Paolo Zanardi
The notion of entanglement can be naturally extended from quantum-states to the level of general quantum evolutions. This is achieved by considering multi-partite unitary transformations as elements of a multi-partite Hilbert space and then extended to general quantum operations. We show some connection between this entanglement and the entangling capabilities of the quantum evolution.
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An example of a quantum game is presented that explicitly shows the impact of entanglement on the game-theoretical concept of evolutionary stability.
Entanglement or entanglement generating interactions permit to achieve the maximum allowed speed in the dynamical evolution of a composite system, when the energy resources are distributed among subsystems. The cases of pre-existing entanglement and of entanglement-building interactions are separately addressed. The role of classical correlations is also discussed.
We analyze the entanglement distribution and the two-qubit residual entanglement in multipartite systems. For a composite system consisting of two cavities interacting with independent reservoirs, it is revealed that the entanglement evolution is restricted by an entanglement monogamy relation derived here. Moreover, it is found that the initial cavity-cavity entanglement evolves completely to the genuine four-partite cavities-reservoirs entanglement in the time interval between the sudden death of cavity-cavity entanglement and the birth of reservoir-reservoir entanglement. In addition, we al…
We determine the entanglement capability of self-inverse Hamiltonian evolution, which reduces to the known result for Ising Hamiltonian, and identify optimal input states for yielding the maximal entanglement rate. We introduce the concept of the operator entanglement rate, and find that the maximal operator entanglement rate gives a lower bound on the entanglement capability of a general Hamiltonian.
We analyze the entanglement evolution of two cavity photons being affected by the dissipation of two individual reservoirs. Under an arbitrary local unitary operation on the initial state, it is shown that there is only one parameter which changes the entanglement dynamics. For the bipartite subsystems, we show that the entanglement of the cavity photons is correlated with that of the reservoirs, although the local operation can delay the time at which the photon entanglement disappears and advance the time at which the reservoir entanglement appears. Furthermore, via a new defined four-qubit …
We investigate the time evolution of the entanglement of assistance when one subsystem undergoes the action of local noisy channels. A general factorization law is presented for the evolution equation of entanglement of assistance. Our results demonstrate that the dynamics of the entanglement of assistance is determined by the action of a noisy channel on the pure maximally entangled state, in which the entanglement reduction turns out to be universal for all quantum states entering the channel. This single quantity will make it easy to characterize the entanglement dynamics of entanglement of…
Symmetries of the initial state of a quantum system and the quantum channels, which simultaneously affect parts of the system, can significantly simplify the description of the entanglement evolution. Using concurrence as the entanglement measure, we study the entanglement evolution of few qubit systems, when each of the qubits is affected by a local channel independently of the others. We show that, for low-rank density matrices of the final quantum state, such complex entanglement dynamics can be completely described by a combination of independent factors representing the evolution of entan…
We investigate the average bipartite entanglement, over all possible divisions of a multipartite system, as a useful measure of multipartite entanglement. We expose a connection between such measures and quantum-error-correcting codes by deriving a formula relating the weight distribution of the code to the average entanglement of encoded states. Multipartite entangling power of quantum evolutions is also investigated.
A complete analysis on the generation of spin entanglement from NRQED is presented. The results of entanglement are obtained with relativistic correction to the leading order of (v/c)^2. It is shown that to this order the degree of entanglement of a singlet state does not change under time evolution whereas the triplet state can change.
Evolution of entanglement with the proceeding of quantum algorithms affects the outcome of the algorithm. Particularly, the performance of Grover's search algorithm gets worsened if the initial state of the algorithm is an entangled one. The success probability of search can be seen as an operational measure of entanglement. This paper demonstrates an entanglement measure based on the performance of Grover's search algorithm for three and five qubit systems. We also show that although the overall pattern shows growth of entanglement, its rise to a maximum and then consequent decay, the presenc…
We discuss entanglement evolution of a multi-qubit system when one of its qubits is subjected to a general noisy channel. For such a system, an evolution equation of entanglement for a lower bound for multi-qubit concurrence is derived. Using this evolution equation, the entanglement dynamics of an initially mixed three-qubit state composed of a GHZ and a W state is analyzed if one of the qubits is affected by a phase, an amplitude or a generalized amplitude damping channel.
Entanglement speeds up evolution of a pure bipartite spin state, in line with the time energy uncertainty. However if the state is mixed this is not necessarily the case. We provide a counter example and point to other factors affecting evolution in mixed states, including classical correlations and entropy.
Two noninteracting atoms, initially entangled in Bell states, are coupled to a one-mode cavity. Based on the reduced non-perturbative quantum master equation, the entanglement evolution of the two atoms with decay is investigated beyond rotating-wave approximation. It is shown that the counter-rotating wave terms have great influence on the disentanglement behavior. The phenomenon of entanglement sudden death and entanglement sudden birth will occur.
We show that the entanglement dynamics for a closed two-qubit system is part of a 10-dimensional complex linear differential equation defined on a supersphere, and the coefficients therein are completely determined by the Hamiltonian. We apply the result to investigate two physical examples of Josephson junction qubits and exchange Hamiltonians, deriving analytic solutions for the time evolution of entanglement. The Hamiltonian coefficients determines whether the entanglement is periodic. These results allow of investigating how to generate and manipulate entanglements efficiently, which are r…
We analyze the multipartite entanglement evolution of three-qubit mixed states composed of a GHZ state and a W state. For a composite system consisting of three cavities interacting with independent reservoirs, it is shown that the entanglement evolution is restricted by a set of monogamy relations. Furthermore, as quantified by the negativity, the entanglement dynamical property of the mixed entangled state of cavity photons is investigated. It is found that the three cavity photons can exhibit the phenomenon of entanglement sudden death (ESD). However, compared with the evolution of a genera…
Batle et al. [Phys. Rev. A {\bf 72}, 032337 (2005)] and Borrás et al. [Phys. Rev. A {\bf 74}, 022326 (2006)] studied the connection between entanglement and speed of quantum evolution for certain low-dimensional bipartite quantum states. However, their studies did not cover all possible cases. And the relation between entanglement and the maximum possible quantum evolution speed for these uncovered cases can very different from the ones that they have studied.
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…
We discuss a model for non-linear quantum evolution based on the idea of time displaced entanglement, produced by taking one member of an entangled pair on a round trip at relativistic speeds, thus inducing a time-shift between the pair. We show that decoherence of the entangled pair is predicted. For non-maximal entanglement this then implies the ability to induce a non-unitary, non-linear quantum evolution. Although exhibiting unusual characteristics, we show that these evolutions cannot be dismissed on the basis of entropic or causal arguments.
We discuss time displaced entanglement, produced by taking one member of a Bell pair on a round trip at relativistic speeds, thus inducing a time-shift between the pair. We show that decoherence with respect to Bell measurements on the pair is predicted. We then study a teleportation protocol, using time displaced entanglement as its resource, in which a time-like loop is apparently formed. The result is non-unitary, non-linear evolution of the teleported state.
Evolution of entanglement with the processing of quantum algorithms affects the outcome of the algorithm. Particularly, the performance of Grover's search algorithm gets worsened if the initial state of the algorithm is an entangled one. Biham et al [14] have shown that the success probability of search algorithm can be seen as an operational measure of entanglement. Following the same line of thought, analytical expressions for entanglement measure for three and five qubit system have been derived, which reveals that entanglement measure based on Grover's search algorithm is valid for any sta…
Entanglement plays a crucial role in quantum processes particularly those pertaining to quantum information and computation. An analytical expression for an entanglement measure defined in terms of success rate of Grover's search algorithm has been obtained for qutrit systems with real coefficients and the calculated results agree well with the conventional entropy based measure. The entanglement measure is further generalised for qudit (d-level) systems with real coefficients.
We provide a relation which describes how the entanglement of two d-level systems evolves as either system undergoes an arbitrary physical process. The dynamics of the entanglement turns out to be of a simple form, and is fully captured by a single quantity.
In this paper I explore the entanglement evolution of qubits that are part of a five qubit quantum error correction code subject to various decohering environments. Specifically, I look for possible parallels between the entanglement degradation and the fidelity of the logical qubit of quantum information stored in the physical qubits. In addition, I note the possible exhibition of entanglement sudden death (ESD) due to decoherence and question whether ESD is actually a roadblock to successful quantum computation.
We point out that the main results-the analytic expressions for the Groverian Measure of Entanglement, in the above mentioned paper are erroneous. The technical mistake of the paper is discussed. It is shown by an explicit example that the formula for calculating the Groverian measure yields G(|ψ>) = 0 for some entangled states.
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.
A model of evolution of bipartite quantum state entanglement is studied. It involves recently introduced quantum block spin-flip dynamics on a lattice. We find that for initially separable states the considered evolution leads, in general, to entangled states. We also present a complete characterization of two-point correlation functions for that type of dynamics to confirm enhancement of quantum correlations for the considered system.
The entanglement evolution of two qubits under local, single- and two- sided noisy channels is investigated. It is found that for all pure initial states, the entanglement under a one-sided noisy channel is completely determined by the maximal trace distance which is the main element to construct the measure of non-Markovianity. For the two-sided noisy channel case, when the qubits are initially prepared in a general class of states, no matter pure or mixed, the entanglement can be expressed as the products of initial entanglement and the channels' action on the maximally entangled state.
In this work, we propose a scheme to design the time evolution of the entropy of entanglement between two qubits. It is shown an explicit accurate solution for the inverse problem of determining the time dependence of the coupling constant from a user-defined dynamical entanglement function. Such an active control of entanglement can be implemented in many different physical implementations of coupled qubits, and we briefly comment on the use of interacting flux qubits.
The dynamical creation of entanglement between three-level atoms coupled to the common vacuum is investigated. For the class of bound entangled initial states we show that the dynamics of closely separated atoms generates stationary distillable entanglement of asymptotic states. We also find that the effect of delayed sudden birth of distillable entanglement occurs in the case of atoms separated by a distance comparable with the radiation wavelength.
The phenomenon of entanglement sudden death (ESD) in finite dimensional composite open systems is described here for both bi-partite as well as multipartite cases, where individual subsystems undergo Lindblad type heat bath evolution. ESD is found to be generic for non-zero temperature of the bath. At T=0, one-sided action of the heat bath on pure entangled states of two qubits does not show ESD.
The unitary evolution can be represented by a finite product of exponential operators. It leads to a perturbative expression of the density operator of a close system. Based on the perturbative expression scheme, we present a entanglement measure, this measure has the advantage that it is easy to compute for a general dynamical process.
A detailed treatment of the entanglement dynamics of two distant but non-identical systems is presented. We study the entanglement evolution of two remote atoms interacting independently with a cavity field, as in the double Jaynes-Cummings (JC) model. The four-qubit pairwise concurrences are studied, allowing for asymmetric atom-cavity couplings and off-resonant ineractions. Counter to intuition, imperfect matching can prove advantageous to entanglement creation and evolution. For two types of initial entanglement, corresponding to spin correlated and anti-correlated Bell states Φand Ψ, a ful…
Entanglement of bosonic systems under monitored evolution
研究重复投影测量下非相互作用玻色子的受监测演化，揭示首次探测概率与二分系统纠缠熵及纠缠谱的直接联系，并发现在特殊时间步长附近纠缠熵呈平稳或多稳态切换。
The dynamics of a cascaded system that consists of two atom-cavity subsystems is studied by using the quantum trajectory method. Unwanted losses are included, such as photon absorption and scattering by the cavity mirrors and spontaneous emission of the atoms. Considering an initially excited two-level atom in the source subsystem, analytical solutions are obtained. The entanglement evolution is studied for the two atoms and for the two intracavity fields.
We study entanglement dynamics in the presence of correlated environmental noises. Specifically, we investigate the quantum entanglement dynamics of two spins in the presence of correlated classical white noises, deriving Markov master equation and obtaining explicit solutions for several interesting classes of initial states including Bell states and X form density matrices. We show how entanglement can be enhanced or reduced by the correlation between the two participating noises.
We explore how entanglement of a general bipartite system evolves when one subsystem undergoes the action of an arbitrary noisy channel. It is found that the dynamics of entanglement for general bipartite systems under the influence of such channel is determined by the channel's action on the maximally entangled state, which includes as a special case the results for two-qubit systems [Nature Physics 4, 99 (2008)]. In particular, for multi-qubit or qubit-qudit systems, we get a general factorization law for evolution equation of entanglement with one qubit being subject to a noisy channel. Our…
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we study the continuous variable entanglement for a system consisting of two independent harmonic oscillators interacting with a general environment. We solve the Kossakowski-Lindblad master equation for the time evolution of the considered system and describe the entanglement in terms of the covariance matrix for an arbitrary Gaussian input state. Using Peres-Simon necessary and sufficient criterion for separability of two-mode Gaussian states, we show that for certain values of diffusion…
The position variance of a single-mode Yuen states can go below the standard quantum limit. For two-mode squeezed states, it is shown that the time-dependent evolution of the entanglement of formation can be contractive, going below that of the squeezed state with minimum Einstein-Podolsky-Rosen dispersions, and increasing thereafter. The rate of change of the Einstein-Podolsky-Rosen dispersions as a function of the two-mode phases control this process. Contractive entanglement is shown to be equivalent to a rotating phase space accompanied by time-dependent single-mode squeezing.
The "speed" of unitary quantum evolution was recently shown to be connected to entanglement in multipartite quantum systems. Here, we discuss a tighter version of the Mandelstam-Tamm uncertainty relation that depends on the Fisher information. The passage time is estimated by a lower bound that depends inversely proportional to the square root of the Fisher information. This leads to a better understanding of the origin of a fast quantum time evolution of entangled states.
In the last two decades, magnetic, thermodynamic properties and bipartite thermal entanglement in diamond spin clusters and chains have been studied. Such spin structures are presented in various compounds. The ions of $Cu^{2+}$ in the natural mineral azurite are arranged in a diamond spin chain. There are no studies of the entanglement behaviour during the quantum evolution of such systems. Herein, we consider the evolution of entanglement in the diamond spin-1/2 cluster. This cluster consists of two central spins described by the anisotropic Heisenberg model, which interact with two side spi…
We consider a pair of three-level atoms interacting with the vacuum. The process of disentanglement due to spontaneous emission and the role of quantum interference between principal transitions in this process, are analysed. We show that the presence of interference can slow down disentanglement. In the limit of maximal interference, some part of initial entanglement can survive.
We examine a class of bipartite mixed states which we call X states and report several analytic results related to the occurrence of so-called entanglement sudden death (ESD) under time evolution in the presence of common types of environmental noise. Avoidance of sudden death by application of purely local operations is shown to be feasible in some cases.
Unique entanglement time evolution of two-qubit product separable and extended Werner-like states in a discrete qubit environment
本文研究两量子比特乘积可分离态与扩展Werner-like态在均匀、白噪声及混合环境中的纠缠时间演化，揭示两者纠缠子空间不相交、环境与子系统耦合的时间反比关系，以及白噪声耗散由相互作用强度分布宽度决定等规律。
We describe a decomposition of the Lie group of unitary evolutions for a bipartite quantum system of arbitrary dimensions. The decomposition is based on a recursive procedure which systematically uses the Cartan classification of the symmetric spaces of the Lie group SO(n). The resulting factorization of unitary evolutions clearly displays the local and entangling character of each factor.
In this paper we study the evolution of the two two-level atoms interacting with a single-mode quantized radiation field, namely, two-atom multiphoton Jaynes-Cummings model when the radiation field and atoms are initially prepared in the superpostion of displaced number states and excited atomic states, respectively. For this system we investigate the atomic inversion, Wigner function, phase distribution and entanglement.
Investigating the evolution of quantum entanglement of a qubit-qubit system with Dzyaloshinskii-Moriya interaction in the presence of magnetic fields
本文研究磁场下具有DM相互作用的XXX和XYZ模型中qubit-qubit系统的纠缠动力学，利用负性判据分析自旋相干态初始条件下的纠缠演化，评估DM相互作用和磁场的影响。
Entanglement is closely related to some fundamental features of the dynamics of composite quantum systems: quantum entanglement enhances the "speed" of evolution of certain quantum states, as measured by the time required to reach an orthogonal state. The concept of "speed" of quantum evolution constitutes an important ingredient in any attempt to determine the fundamental limits that basic physical laws impose on how fast a physical system can process or transmit information. Here we explore the relationship between entanglement and the speed of quantum evolution in the context of the quantum…
We explore the connection between quantum brachistochrone (time-optimal) evolution of a three-qubit system and its residual entanglement called three-tangle. The result shows that the entanglement between two qubits is not required for some brachistochrone evolutions of a three-qubit system. However, the evolution between two distinct states cannot be implemented without its three-tangle, except for the trivial cases in which less than three qubits attend evolution. Although both the probability density function of the time-averaged three-tangle and that of the time-averaged squared concurrenc…
This paper discusses relationships between topological entanglement and quantum entanglement. Specifically, we propose that for this comparison it is fundamental to view topological entanglements such as braids as "entanglement operators" and to associate to them unitary operators that are capable of creating quantum entanglement.
Entanglement plays a crucial role in quantum processes particularly those pertaining to quantum information and computation. An analytical expression for entanglement measure defined in terms of success rate of Grover's search algorithm has been obtained for a two-qutrit system and the calculated results agree well with the conventional entropy based measure. Qutrit system are of special interest because the Hilbert space dimensionality (for a given number of qudits-d-dimensional system)is optimal for d=3 and this may be of significance in the enhancement of computing power.
The occurrence of entanglement sudden death in the evolution of a bipartite system depends on both the initial state and the channel responsible for the evolution. An extreme case is that of entanglement braking channels, which are channels that acting on only one of the subsystems drives them to full disentanglement regardless of the initial state. In general, one can find certain combinations of initial states and channels acting on one or both subsystems that can result in entanglement sudden death or not. Neither the channel nor the initial state, but their combination, is responsible for …
We present analytical compact solution for the density matrix and correlation functions of two collective-macroscopic spins evolving via Ising-like Hamiltonian in the presence of particle losses. The losses introduce non-local phase noise which destroys highly entangled states arising in the evolution. On the other hand, the states appearing at relatively short timescales, possessing EPR-like entanglement will survive. Applying our solutions to the recently proposed scheme to entangle two Bose-Einstein condensates, we estimate the optimal number of atoms for EPR correlations.
It has been recently pointed out [V. Giovanetti, S. Lloyd, and L. Maccone, Europhys. Lett., {\bf 62} pp. 615-621 (2003)] that, for certain classes of states, quantum entanglement enhances the "speed" of evolution of composite quantum systems, as measured by the time a given initial state requires to evolve to an orthogonal state. We provide here a systematic study of this effect for pure states of bipartite systems of low dimensionality, considering both distinguishable (two-qubits) subsystems, and systems constituted of two indistinguishable particles.
We study how multi-partite entanglement evolves under the paradigm of separable operations, which include the local operations and classical communication (LOCC) as a special case. We prove that the average "decay" of entanglement induced by a separable operation is measure independent (among SL-invariant ones) and state independent: the ratio between the average output entanglement and the initial entanglement is solely a function of the separable operation, regardless of the input state and of the SL-invariant entanglement measure being used. We discuss the "disentangling power" of a quantum…
We investigate the evolution of quantum correlations over the lifetime of a multi-photon state. Measurements reveal time-dependent oscillations of the entanglement fidelity for photon pairs created by a single semiconductor quantum dot. The oscillations are attributed to the phase acquired in the intermediate, non-degenerate, exciton-photon state and are consistent with simulations. We conclude that emission of photon pairs by a typical quantum dot with finite polarisation splitting is in fact entangled in a time-evolving state, and not classically correlated as previously regarded.
A simple relation is introduced for concurrence to describe how much the entanglement of bipartite system is at least left if either (or both) subsystem undergoes an arbitrary physical process. This provides a lower bound for concurrence of mixed states (pure states are included) in contrast to the upper bound given by Konrad et al [Nature Physics \textbf{4}, 99 (2008)]. Our results are also suitable for a general high dimensional bipartite quantum systems.
It is shown that Smolin four-qubit bound entangled states [Phys. Rev. A, 63 032306 (2001)] can maximally violate two-setting Bell inequality similar to standard CHSH inequality. Surprisingly this entanglement does not allow for secure key distillation, so neither entanglement nor violation of Bell inequalities implies quantum security. It is also pointed out how that kind of bound entanglement can be useful in reducing communication complexity.
Geometric Aspects of Entanglement Generating Hamiltonian Evolutions
研究从可分离态到最大纠缠两量子比特态的稳态哈密顿演化中纠缠的几何特性，发现时间最优演化具有高测地线效率、零曲率和较低的平均路径纠缠。
We propose a qubit-environment entanglement measure which is tailored for evolutions that lead to pure dephasing of the qubit, such as are abundant in solid state scenarios. The measure can be calculated directly form the density matrix without minimization of any kind. In fact it does not require the knowledge of the full density matrix, and it is enough to know the initial qubit state and the states of the environment conditional on qubit pointer states. This yields a computational advantage over standard entanglement measures, which becomes large when there are no correlations between envir…
Using entanglement of assistance, we establish a general polygamy inequality of multi-party entanglement in arbitrary dimensional quantum systems. For multi-party closed quantum systems, we relate our result with the monogamy of entanglement to show that the entropy of entanglement is an universal entanglement measure that bounds both monogamy and polygamy of multi-party quantum entanglement.
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