Quantum teleportation-the transmission and reconstruction over arbitrary distances of the state of a quantum system-is demonstrated experimentally. During teleportation, an initial photon which carries the polarization that is to be transferred and one of a pair of entangled photons are subjected to a measurement such that the second photon of the entangled pair acquires the polarization of the initial photon. This latter photon can be arbitrarily far away from the initial one. Quantum teleportation will be a critical ingredient for quantum computation networks.The dream of teleportation is to be able to travel by simply reappearing at some distant location. An object to be teleported can be fully characterized by its properties, which in classical physics can be determined by measurement. To make a copy of that object at a distant location one does not need the original parts and piecesall that is needed is to send the scanned information so that it can be used for reconstructing the object. But how precisely can this be a true copy of the original? What if these parts and pieces are electrons, atoms and molecules? What happens to their individual quantum properties, which according to the Heisenberg's uncertainty principle cannot be measured with arbitrary precision?Bennett et al. 1 have suggested that it is possible to transfer the quantum state of a particle onto another particle-the process of quantum teleportation-provided one does not get any information about the state in the course of this transformation. This requirement can be fulfilled by using entanglement, the essential feature of quantum mechanics 2 . It describes correlations between quantum systems much stronger than any classical correlation could be.The possibility of transferring quantum information is one of the cornerstones of the emerging field of quantum communication and quantum computation 3 . Although there is fast progress in the theoretical description of quantum information processing, the difficulties in handling quantum systems have not allowed an equal advance in the experimental realization of the new proposals. Besides the promising developments of quantum cryptography 4 (the first provably secure way to send secret messages), we have only recently succeeded in demonstrating the possibility of quantum dense coding 5 , a way to quantum mechanically enhance data compression. The main reason for this slow experimental progress is that, although there exist methods to produce pairs of entangled photons 6 , entanglement has been demonstrated for atoms only very recently 7 and it has not been possible thus far to produce entangled states of more than two quanta.Here we report the first experimental verification of quantum teleportation. By producing pairs of entangled photons by the process of parametric down-conversion and using two-photon interferometry for analysing entanglement, we could transfer a quantum property (in our case the polarization state) from one photon to another. The methods developed for this experiment will be of...

We show that a set of gates that consists of all one-bit quantum gates (U(2)) and the two-bit exclusive-or gate (that maps Boolean values $(x,y)$ to $(x,x \oplus y)$) is universal in the sense that all unitary operations on arbitrarily many bits $n$ (U($2^n$)) can be expressed as compositions of these gates. We investigate the number of the above gates required to implement other gates, such as generalized Deutsch-Toffoli gates, that apply a specific U(2) transformation to one input bit if and only if the logical AND of all remaining input bits is satisfied. These gates play a central role in many proposed constructions of quantum computational networks. We derive upper and lower bounds on the exact number of elementary gates required to build up a variety of two-and three-bit quantum gates, the asymptotic number required for $n$-bit Deutsch-Toffoli gates, and make some observations about the number required for arbitrary $n$-bit unitary operations.Comment: 31 pages, plain latex, no separate figures, submitted to Phys. Rev. A. Related information on http://vesta.physics.ucla.edu:7777

We report on a high-intensity source of polarization-entangled photon pairs with high momentum definition. Type-II noncollinear phase matching in parametric down conversion produces true entanglement: No part of the wave function must be discarded, in contrast to previous schemes. With two-photon fringe visibilities in excess of 97%, we demonstrated a violation of Bell s inequality by over 100 standard deviations in less than 5 min. The new source allowed ready preparation of all four of the EPR-Bell states.

We observe strong violation of Bell's inequality in an Einstein, Podolsky and Rosen type experiment with independent observers. Our experiment definitely implements the ideas behind the well known work by Aspect et al. We for the first time fully enforce the condition of locality, a central assumption in the derivation of Bell's theorem. The necessary space-like separation of the observations is achieved by sufficient physical distance between the measurement stations, by ultra-fast and random setting of the analyzers, and by completely independent data registration.The stronger-than-classical correlations between entangled quantum systems, as first discovered by Einstein, Podolsky and Rosen (EPR) in 1935 [1], have ever since occupied a central position in the discussions of the foundations of quantum mechanics. After Bell's discovery [2] that EPR's implication to explain the correlations using hidden parameters would contradict the predictions of quantum physics, a number of experimental tests have been performed [3][4][5]. All recent experiments confirm the predictions of quantum mechanics. Yet, from a strictly logical point of view, they don't succeed in ruling out a local realistic explanation completely, because of two essential loopholes. The first loophole builds on the fact that all experiments so far detect only a small subset of all pairs created [6]. It is therefore necessary to assume that the pairs registered are a fair sample of all pairs emitted. In principle this could be wrong and once the apparatus is sufficiently refined the experimental observations will contradict quantum mechanics. Yet we agree with John Bell that ". . . it is hard for me to believe that quantum mechanics works so nicely for inefficient practical set-ups and is yet going to fail badly when sufficient refinements are made. Of more importance, in my opinion, is the complete absence of the vital time factor in existing experiments. The analyzers are not rotated during the flight of the particles." [7] This is the second loophole which so far has only been encountered in an experiment by Aspect et al. [4] where the directions of polarization analysis were switched after the photons left the source. Aspect et al., however, used periodic sinusoidal switching, which is predictable into the future. Thus communication slower than the speed of light, or even at the speed of light [8] could in principle explain the results obtained. Therefore this second loophole is still open.The assumption of locality in the derivation of Bell's theorem requires that the measurement processes of the two observers are space-like separated (Fig. 1). This means that it is necessary to freely choose a direction for analysis, to set the analyzer and finally to register the particle such that it is impossible for any information about these processes to travel via any (possibly unknown) channel to the other observer before he, in turn, finishes his measurement [9]. Selection of an analyzer direction has to be completely unpredictable which necessitates a...

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