Entanglement generated by dissipation and steady state entanglement of two macroscopic objects

Entanglement is a striking feature of quantum mechanics and an essential ingredient in most applications in quantum information. Typically, coupling of a system to an environment inhibits entanglement, particularly in macroscopic systems. Here we report on an experiment where dissipation continuously generates entanglement between two macroscopic objects. This is achieved by engineering the dissipation using laser and magnetic fields, and leads to robust event-ready entanglement maintained for 0.04 s at room temperature. Our system consists of two ensembles containing about 10(12) atoms and separated by 0.5 m coupled to the environment composed of the vacuum modes of the electromagnetic field. By combining the dissipative mechanism with a continuous measurement, steady state entanglement is continuously generated and observed for up to 1 h.     

Generic dissipation of entanglement

We find states for a multi-level system which are stable under a very general model of dissipation, one which is governed simply by generic rate parameters; in general such stable states are not entangled. We exhibit such a state explicitly for a two-qubit system. We then specialize to a more physical model of dissipation, one which is governed by pure dephasing. In such a case it is possible, by choice of the dephasing rates, to have a stable, and limiting, entangled state under the evolution governed by the free hamiltonian and pure decoherence. We exhibit such a choice explicitly which has a stable and limiting two-qubit state of maximum entanglement (Bell state).     

Entanglement and decoherence: fragile and robust entanglement

The destruction of entanglement of open quantum systems by decoherence is investigated in the asymptotic long-time limit. For this purpose a general and analytically solvable decoherence model is presented which does not involve any weak-coupling or Markovian assumption. It is shown that two fundamentally different classes of entangled states can be distinguished and that they can be influenced significantly by two important environmental properties, namely, its initially prepared state and its size. Quantum states of the first class are fragile against decoherence so that they can be disentangled asymptotically even if coherences between pointer states are still present. Quantum states of the second type are robust against decoherence. Asymptotically they can be disentangled only if also decoherence is perfect. A simple criterion for identifying these two classes on the basis of two-qubit entanglement is presented.     

Thermalizing quantum machines: dissipation and entanglement

We study the relaxation of a quantum system towards the thermal equilibrium using tools developed within the context of quantum information theory. We consider a model in which the system is a qubit, and reaches equilibrium after several successive two-qubit interactions (thermalizing machines) with qubits of a reservoir. We characterize completely the family of thermalizing machines. The model shows a tight link between dissipation, fluctuations, and the maximal entanglement that can be generated by the machines. The interplay of quantum and classical information processes that give rise to practical irreversibility is discussed.     

Quantum control of two-qubit entanglement dissipation

We investigate quantum control of the dissipation of entanglement under environmental decoherence. We show by means of a simple two-qubit model that standard control methods – coherent or openloop control – will not in general prevent entanglement loss induced by a Markovian environment. However, we propose a control method utilizing a Wiseman–Milburn feedback/measurement control scheme which will effectively negate environmental entanglement dissipation.     

Entanglement measures with asymptotic weak-monotonicity as lower (upper) bound for the entanglement of cost (distillation)

We propose entanglement measures with asymptotic weak-monotonicity. We show that a normalized form of entanglement measures with the asymptotic weak-monotonicity are lower (upper) bound for the entanglement of cost (distillation).     

BCFT and OSFT moduli: an exact perturbative comparison

Starting from the pseudo-\({\mathcal {B}}_0\) gauge solution for marginal deformations in OSFT, we analytically compute the relation between the perturbative deformation parameter \(\tilde{\lambda }\) in the solution and the BCFT marginal parameter \(\lambda \), up to fifth order, by evaluating the Ellwood invariants. We observe that the microscopic reason why \(\tilde{\lambda }\) and \(\lambda \) are different is that the OSFT propagator renormalizes contact-term divergences differently from the contour deformation used in BCFT.     

Entanglement witnesses and geometry of entanglement of two-qutrit states

We construct entanglement witnesses with regard to the geometric structure of the Hilbert-Schmidt space and investigate the geometry of entanglement. In particular, for a two-parameter family of two-qutrit states that are part of the magic simplex, we calculate the Hilbert-Schmidt measure of entanglement. We present a method to detect bound entanglement which is illustrated for a three-parameter family of states. In this way, we discover new regions of bound entangled states. Furthermore, we outline how to use our method to distinguish entangled from separable states.     

Rescaling multipartite entanglement measures for mixed states

A relevant problem regarding entanglement measures is the following: Given an arbitrary mixed state, how does a measure for multipartite entanglement change if general local operations are applied to the state? This question is nontrivial as the normalization of the states has to be taken into account. Here we answer it for pure-state entanglement measures which are invariant under determinant-one local operations and homogeneous in the state coefficients, and their convex-roof extension which quantifies mixed-state entanglement. Our analysis allows us to enlarge the set of mixed states for which these important measures can be calculated exactly. In particular, our results hint at a distinguished role of entanglement measures which have homogeneous degree 2 in the state coefficients.     

Entanglement witnesses and characterizing entanglement properties of some PPT states

On the basis of linear programming, new sets of entanglement witnesses (EWs) for 3⊗3 and 4⊗4 systems are constructed. In both cases, the constructed EWs correspond to the hyper-planes contacting, without intersecting, the related feasible regions at line segments and restricted planes respectively. Due to the special property of the contacting area between the hyper-planes and the feasible regions, the corresponding hyper-planes can be turned around the contacting area throughout a bounded interval and hence create an infinite number of EWs. As these EWs are able to detect entanglement of some PPT states, they are non-decomposable (nd-EWs).     

Engineering multipartite steady entanglement of distant atoms via dissipation

We propose a scheme for generating an entangled state for three atoms trapped in separate optical cavities that are coupled to each other through two optical fibers based on coherent driving and dissipation, which are induced by the classical fields and the decay of non-local bosonic modes, respectively. In our scheme, the interaction time need not be controlled strictly in the overall dynamics process, and the cavity field decay can be changed into a vital resource. The numerical simulation shows that the fidelity of the target state is insensitive to atomic spontaneous emission, and our scheme is good enough to generate the W state of distant atoms with a high fidelity and purity. In addition, the present scheme can also be generalized to prepare the N-partite W state of distant atoms.     

一种新的利用不可扩展乘积基和严格纠缠基的量子密钥分配方案

提出了一种新的利用33 Hilbert空间的不可扩展乘积基和严格纠缠基的量子密钥分配方案.对窃听者的窃听成功概率进行了分析.该方案具有许多诸如容量大以及效率高等独特的特点. 关键词： 量子密钥分配 不可扩展乘积基 严格纠缠基 正交完备基     

Complete set of operational measures for the characterization of three-qubit entanglement

We characterize the entanglement contained in a pure three-qubit state via operational entanglement measures. To this end, we derive a new decomposition for arbitrary three-qubit states which is characterized by five parameters (up to local unitary operations). We show that these parameters are uniquely determined by bipartite entanglement measures. These quantities measure the entanglement required to generate the state following a particular preparation procedure and have a clear physical meaning. Moreover, we show that the classification of states obtained in this way is strongly related to the one obtained when considering general local operations and classical communication.     

Decoherence and entanglement in coherent quantum tunneling of magnetization with dissipation

We study the coherent quantum tunneling of magnetization, for example, in a biaxial molecular magnet with dissipation of the environment which results in the suppression of the tunneling and therefore the decoherence of superposition of macroscopic quantum states in terms of the general spin-boson model. The degree of entanglement between the magnet and the environment is evaluated explicitly with the help of reduced density matrix. We show an interesting relation that the degree of entanglement approaches maximum value when the coherent tunneling is suppressed completely.     

An exact solution of the Korteweg-de Vries equation with dissipation

By means of the method proposed in the papers [1, 2] we look for solutions of the Korteweg—de Vries equation with dissipation. A new solution is found and expressed by means of the Weierstrass P-function.Partially supported by NSF Grant No. INT 73.20002 A01 formerly GF-41958.     

Tetrapartite entanglement measures of W-class in noninertial frames

We present the entanglement measures of a tetrapartite W-class entangled system in a noninertial frame, where the transformation between Minkowski and Rindler coordinates is applied.Two cases are considered.First, when one qubit has uniform acceleration whilst the other three remain stationary.Second, when two qubits have nonuniform accelerations and the others stay inertial.The 1–1 tangle, 1–3 tangle, and whole entanglement measurements π_4 and Π_4, are studied and illustrated with graphics through their dependence on the acceleration parameter r_d for the first case and r_c and r_d for the second case.It is found that the negativities(1–1 tangle and 1–3 tangle) and π-tangle decrease when the acceleration parameter r_d or in the second case r_c and r_d increase, remaining a nonzero entanglement in the majority of the results.This means that the system will be always entangled except for special cases.It is shown that only the 1–1 tangle for the first case vanishes at infinite accelerations, but for the second case the 1–1 tangle disappears completely when r 0.472473.An analytical expression for the von Neumann information entropy of the system is found and we note that it increases with the acceleration parameter.     

Detection of entanglement with polarized photons: experimental realization of an entanglement witness

We report on the first experimental realization of an entanglement witness, a method to detect entanglement with few local measurements. The present demonstration has been performed with polarized photons in Werner states, a well-known family of mixed states that can be either separable or nonseparable. The Werner states are generated by a novel high brilliance source of bipartite entangled states by which the state mixedness can be easily adjusted.     

Entanglement dynamics of two interacting qubits under the influence of local dissipation

We investigate the dynamics of entanglement given by the concurrence of a two-qubit system in the non-Markovian setting. A quantum master equation is derived, which is solved in the eigenbasis of the system Hamiltonian for X-type initial states. A closed formula for time evolution of concurrence is presented for a pure state. It is shown that under the influence of dissipation non-zero entanglement is created in unentangled two-qubit states which decay in the same way as pure entangled states. We also show that under real circumstances, the decay rate of concurrence is strongly modified by the non-Markovianity of the evolution.