Invertible local transformations of a multipartite system are used to define equivalence classes in the set of entangled states. This classification concerns the entanglement properties of a single copy of the state. Accordingly, we say that two states have the same kind of entanglement if both of them can be obtained from the other by means of local operations and classical communication (LOCC) with nonzero probability. When applied to pure states of a three-qubit system, this approach reveals the existence of two inequivalent kinds of genuine tripartite entanglement, for which the GHZ state and a W state appear as remarkable representatives. In particular, we show that the W state retains maximally bipartite entanglement when any one of the three qubits is traced out. We generalize our results both to the case of higher dimensional subsystems and also to more than three subsystems, for all of which we show that, typically, two randomly chosen pure states cannot be converted into each other by means of LOCC, not even with a small probability of success. 03.65.Bz, 03.65.Ca, 03.67.Hk

We present an exact model of the detection statistics of a probabilistic source of photon pairs from which a fast, simple and precise method to measure the source's brightness and photon channel transmissions is demonstrated. We measure such properties for a source based on spontaneous parametric downconversion in a periodically poled LiNbO 3 crystal producing pairs at 810 and 1550 nm wavelengths. We further validate the model by comparing the predicted and measured values for the g (2) (0) of a heralded single photon source over a wide range of the brightness. Our model is of particular use for monitoring and tuning the brightness on demand as required for various quantum communication applications. We comment on its applicability to sources involving spectral and/or spatial filtering.

Entanglement, its generation, manipulation and fundamental understanding is at the very heart of quantum mechanics. The phrase entanglement was coined by Erwin Schrödinger in 1935 for particles that are described by a common wave function where individual particles are not independent of each other but where their quantum properties are inextricably interwoven 1 . Entanglement properties of two and three particles have been studied extensively and are very well understood. Entanglement of four 2 and five 3 particles was demonstrated experimentally. However, both creation and characterization of entanglement become exceedingly difficult for multi-particle systems. Thus the availability of such multiparticle entangled states together with the full information on these states in form of their 1

We analyze the existence of activable bound entangled states in multi-particle systems. We first give a series of examples which illustrate some different ways in which bound entangled states can be activated by letting some of the parties to share maximally entangled states. Then, we derive necessary conditions for a state to be distillable as well as to be activable. These conditions turn out to be also sufficient for a certain family of multi-qubit states. We use these results to explicitely to construct states displaying novel properties related to bound entanglement and its activation. 03.67.-a, 03.65.Bz, 03.65.Ca, 03.67.Hk

Quantum computation offers a promising new kind of information processing, where the non-classical features of quantum mechanics can be harnessed and exploited. A number of models of quantum computation exist, including the now well-studied quantum circuit model. Although these models have been shown to be formally equivalent, their underlying elementary concepts and the requirements for their practical realization can differ significantly. The new paradigm of measurement-based quantum computation, where the processing of quantum information takes place by rounds of simple measurements on qubits prepared in a highly entangled state, is particularly exciting in this regard. In this article we discuss a number of recent developments in measurement-based quantum computation in both fundamental and practical issues, in particular regarding the power of quantum computation, the protection against noise (fault tolerance) and steps toward experimental realization. Moreover, we highlight a number of surprising connections between this field and other branches of physics and mathematics.

We study the use of entanglement purification for quantum communication over long distances. For distances much longer than the coherence length of a corresponding noisy quantum channel, the fidelity of transmission is usually so low that standard purification methods are not applicable. It is however possible to divide the channel into shorter segments that are purified separately and then connected by the method of entanglement swapping. This method can be much more efficient than schemes based on quantum error correction, as it makes explicit use of two-way classical communication. An important question is how the noise, introduced by imperfect local operations (that constitute the protocols of purification and the entanglement swapping), accumulates in such a compound channel, and how it can be kept below a certain noise level. To treat this problem, we first study the applicability and the efficiency of entanglement purification protocols in the situation of imperfect local operations. We then present a scheme that allows entanglement purification over arbitrary long channels and tolerates errors on the per-cent level. It requires a polynomial overhead in time, and an overhead in local resources that grows only logarithmically with the length of the channel.Comment: 19 pages, 16 figure

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We study the distillability of a certain class of bipartite density operators which can be obtained via depolarization starting from an arbitrary one. Our results suggest that non-positivity of the partial transpose of a density operator is not a sufficient condition for distillability, when the dimension of both subsystems is higher than two.Comment: 8 pages, 1 figur