Invertible local transformations of a multipartite system are used to define equivalence classes in the set entangled states. This classification concerns entanglement properties single copy state. Accordingly, we say that two states have same kind if both them can be obtained from other by means operations and classical communcication (LOCC) with nonzero probability. When applied pure three-qubit system, this approach reveals existence inequivalent kinds genuine tripartite entanglement, for...

In quantum communication via noisy channels, the error probability scales exponentially with length of channel. We present a scheme repeater that overcomes this limitation. The central idea is to connect string (imperfect) entangled pairs particles by using novel nested purification protocol, thereby creating single distant pair high fidelity. Our tolerates general errors on percent level, it works polynomial overhead in time and logarithmic number need be controlled locally.

We study the use of entanglement purification for quantum communication over long distances. For distances much longer than coherence length a corresponding noisy channel, fidelity transmission is usually so low that standard methods are not applicable. It possible, however, to divide channel into shorter segments purified separately and then connected by method swapping. This can be more efficient schemes based on error correction, as it makes explicit two-way classical communication. An...

We consider quantum metrology in noisy environments, where the effect of noise and decoherence limits achievable gain precision by entanglement. show that using tools from error correction this limitation can be overcome. This is demonstrated two scenarios, including a many-body Hamiltonian with single-qubit dephasing or depolarizing single-body transversal noise. In both cases, we Heisenberg scaling, hence quadratic improvement over classical case, retained. Moreover, for case frequency...

Large-scale quantum effects have always played an important role in the foundations of theory. With recent experimental progress and aspiration for enhanced applications, interest macroscopic has been reinforced. In this review, measures aiming to quantify various aspects quantumness are critically analyzed discussed. Recent results on difficulties prospects create, maintain, detect states surveyed. The foundational questions as well practical applications is outlined. Finally, past ongoing...

We investigate the lifetime of macroscopic entanglement under influence decoherence. For Greenberger-Horne-Zeilinger--type superposition states, we find that decreases with size system (i.e., number independent degrees freedom), and effective subsystems remain entangled time. a class other states (e.g., cluster states), however, show is system.

Graph states form a rich class of entangled that exhibit important aspects multi-partite entanglement. At the same time, they can be described by number parameters grows only moderately with system size. They have variety applications in quantum information theory, most prominently as algorithmic resources context one-way computer, but also other fields such error correction and communication, well study foundational issues non-locality decoherence. In this review, we give tutorial...

We give a complete, hierarchic classification for arbitrary multi-qubit mixed states based on the separability properties of certain partitions. introduce family N-qubit to which any state can be depolarized. This viewed as generalization Werner systems. fully classify those with respect their and distillability properties. provides sufficient conditions nonseparability states.

We present a family of 3-qubit states to which any arbitrary state can be depolarized. fully classify those with respect their separability and distillability properties. This provides sufficient condition for nonseparability states. generalize our results $N$-particle

We propose an experimental realization of discrete quantum walks using neutral atoms trapped in optical lattices. The walk is taking place position space and implementation with present-day technology---even existing setups---seems feasible. analyze the influence possible imperfections experiment investigate transition from a to classical random for increasing errors decoherence.

We give a review on entanglement purification for bipartite and multipartite quantum states, with the main focus theoretical work carried out by our group in last couple of years. discuss context communication, where we emphasize its close relation to error correction. Various protocols are discussed, their performance under idealized realistic conditions is studied. Several applications communication computation presented, which highlights fact that fundamental tool information processing.

We study when a physical operation can produce entanglement between two systems initially disentangled. The formalism we develop allows us to show that one perform certain nonlocal operations with unit probability by performing local measurement on states are weakly entangled.

We investigate which entanglement resources allow universal measurement-based quantum computation via single-qubit operations. find that any feature exhibited by the 2D cluster state must also be present in other resource. obtain a powerful criterion to assess universality of graph states introducing an measure necessarily grows unboundedly with system size for all resource states. Furthermore, we prove associated lattices such as hexagonal and triangular lattice are universal, first example...

We study the distillability of a certain class bipartite density operators which can be obtained via depolarization starting from an arbitrary one. Our results suggest that non-positivity partial transpose operator is not sufficient condition for distillability, when dimension both subsystems higher than two.

We introduce a class of multiparticle entanglement purification protocols that allow us to distill large entangled states. These include cluster states, Greenberger-Horne-Zeilinger and various error correction codes all which belong the two-colorable graph analyze these schemes under realistic conditions observe they are scalable; i.e., threshold value for imperfect local operations does not depend on number parties many When compared based bipartite purification, protocol is more efficient...

We investigate entanglement properties of multipartite states under the influence decoherence. show that lifetime (distillable) for GHZ-type superposition decreases with size system, while a class other -namely all graph constant degree- is independent system size. these results are largely specific decoherence model and in particular valid models which deal individual couplings particles to environments, described by some quantum optical master equation Lindblad form. For GHZ states, we...

We propose an experimentally accessible scheme to determine the lower bounds on quantum Fisher information (QFI), which ascertains multipartite entanglement or usefulness for metrology. The is based comparing measurement statistics of a state before and after small unitary rotation. argue that, in general, limited resolution collective observables prevents detection large QFI. This can be overcome by performing additional operation prior measurement. illustrate power this protocol...

We investigate the notion of 'macroscopicity' in case quantum spin systems and provide two main results. Firstly, we motivate Fisher information as a measure macroscopicity states. Secondly, make comparison with existing literature on this topic. report hierarchy among measures conclude that one should carefully distinguish between 'macroscopic states' superpositions', which is strict subclass former.

We establish general limits on how precise a parameter, e.g. frequency or the strength of magnetic field, can be estimated with aid full and fast quantum control. consider uncorrelated noisy evolutions N qubits show that control allows to fully restore Heisenberg scaling (~1/N^2) for all rank-one Pauli noise except dephasing. For other types asymptotic enhancement is unavoidably limited constant-factor improvement over standard limit (~1/N) even when allowing power The latter holds both in...

Measurement-based quantum computation represents a powerful and flexible framework for information processing, based on the notion of entangled states as computational resources. The most prominent application is one-way computer, with cluster state its universal resource. Here we demonstrate principles measurement-based using deterministically generated states, in system trapped calcium ions. First implement set operations computing. Second family error correction codes show their improved...

We present setups for the practical realization of adding control to unknown subroutines, supplementing existing quantum optical scheme black-box with a counterpart ordering sequences operations. also provide schemes realize either task using trapped ions. These circumventions recent no-go theorems are based on technologies. argue that possibility add operations in practice is common feature many physical systems. Based proposed implementations we discuss apparent contradictions between...