits subject to local environment noises. Based on exactly solvable models for non-Markovian amplitude damping and phase damping noises, we are able to analyze the entanglement dynamics of the two qubits for different coupling bandwidths and different detunings. We show that entanglement oscillations can occur for both amplitude and phase damping noises. Moreover, we demonstrate that changing the coupling bandwidth can lead to crossover between dissipative and non-dissipative entanglement dynamics, while varying t…
In this work we study the steady state entanglement between two qubits interacting asymetrically with a common non-Markovian environment. Depending on the initial two-qubit state, the asymmetry in the couplings between each qubit and the non-Markovian environment may lead to enhanced entanglement in the steady state of the system, measured in terms of the two-qubit concurrence. Our results indicate that, if a qubit-qubit interaction is also present, the two-qubit steady state concurrence is always favored by the symmetric or anti-symmetric coupling configuration. Although finite, the steady co…
The dynamic behavior of the entanglement for two two-level atoms coupled to a common lossy cavity is studied. We find that the speed of disentanglement is a decreasing (increasing) function of the damping rate of the cavity for on/near (far-off) resonant couplings. The quantitative explanations for these phenomena are given, and further, it is shown that they are related to the quantum Zeno and anti-Zeno effect induced by the non-Markovian environment.
Dynamical aspects of quantum Brownian motion in a low temperature environment are investigated. We give a systematic calculation of quantum entanglement among two Brownian oscillators without invoking Born-Markov approximation widely used for the study of open systems. Our approach is suitable to probe short time dynamics at cold temperatures where many experiments on quantum information processing are performed.
We solve exactly the non-Markovian dynamics of a cavity mode in the presence of a feedback loop based on homodyne measurements, in the case of a non-zero feedback delay time. With an appropriate choice of the feedback parameters, this scheme is able to significantly increase the decoherence time of the cavity mode, even for delay times not much smaller than the decoherence time itself.
We suggest and demonstrate an all-optical experimental setup to observe and engineer entanglement oscillations of a pair of polarization qubits in a non-Markovian channel. We generate entangled photon pairs by spontaneous parametric downconversion (SPDC), and then insert a programmable spatial light modulator in order to impose a polarization dependent phase-shift on the spatial domain of the SPDC output and to create an effective non-Markovian environment. Modulation of the enviroment spectrum is obtained by inserting a spatial grating on the signal arm. In our experiment, programmable oscill…
We investigate the entanglement dynamics of continuous-variable quantum channels in terms of an entangled squeezed state of two cavity fields in a general non-Markovian environment. Using the Feynman-Vernon influence functional theory in the coherent-state representation, we derive an exact master equation with time-dependent coefficients reflecting the non-Markovian influence of the environment. The influence of environments with different spectral densities, e.g., Ohmic, sub-Ohmic, and super-Ohmic, is numerically studied. The non-Markovian process shows its remarkable influences on the entan…
We study the non-Markovian dynamics of a two-mode bosonic system interacting with two uncorrelated thermal bosonic reservoirs. We present the solution to the exact microscopic Master equation in terms of the quantum characteristic function and study in details the dynamics of entanglement for bipartite Gaussian states. In particular, we analyze the effects of short-time system-reservoir correlations on the separability thresholds and show that the relevant parameter is the reservoir spectral density. If the frequencies of the involved modes are within the reservoir spectral density entanglemen…
The entanglement between a Pauli-like two-level system and a quantum harmonic oscillator enhanced by an interaction between them and a $δ$-pulse sequence is studied, with the decoherence due to their coupling with a Markovian bath. Without the Markovian bath, the entanglement is enhanced to maximum possible values. With the Markovian bath, the entanglement is enhanced up to some time and then dissipated, with the system in thermal equilibrium with the Markovian bath after a very long time. The time for achieving the maximum entanglement shows discontinuous jumps over the parameters of decohere…
We study the properties of a refined weak coupling limit that preserves complete positivity in order to describe non-Markovian dynamics in the spin-boson model. With this tool, we show the system presents a rich and new non-Markovian phenomenology. This implies a dynamical difference between entanglement and coherence: the latter undergoes revivals whereas the former not, despite the induced dynamics being fully incoherent. In addition, the evolution presents "quasieternal" non-Markovianity, becoming non-divisible at any time period where the system evolves qualitatively. Furthermore, the meth…
We study on the tripartite entanglement dynamics when each party is initially entangled with other parties, but they locally interact with their own non-Markovian environment. First, we consider three GHZ-type initial states, all of which have GHZ symmetry provided that the parameters are chosen appropriately. However, this symmetry is broken due to the effect of environment. The corresponding $π$-tangles, one of the tripartite entanglement measure, are analytically computed at arbitrary time. The revival phenomenon of entanglement occurs after complete disappearance of entanglement. We also c…
Entanglement dynamics for a couple of two-level atoms interacting with independent structured reservoirs is studied using a non-perturbative approach. It is shown that the revival of atom entanglement is not necessarily accompanied by the sudden death of reservoir entanglement, and vice versa. In fact, atom entanglement can revive before, simultaneously or even after the disentanglement of reservoirs. Using a novel method based on the population analysis for the excited atomic state, we present the quantitative criteria for the revival and death phenomena. For giving a more physically intuitiv…
This paper presents a non-Markovian coherent feedback scheme to control single quantum dot systems. The feedback loop is closed via a quantum tunneling junction between the natural source and drain baths of the quantum dot. The exact feedback-controlled non-Markovian Langevin equation is derived for describing the dynamics of the quantum dot. To deal with the nonlinear memory function in the Langevin equation, we analyze the Green's function-based root locus, from which we show that the decoherence of the quantum dot can be suppressed via increasing the feedback coupling strength. This effecti…
We theoretically analyze the entanglement generation and dynamics by coupled Josephson junction qubits. Considering a current-biased Josephson junction (CBJJ), we generate maximally entangled states. In particular, the entanglement dynamics is considered as a function of the decoherence parameters, such as the temperature, the ratio $r\equivω_c/ω_0$ between the reservoir cutoff frequency $ω_c$ and the system oscillator frequency $ω_0$, % between $ω_0$ the characteristic frequency of the %quantum system of interest, and $ω_c$ the cut-off frequency of %Ohmic reservoir and the energy levels split…
Non-Markovian noise limits for sustaining entanglement in multiparty quantum states
本文研究非马尔可夫环境噪声对多体纠缠的影响，证明退相位信道中 GHZ cat 态与 W 态的纠缠可饱和至非零值，并揭示 W 态的奇偶效应及退极化信道中的纠缠复苏。
Sudden change of genuine multipartite entanglement in non-Markovian dynamics
本文通过两对腔—库四量子比特模型研究非马尔可夫纠缠动力学，揭示腔间纠缠延长、库间纠缠延迟诞生及四体真正纠缠冻结突变，并指出该突变可在非马尔可夫 regime 中反复出现。
Characterizing stationary optomechanical entanglement in the presence of non-Markovian noise
本研究解析证明，在非马尔可夫噪声下，真空或频率无关压缩输入光场中光机械静态纠缠具有普适性，且频率相关压缩无法产生纠缠。
A procedure that allows to obtain the dynamics of $N$ independent bodies each locally interacting with its own reservoir is presented. It relies on the knowledge of single body dynamics and it is valid for any form of environment noise. It is then applied to the study of non-Markovian dynamics of two independent qubits, each locally interacting with a zero temperature reservoir. It is shown that, although no interaction is present or mediated between the qubits, there is a revival of their entanglement, after a finite period of time of its complete disappearance.
In this paper we present a linear quadratic Gaussian (LQG) feedback control strategy for a class of linear non-Markovian quantum systems. The feedback control law is designed based on the estimated states of a whitening quantum filter for an augmented Markovian model of the non-Markovian open quantum systems. In this augmented Markovian model, an ancillary system plays the role of internal modes of the environment converting white noise into Lorentzian noise and a principal system obeys non-Markovian dynamics due to the direct interaction with the ancillary system. The simulation results show …
We investigate entanglement breaking times of Markovian evolutions in discrete and continuous time. In continuous time, we characterize which Markovian evolutions are eventually entanglement breaking, that is, evolutions for which there is a finite time after which any entanglement initially present has been destroyed by the noisy evolution. In the discrete time framework, we consider the entanglement breaking index, that is, the number of times a quantum channel has to be composed with itself before it becomes entanglement breaking. The PPT-square conjecture is that every PPT quantum channel …
We study the exact decoherence dynamics of the entangled squeezed state of two single-mode optical fields interacting with two independent and uncorrelated environments. We analyze in detail the non-Markovian effects on the entanglement evolution of the initially entangled squeezed state for different environmental correlation time scales. We find that the environments have dual actions on the system: backaction and dissipation. In mparticular, when the environmental correlation time scale is comparable to the time scale for significant change in the system, the backaction would counteract the…
We consider four two-level atoms interacting with independent non-Markovian reservoirs with detuning. We mainly investigate the effects of the detuning and the length of the reservoir correlation time on the decoherence dynamics of the multipartite entanglement. We find that the time evolution of the entanglement of atomic and reservoir subsystems is determined by a parameter, which is a function of the detuning and the reservoir correlation time. We also find that the decay and revival of the entanglement of the atomic and reservoir subsystems are closely related to the sign of the decay rate…
In this paper, a scheme for the generation of long-living entanglement between two distant Λ-type three-level atoms separately trapped in two dissipative cavities is proposed. In this scheme, two dissipative cavities are coupled to their own non-Markovian environments and two three-level atoms are driven by the classical fields. The entangled state between the two atoms is produced by performing Bell state measurement (BSM) on photons leaving the dissipative cavities. Using the time-dependent Schördinger equation, we obtain the analytical results for the evolution of the entanglement. It is re…
We propose a new characterization of non-Markovian quantum evolution based on the concept of non-Markovianity degree. It provides an analog of a Schmidt number in the entanglement theory and reveals the formal analogy between quantum evolution and the entanglement theory: Markovian evolution corresponds to a separable state and non-Markovian one is further characterized by its degree. It enables one to introduce a non-Markovinity witness -- an analog of an entanglement witness -- and a family of measures -- an analog of Schmidt coefficients -- and finally to characterize maximally non-Markovia…
Efficient entanglement preservation in open quantum systems is a crucial scope towards a reliable exploitation of quantum resources. We address this issue by studying how two-qubit entanglement dynamically behaves when two atom qubits move inside two separated identical cavities. The moving qubits independently interact with their respective cavity. As a main general result, we find that under resonant qubit-cavity interaction the initial entanglement between two moving qubits remains closer to its initial value as time passes compared to the case of stationary qubits. In particular, we show t…
A complete treatment of the entanglement of two-level systems, which evolves through the contact with a thermal bath, must include the fact that the system and the bath are not fully separable. Therefore, quantum coherent superpositions of system and bath states, which are almost never fully included in theoretical models, are invariably present when an entangled state is prepared experimentally. We show their importance for the time evolution of the entanglement of two qubits coupled to independent baths. In addition, our treatment is able to handle slow and low-temperature thermal baths.
In many applications entanglement must be distributed through noisy communication channels that unavoidably degrade it. Entanglement cannot be generated by local operations and classical communication (LOCC), implying that once it has been distributed it is not possible to recreate it by LOCC. Recovery of entanglement by purely local control is however not forbidden in the presence of non-Markovian dynamics, and here we demonstrate in two all-optical experiments that such entanglement restoration can even be achieved on-demand. First, we implement an open-loop control scheme based on a purely …
Entanglement and Quantum Coherence in Coupled Double Quantum Dots under Markovian and Non-Markovian Noisy Channels
研究耦合双量子点在马尔可夫和非马尔可夫噪声通道中量子纠缠和相干的动力学，发现环境记忆在非马尔可夫 regime 中促进量子相关性的振荡与部分复兴，且量子相干性比纠缠更鲁棒。
Characterization of non-Markovianity with maximal extractable qubit-reservoir entanglement
本文提出基于最大可提取量子比特-库纠缠来量化洛伦兹谱库非马尔可夫效应的方法，并通过超导量子比特与有损谐振器耦合实验验证其有效性。
We have studied the analytical Markovian and non-Markovian dynamics of quantum correlations, such as entanglement, quantum discord and Bell nonlocalities for three noisy qubits. Quantum correlation as measured by quantum discord is found to be immune to death contrary to entanglement and Bell nonlocality for initial GHZ- or W-type mixed states.
Giant-atom entanglement in waveguide-QED systems including non-Markovian effect
该研究针对耦合到同一维波导的两个巨原子，推导三种耦合构型下的含时滞量子主方程，分析其马尔可夫与非马尔可夫纠缠动力学，揭示相移、时滞等因素对纠缠的调控规律，为量子网络中的纠缠操控提供理论支撑。
Statistical Characterization of Entanglement Degradation Under Markovian Noise in Composite Quantum Systems
本文提出统计方法研究不同噪声模型对复合量子系统中纠缠退化的影响，通过PPTT度量揭示全局噪声与局部噪声对纠缠持续时间的影响差异。
A procedure to obtain the dynamics of $N$ independent qudits ($d$-level systems) each interacting with its own reservoir, for any arbitrary initial state, is presented. This is then applied to study the dynamics of the entanglement of two qubits, initially in an extended Werner-like mixed state with each of them in a zero temperature non-Markovian environment. The dependence of the entanglement dynamics on the purity and degree of entanglement of the initial states and on the amount of non-Markovianity is also given. This extends the previous work about non-Markovian effects on the two-qubit e…
We study the evolution of the entanglement of noninteracting qubits coupled to reservoirs under monitoring of the reservoirs by means of continuous measurements. We calculate the average of the concurrence of the qubits wavefunction over all quantum trajectories. For two qubits coupled to independent baths subjected to local measurements, this average decays exponentially with a rate depending on the measurement scheme only. This contrasts with the known disappearance of entanglement after a finite time for the density matrix in the absence of measurements. For two qubits coupled to a common b…
We investigate the decay of the global entanglement, due to decoherence, of multiqubit systems interacting with a reservoir in a non Markovian regime. We assume that during the decoherence process each qubit of the system interacts with its own, independent environment. Most previous works on this problem focused on particular initial states or families of initial states amenable of analytical treatment. Here we determine numerically the typical, average behaviour of the system corresponding to random initial pure states uniformly distributed (in the whole Hilbert space of $n$-qubit pure state…
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