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Distribution of entangled states between distant locations is essential for quantum communication over large distances. But owing to unavoidable decoherence in the quantum communication channel, the quality of entangled states generally decreases exponentially with the channel length. Entanglement purification--a way to extract a subset of states of high entanglement and high purity from a large set of less entangled states--is thus needed to overcome decoherence. Besides its important application in quantum communication, entanglement purification also plays a crucial role in error correction for quantum computation, because it can significantly increase the quality of logic operations between different qubits. Here we demonstrate entanglement purification for general mixed states of polarization-entangled photons using only linear optics. Typically, one photon pair of fidelity 92% could be obtained from two pairs, each of fidelity 75%. In our experiments, decoherence is overcome to the extent that the technique would achieve tolerable error rates for quantum repeaters in long-distance quantum communication. Our results also imply that the requirement of high-accuracy logic operations in fault-tolerant quantum computation can be considerably relaxed.

We experimentally demonstrate observation of highly pure four-photon GHZ entanglement produced by parametric down-conversion and a projective measurement. At the same time this also demonstrates teleportation of entanglement with very high purity. Not only does the achieved high visibility enable various novel tests of quantum nonlocality, it also opens the possibility to experimentally investigate various quantum computation and communication schemes with linear optics. Our technique can in principle be used to produce entanglement of arbitrarily high order or, equivalently, teleportation and entanglement swapping over multiple stages.Entanglement is not only the essence of quantum mechanics as suggested by Erwin Schrödinger [1], but is also at the basis of nearly all quantum information protocols such as quantum cryptography, quantum teleportation and quantum computation [2]. While entanglement of two qubits is routine in the laboratory, entanglement of three photons [3] with high quality has only recently been experimentally realized [4] and used to experimentally demonstrate the extreme contradiction between local realism and quantum mechanics [5] in so-called GHZ states. In a parallel development entanglement of the quantum states of three atoms [6] or four qubits in ions [7] has been demonstrated, yet in all these cases the quality of the entangled states still needs to be significantly improved in order to be useful for tests of quantum mechanics or in quantum information schemes.A similar situation is found in the recent teleportation experiments [8][9][10][11]. To verify the nonlocal character of teleportation, two conditions must be satisfied in any experiment. On the one hand, one has to demonstrate that a genuinely unknown state (in the optimal case, a qubit which itself is still entangled to another one) is teleported [12], on the other hand a high experimental visibility is necessary in order to exclude local hidden variable models (LHV) [13][14][15][16]. The so-called entanglement swapping experiment [10] is the only one to date that demonstrates the teleportation of a genuinely unknown state. However, since its observed visibility was lower than 71%, one could in principle still doubt the nonlocal feature of teleportation [13].In this letter we report on an experiment that not only demonstrates the observation of four-photon entanglement but also shows high-fidelity entanglement swapping, thus proving the nonlocal character of quantum teleportation. Both features are not only important for performing novel fundamental experiments to test quantum mechanics or to demonstrate its counter-intuitive features, but also to expand our toolbox for quantum computation and quantum communication.Our technique of observing four-photon GHZ entanglement uses two independently created photon pairs (Fig. 1). Suppose that the two pairs are in the statewhich is a tensor product of two polarization entangled photon pairs. Here |H (|V ) indicates the state of a horizontally (vertically) polarized photon. Principle fo...

We report the first experimental demonstration of a quantum controlled-NOT gate for different photons, which is classically feed-forwardable. In the experiment, we achieved this goal with the use only of linear optics, an entangled ancillary pair of photons and post-selection. The techniques developed in our experiment will be of significant importance for quantum information processing with linear optics. PACS numbers:Polarization-encoded qubits are well suited for information transmission in Quantum Information Processing (QIP) [1]. In recent years, the polarization state of single photons has been used to experimentally demonstrate quantum dense coding [2], quantum teleportation [3] and quantum cryptography [4,5,6]. However, due to the difficulty of achieving quantum logic operations between independent photons, the application of photon states has been limited primarily to the field of quantum communication. More precisely, the two-qubit gates suitable for quantum computation generically require strong interactions between individual photons, implying the need for massive, reversible non-linearities well beyond those presently available for photons, as opposed to other physical systems [7].Remarkably, Knill, Laflamme and Milburn [8] found a way to circumvent this problem and implement efficient quantum computation using only linear optics, photo-detectors and single-photon sources. In effect they showed that measurement induced nonlinearity was sufficient to obtain efficient quantum computation.The logic schemes KLM proposed were not, however, economical in their use of optical components or ancillary photons. Various groups have been working on reducing the complexity of these gates while improving their theoretical efficiency (see e.g. Koashi et al. [9]). In an exciting recent development, Nielsen [10] has shown that efficient linear optical quantum computation is in fact possible without the elaborate teleportation and Z-measurement error correction steps in KLM. This is achieved by creation of linear optical versions of Raussendorf and Briegel's [11] cluster states. Nielsen's method works for any non-trivial linear optical gate which succeeds with finite probability, but which, when it fails, effects a measurement in the computational * Present address: Physikalisches Institut, Universität Heidelberg, D-69120 Heidelberg, Germany † Present address: Imperial College, Blackett Labs, Prince Consort Rd, London SW7 2AZ ‡ also at Institut für Quantenoptik und Quanteninformation, Osterreichische Akademie der Wissenschaften basis.A crucial requirement of both KLM's and Nielsen's constructions is classical feed-forwardability. Specifically, it must be in principle possible to detect when the gate has succeeded by measurement of ancilla photons in some appropriate state. This information can then be fedforward in such a way as to condition future operations on the photon modes.Recently [12,13,14] destructive linear optical gate operations have been realized. As they necessarily destroy the output state, such sche...

Quantum teleportation is central to quantum communication, and plays an important role in a number of quantum computation protocols. Most information-processing applications of quantum teleportation include the subsequent manipulation of the qubit (the teleported photon), so it is highly desirable to have a teleportation procedure resulting in high-quality, freely flying qubits. In our previous teleportation experiment, the teleported qubit had to be detected (and thus destroyed) to verify the success of the procedure. Here we report a teleportation experiment that results in freely propagating individual qubits. The basic idea is to suppress unwanted coincidence detection events by providing the photon to be teleported much less frequently than the auxiliary entangled pair. Therefore, a case of successful teleportation can be identified with high probability without the need actually to detect the teleported photon. The experimental fidelity of our procedure surpasses the theoretical limit required for the implementation of quantum repeaters.