We study the dynamics of the entanglement structure of a multipartite system experiencing a dissipative evolution. We characterize the processes leading to a particular form of output-system entanglement and provide a recipe for their identification via concatenations of particular linear maps with entanglement-breaking operations. We illustrate the applicability of our approach by considering local and global depolarizing noises acting on general multiqubit states. A difference in the typical entanglement behavior of systems subjected to these noises is observed: the originally genuine entanglement dissociates by splitting off particles one by one in the case of local noise, whereas intermediate stages of entanglement clustering are present in the case of global noise. We also analyze the definitive phase of evolution when the annihilation of the entanglement compound finally takes place.
We study the dynamics of the entanglement structure of a multipartite system experiencing a dissipative evolution. We characterize the processes leading to a particular form of output-system entanglement and provide a recipe for their identification via concatenations of particular linear maps with entanglement-breaking operations. We illustrate the applicability of our approach by considering local and global depolarizing noises acting on general multiqubit states. A difference in the typical entanglement behavior of systems subjected to these noises is observed: the originally genuine entanglement dissociates by splitting off particles one by one in the case of local noise, whereas intermediate stages of entanglement clustering are present in the case of global noise. We also analyze the definitive phase of evolution when the annihilation of the entanglement compound finally takes place.
We introduce and investigate a family of entanglement-annihilating channels. These channels are capable of destroying any quantum entanglement within the system they act on. We show that they are not necessarily entanglement breaking. In order to achieve this result we analyze the subset of locally entanglement-annihilating channels. In this case, the same local noise applied on each subsystem individually is less entanglement annihilating (with respect to multi-partite entanglement) as the number of subsystems is increasing. Therefore, the bipartite case provides restrictions on the set of local entanglement-annihilating channels for the multipartite case. The introduced concepts are illustrated on the family of single-qubit depolarizing channels.
We fully characterize bipartite entanglement-annihilating (EA) channels that destroy entanglement of any state shared by subsystems and, thus, should be avoided in any entanglement-enabled experiment. Our approach relies on extending the problem to EA positive maps, the cone of which remains invariant under concatenation with partially positive maps. Due to this invariancy, positive EA maps adopt a well characterization and their intersection with completely positive trace-preserving maps results in the set of EA channels. In addition to a general description, we also provide sufficient operational criteria revealing EA channels. They have a clear physical meaning since the processes involved contain stages of classical information transfer for subsystems. We demonstrate the applicability of derived criteria for local and global depolarizing noises, and specify corresponding noise levels beyond which any initial state becomes disentangled after passing the channel. The robustness of some entangled states is discussed.
We address the problem of the robustness of entanglement of bipartite systems (qubits) interacting with dynamically independent environments. In particular, we focus on the characterization of so-called local entanglement-annihilating (EA) two-qubit channels, which set the maximum permissible noise level allowing us to perform entanglement-enabled experiments. The differences, but also the subtle relations, between entanglement-breaking and local EA channels are emphasized. A detailed characterization of the latter ones is provided for a variety of channels including depolarizing, unital, (generalized) amplitude-damping, and extremal channels. We also consider the convexity structure of local EA qubit channels and introduce a concept of EA duality.
Quantum entanglement manifests itself in non-local correlations between the constituents of a system. In its simplest realization, a measurement on one subsystem is affected by a prior measurement on its partner, irrespective of their separation. For multiple parties, purely collective types of entanglement exist but their detection, even theoretically, remains an outstanding open question. Here, we argue that all forms of multipartite entanglement entirely disappear during the typical evolution of a physical state as it heats up, evolves in time in a large family of dynamical protocols, or as its parts become separated. We focus on the generic case where the system interacts with an environment. These results mainly follow from the geometry of the entanglement-free continent in the space of physical states, and hold in great generality. We illustrate these phenomena with a frustrated molecular quantum magnet in and out of equilibrium, and a quantum spin chain. In contrast, if the particles are fermions, such as electrons, another notion of entanglement exists that protects bipartite quantum correlations. However, genuinely collective fermionic entanglement disappears during typical evolution, thus sharing the same fate as in bosonic systems. These findings provide fundamental knowledge about the structure of entanglement in quantum matter and architectures, paving the way for its manipulation.
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.
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.