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We study the dynamics of multipartite entanglement under the influence of decoherence. A suitable generalization of concurrence reveals distinct scaling of the entanglement decay rate of GHZ and W states, for various environments.PACS numbers: 03.67.Mn,03.65.Yz,03.65.Ud The notion of entangled states is, since the early days of quantum mechanics, a key concept when it comes to distinguish between the quantum and the classical world. Besides this fundamental aspect, entanglement attracts considerable interest since it can be viewed as an indispensable ingredient for quantum information processing. Numerous experiments have recently been carried out in this area, in particular on the controlled generation of entanglement between many quantum systems [1,2,3,4,5] -such as to accomplish fundamental scalability requirements for quantum computation.An obstacle for the production and observation of multipartite entanglement resides in its fragility under the unavoidable interaction with the environment. This challenges the experimentalist, but also demands a proper theoretical description of multipartite entanglement in open systems. Despite recent progress in the understanding of decoherence processes in quantum systems, a systematic characterization of the environment induced loss of many-particle quantum correlations is still lacking, and this is specifically due to the difficulties in quantifying multipartite entanglement.Even for bipartite mixed states, apart from the particular case of two level systems where an exact solution is known [6], the situation is far from being simple. Some of the widely used indicators of entanglement, such as the positive partial transpose and negativity [7], fail to detect certain entangled states, while some other entanglement measures for mixed states require a high dimensional optimization procedure which only provides an upper bound, unable to reliably distinguish entangled from separable states. Only recently [8], a lower bound (together with a numerically manageable upper bound) for the concurrence of mixed bipartite quantum states was derived. In the multipartite case, one usually has to deal with bipartite cuts, where the N individual constituents are partitioned into two (arbitrarily chosen) subgroups. The available entanglement measures for bipartite systems thus become applicable, though different cuts or partitions may lead to different values of entanglement and, furthermore, the number of possible bipartite cuts increases rapidly with N .To improve on this situation, we will here scrutinize the effects of decoherence on multipartite entanglement measured by a suitable generalization of concurrencesensitive to multipartite correlations. Moreover, since different experimental strategies to produce multipartite entanglement are subject to different sources of decoherence, we implement our approach for different types of environment coupling, acting on different types of initially maximally entangled multipartite quantum states. This finally provides a versatile toolbox ...

Nearly all protocols requiring shared quantum information--such as quantum teleportation or key distribution--rely on entanglement between distant parties. However, entanglement is difficult to characterize experimentally. All existing techniques for doing so, including entanglement witnesses or Bell inequalities, disclose the entanglement of some quantum states but fail for other states; therefore, they cannot provide satisfactory results in general. Such methods are fundamentally different from entanglement measures that, by definition, quantify the amount of entanglement in any state. However, these measures suffer from the severe disadvantage that they typically are not directly accessible in laboratory experiments. Here we report a linear optics experiment in which we directly observe a pure-state entanglement measure, namely concurrence. Our measurement set-up includes two copies of a quantum state: these 'twin' states are prepared in the polarization and momentum degrees of freedom of two photons, and concurrence is measured with a single, local measurement on just one of the photons.

Entanglement is nowadays considered as a key quantity for the understanding of correlations, transport properties, and phase transitions in composite quantum systems, and thus receives interest beyond the engineered applications in the focus of quantum information science. We review recent experimental and theoretical progress in the study of quantum correlations under that wider perspective, with an emphasis on rigorous definitions of the entanglement of identical particles, and on entanglement studies in atoms and molecules.

We derive a lower bound for the concurrence of mixed bipartite quantum states, valid in arbitrary dimensions. As a corollary, a weaker, purely algebraic estimate is found, which detects mixed entangled states with positive partial transpose.PACS numbers: 03.67.Mn, 89.70.+c In classical physics, one can always divide a system into subsystems, such that complete information on the entity implies a complete description of its individual parts, and vice versa. In quantum physics, this no longer holds true: whilst one can still divide a system into subsystems, a complete description of the system state in terms of a pure state does not necessarily assign a pure state to each subsystem. The subsystems of generic pure states are correlated in a way without classical analog -they are entangled.While such quantum entanglement arguably incarnates the key difference between the quantum and the classical world, and is nowadays understood as a resource in various tasks of quantum information processing [1] such as cryptography, teleportation, and quantum computation, it remains hard to quantify, for arbitrary quantum states [2]. In particular, when coupled to an environment, pure quantum states rapidly evolve into mixed states which bear entanglement together with classical probabilistic correlations, and the latter have to be distinguished from the former. Furthermore, the complete characterization of the nonclassical correlations of a given state becomes an ever more complex task as the Hilbert space dimension increases, thus turning into a computationally extremely intricate problem.No equally versatile as computationally manageable entanglement measure for mixed states is available so far, although various more or less pragmatically motivated quantities have been proposed. The most popular indicator of entanglement is the positive partial transpose (ppt) criterion [3] and variants thereof, such as negativity [4], though these do not reliably detect arbitrary entangled states. Another approach for quantifying entanglement is through entanglement witnesses [5] which, however, need to be constructed anew for each given quantum state, and such construction can be rather involved [6]. Finally, there are mixed state generalizations of pure state entanglement measures [7,8,9,10,11], which, in general, require a high dimensional optimisation procedure. By construction, any numerical evaluation of these latter quantities only yields upper bounds for the entanglement of a given state but cannot reliably distinguish it from separable states, let alone provide a reliable quantitative estimate of the state's actual degree of entanglement.In the present Letter, we improve on that situation: We derive a lower bound of concurrence [7,9] -a quantity which is strictly larger than zero for nonvanishing entanglement -of mixed bipartite quantum states in arbitrary dimensions. Our bound is given by a purely algebraic expression which is readily evaluated for arbitrary states, and can be tightened numerically on a relatively lowdimensional...

We develop an original approach for the quantitative characterisation of the entanglement properties of, possibly mixed, bi-and multipartite quantum states of arbitrary finite dimension. Particular emphasis is given to the derivation of reliable estimates which allow for an efficient evaluation of a specific entanglement measure, concurrence, for further implementation in the monitoring of the time evolution of multipartite entanglement under incoherent environment coupling. The flexibility of the technical machinery established here is illustrated by its implementation for different, realistic experimental scenarios.

We are taught by conventional wisdom that the transmission and detection of signals is hindered by noise. However, during the last two decades, the paradigm of stochastic resonance (SR) proved this assertion wrong: indeed, addition of the appropriate amount of noise can boost a signal and hence facilitate its detection in a noisy environment. Due to its simplicity and robustness, SR has been implemented by mother nature on almost every scale, thus attracting interdisciplinary interest from physicists, geologists, engineers, biologists and medical doctors, who nowadays use it as an instrument for their specific purposes.At the present time, there exist a lot of diversified models of SR. Taking into account the progress achieved in both theoretical understanding and practical application of this phenomenon, we put the focus of the present review not on discussing in depth technical details of different models and approaches but rather on presenting a general and clear physical picture of SR on a pedagogical level. Particular emphasis will be given to the implementation of SR in generic quantum systems-an issue that has received limited attention in earlier review papers on the topic.The major part of our presentation relies on the two-state model of SR (or on simple variants thereof), which is general enough to exhibit the main features of SR and, in fact, covers many (if not most) of the examples of SR published so far. In order to highlight the diversity of the two-state model, we shall discuss several examples from such different fields as condensed matter, nonlinear and quantum optics and biophysics. Finally, we also discuss some situations that go beyond the generic SR scenario but are still characterized by a constructive role of noise.

With the exception of the harmonic oscillator, quantum wave packets usually spread as time evolves. This is due to the non-linear character of the classical equations of motion which makes the various components of the wave packet evolve at various frequencies. We show here that, using the non-linear resonance between an internal frequency of a system and an external periodic driving, it is possible to overcome this spreading and build non-dispersive (or non-spreading) wave packets which are well localized and follow a classical periodic orbit without spreading. From the quantum mechanical point of view, the non-dispersive wave packets are time periodic eigenstates of the Floquet Hamiltonian, localized in the non-linear resonance island. We discuss the general mechanism which produces the non-dispersive wave packets, with emphasis on simple realization in the electronic motion of a Rydberg electron driven by a microwave field. We show the robustness of such wave packets for a model one-dimensional as well as for realistic three-dimensional atoms. We consider their essential properties such as the stability versus ionization, the characteristic energy spectrum and long lifetimes. The requirements for experiments aimed at observing such non-dispersive wave packets are also considered. The analysis is extended to situations in which the driving frequency is a multiple of the internal atomic frequency. Such a case allows us to discuss non-dispersive states composed of several, macroscopically separated wave packets communicating among themselves by tunneling. Similarly we briefly discuss other closely related phenomena in atomic and molecular physics as well as possible further extensions of the theory. (C) 2002 Elsevier Science B.V. All rights reserved