We demonstrate the difference between local, single-particle dynamics and global dynamics of entangled quantum systems coupled to independent environments. Using an all-optical experimental setup, we showed that, even when the environment-induced decay of each system is asymptotic, quantum entanglement may suddenly disappear. This "sudden death" constitutes yet another distinct and counterintuitive trait of entanglement.

One of the greatest challenges in the fields of quantum information processing and quantum technologies is the detailed coherent control over each and every constituent of quantum systems with an ever increasing number of particles. Within this endeavor, harnessing of many-body entanglement against the detrimental effects of the environment is a major pressing issue. Besides being an important concept from a fundamental standpoint, entanglement has been recognized as a crucial resource for quantum speed-ups or performance enhancements over classical methods. Understanding and controlling many-body entanglement in open systems may have strong implications in quantum computing, quantum simulations of many-body systems, secure quantum communication or cryptography, quantum metrology, our understanding of the quantum-to-classical transition, and other important questions of quantum foundations.In this paper we present an overview of recent theoretical and experimental efforts to underpin the dynamics of entanglement under the influence of noise. Entanglement is thus taken as a dynamic quantity on its own, and we survey how it evolves due to the unavoidable interaction of the entangled system with its surroundings. We analyze several scenarios, corresponding to different families of states and environments, which render a very rich diversity of dynamical behaviors.In contrast to single-particle quantities, like populations and coherences, which typically vanish only asymptotically in time, entanglement may disappear at a finite time. In addition, important classes of entanglement display an exponential decay with the number of particles when subject to local noise, which poses yet another threat to the already-challenging scaling of quantum technologies. Other classes, however, turn out to be extremely robust against local noise. Theoretical results and recent experiments regarding the difference between local and global decoherence are summarized. Control and robustness-enhancement techniques, scaling laws, statistical and geometrical aspects of multipartite-entanglement decay are also reviewed; all in order to give a broad picture of entanglement dynamics in open quantum systems addressed to both theorists and experimentalists inside and outside the field of quantum information.

Quantum information technology 1 largely relies on a precious and fragile resource, quantum entanglement, a highly nontrivial manifestation of the coherent superposition of states of composite quantum systems. However, our knowledge of the time evolution of this resource under realistic conditions-that is, when corrupted by environment-induced decoherence-is so far limited, and general statements on entanglement dynamics in open systems are scarce 2-11 . Here we prove a simple and general factorization law for quantum systems shared by two parties, which describes the time evolution of entanglement on passage of either component through an arbitrary noisy channel. The robustness of entanglement-based quantum information processing protocols is thus easily and fully characterized by a single quantity.Whenever we contemplate the potential technological applications of quantum information theory 1 , from secure quantum communication to quantum teleportation 12 , to quantum computation 13 , we need to worry about the unavoidable and detrimental coupling of any such quantum device to uncontrolled degrees of freedom-typically lumped together under the label 'environment' . Coupling to the environment induces decoherence [14][15][16] ; that is, it gradually destroys the phase relationship between quantum states, and thus their ability to interfere. In composite quantum systems, these phase relationships (or 'coherences') are at the origin of strong quantum correlations between measurements on distinct system constituents-which then are entangled. The promises of quantum information technology rely on exploring precisely these nonclassical correlations.Yet, entanglement is not equivalent to many-particle coherences: it is an even stronger property, and hard to quantifyall commonly accepted entanglement measures 17 are nonlinear functions of the density matrix, which describes the state of the composite quantum system, and in particular the coherences. Although an elaborate theory on the time evolution of quantum states under environment coupling is to hand, virtually no general results on entanglement dynamics have been stated. Hitherto, the time evolution of entanglement always needed to be deduced from the time evolution of the state 2-10 . In the present letter, a direct relationship between the initial and final entanglements

We report on an experimental investigation of the dynamics of entanglement between a single qubit and its environment, as well as for pairs of qubits interacting independently with individual environments, using photons obtained from parametric down-conversion. The qubits are encoded in the polarizations of single photons, while the interaction with the environment is implemented by coupling the polarization of each photon with its momentum. A convenient Sagnac interferometer allows for the implementation of several decoherence channels and for the continuous monitoring of the environment. For an initially-entangled photon pair, one observes the vanishing of entanglement before coherence disappears. For a single qubit interacting with an environment, the dynamics of complementarity relations connecting single-qubit properties and its entanglement with the environment is experimentally determined. The evolution of a single qubit under continuous monitoring of the environment is investigated, demonstrating that a qubit may decay even when the environment is found in the unexcited state. This implies that entanglement can be increased by local continuous monitoring, which is equivalent to entanglement distillation. We also present a detailed analysis of the transfer of entanglement from the two-qubit system to the two corresponding environments, between which entanglement may suddenly appear, and show instances for which no entanglement is created between dephasing environments, nor between each of them and the corresponding qubit: the initial two-qubit entanglement gets transformed into legitimate multiqubit entanglement of the Greenberger-Horne-Zeilinger (GHZ) type.

The Hong-Ou-Mandel effect is generalized to a configuration of n bosons prepared in the n input ports of a Bell multiport beam splitter. We derive a strict suppression law for most possible output events, consistent with a generic bosonic behavior after suitable coarse graining.PACS numbers: 03.67. Lx, 05.30.Jp, The Hong-Ou-Mandel (HOM) effect [1] is an impressive manifestation of the bosonic quantum nature of photons. In the original experiment, two identical photons are sent simultaneously (within their coherence time) through the two input ports of a balanced beam splitter. Since no interaction between the photons takes place, one would intuitively expect the photons to propagate independently and not presume any correlations in the number of photons measured at both output ports. Surprisingly, the photons always leave the setup together, but never exit at different ports. Such coincident events at both output ports are completely suppressed.This effect is used in many applications: The visibility of the dip in the coincident detection rate provides a characterization for the indistinguishability of two photons [2,3], and therewith for the quality of photon sources. HOM setups are used to project photons onto the maximally entangled |Ψ − Bell-state, and consequently to, both, create and detect such states [4]. This is used for example in entanglement swapping protocols [5] and quantum metrology [6]. Furthermore, the nondeterministic gate operations in linear optics quantum computation [7] are based on the HOM effect.It is suggestive to generalize the HOM setup for more than two photons and more than two input or output ports. Indeed, the enhancement of events with all particles in one port -bunching events -has been observed experimentally when several photons enter each of the two modes of an unbiased (i.e., balanced) two-port beam splitter [8,9]. For a specially designed biased setup of three particles and three input ports, the suppression of coincident events was shown [10]. In the case of a Bell multiport beam splitter [11,12] which redistributes n incoming particles to n ports in an unbiased way, it is known that coincident events are suppressed when n is even [13].All these results imply important applications, from the creation and detection of multipartite quditentangled states [14,15], over the implementation of entanglement swapping protocols for many particles and the design of efficient quantum gates for qudits [16], to the experimentally controlled transition from indistinguishability to distinguishability for many identical particles [17]. However, we still lack a comprehensive understanding of the n-particle, n-port generalization of the HOM effect, since the complexity of such a scattering problem scales very unfavorably with n: The number of interfering amplitudes as well as that of possible output events grow faster than exponentially. Hence, a detailed analysis of individual output events is prohibitive, and needs to be substituted by statistical considerations. This is the purpose of the ...

We show that finite-size, disordered molecular networks can mediate highly efficient, coherent excitation transfer which is robust against ambient dephasing and associated with strong multisite entanglement. Such optimal, random molecular conformations may explain efficient energy transfer in the photosynthetic Fenna-Matthews-Olson complex.

We introduce detector-level entanglement, a unified entanglement concept for identical particles that takes into account the possible deletion of many-particle which-way information through the detection process. The concept implies a measure for the effective indistinguishability of the particles, which is controlled by the measurement setup and which quantifies the extent to which the (anti-)symmetrization of the wave-function impacts on physical observables. Initially indistinguishable particles can gain or loose entanglement on their transition to distinguishability, and their quantum statistical behavior depends on their initial entanglement. Our results show that entanglement cannot be attributed to a state of identical particles alone, but that the detection process has to be incorporated in the analysis.

We consider the realization of universal quantum computation through braiding of Majorana fermions supplemented by unprotected preparation of noisy ancillae. It has been shown by Bravyi (2006 Phys. Rev. A 73 042313) that under the assumption of perfect braiding operations, universal quantum computation is possible if the noise rate on a particular four-fermion ancilla is below 40%. We show that beyond a noise rate of 89% on this ancilla the quantum computation can be efficiently simulated classically: we explicitly show that the noisy ancilla is a convex mixture of Gaussian fermionic states in this region, while for noise rates below 53% we prove that the state is not a mixture of Gaussian states. These results are obtained by generalizing concepts in entanglement theory to the setting of Gaussian states and their convex mixtures. In particular, we develop a complete set of criteria, namely the existence of a Gaussian-symmetric extension, which determine whether a state is a convex mixture of Gaussian states.