We report measurements of two-photon interference using a cw-pumped type-II spontaneous parametric down-conversion source based on a multimode perodically poled potassium titanyl phosphate (PPKTP) waveguide. We have used the recently demonstrated technique of controlling the spatial characteristics of the down-conversion process via intermodal dispersion to generate photon pairs in fundamental transverse modes, thus ensuring their spatial indistinguishability. Good overlap of photon modes within the pairs has been verified using the Hong-Ou-Mandel interferometer and the preparation of polarization entanglement in the Shih-Alley configuration, yielding visibilities consistently above 90%.

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Quantum physics has remarkable distinguishing characteristics. For example, it gives only probabilistic predictions (non-determinism) and does not allow copying of unknown states (no-cloning). Quantum correlations may be stronger than any classical ones, but information cannot be transmitted faster than light (no-signalling). However, these features do not uniquely define quantum physics. A broad class of theories exist that share such traits and allow even stronger (than quantum) correlations. Here we introduce the principle of 'information causality' and show that it is respected by classical and quantum physics but violated by all no-signalling theories with stronger than (the strongest) quantum correlations. The principle relates to the amount of information that an observer (Bob) can gain about a data set belonging to another observer (Alice), the contents of which are completely unknown to him. Using all his local resources (which may be correlated with her resources) and allowing classical communication from her, the amount of information that Bob can recover is bounded by the information volume (m) of the communication. Namely, if Alice communicates m bits to Bob, the total information obtainable by Bob cannot be greater than m. For m = 0, information causality reduces to the standard no-signalling principle. However, no-signalling theories with maximally strong correlations would allow Bob access to all the data in any m-bit subset of the whole data set held by Alice. If only one bit is sent by Alice (m = 1), this is tantamount to Bob's being able to access the value of any single bit of Alice's data (but not all of them). Information causality may therefore help to distinguish physical theories from non-physical ones. We suggest that information causality-a generalization of the no-signalling condition-might be one of the foundational properties of nature.

Tests of local realism versus quantum mechanics based on Bell's inequality employ two entangled qubits. We investigate the general case of two entangled quantum systems defined in N-dimensional Hilbert spaces, or " quNits." Via a numerical linear optimization method we show that violations of local realism are stronger for two maximally entangled quNits ( 3

We derive a single general Bell inequality which is a necessary and sufficient condition for the correlation function for N particles to be describable in a local and realistic picture, for the case in which measurements on each particle can be chosen between two arbitrary dichotomic observables. We also derive a necessary and sufficient condition for an arbitrary N-qubit mixed state to violate this inequality. This condition is a generalization and reformulation of the Horodeccy family condition for two qubits.PACS numbers: 03.65. Ud, 42.50.Ar Local realism imposes constraints on statistical correlations of measurements on multiparticle systems. They are in the form of Bell-type inequalities [1,2,3,4,5,6,7,8]. In a realistic theory the measurement results are determined by "hidden" properties the particles carry prior to and independent of observation. In a local realistic theory the results obtained at one location are independent of any measurements, or actions, performed at space-like separation. Quantum mechanics predicts violation of these constraints. This is known as Bell's theorem [1] .However the problems a) what are the most general constraints on correlations imposed by local realism, and b) which quantum states violate these constraints, are still open. The latter has been solved in general only in the case of two particles in pure states [9,10] and for two-qubit mixed states [11]. Only recently bounds for local realistic description of a higher-dimensional system have been found in some simple cases [12,13,14].Here the answer to the two long-standing questions (a) and (b) is presented for the case of a standard Bell type experiment on N qubits. By a standard Bell experiment we mean, one in which each local observer is given a choice between two dichotomic observables. We first derive a single general Bell inequality that summarizes all possible local realistic constraints on the correlation functions for a N-particle system. From this inequality one obtains as corollaries the Clauser-Horne-ShimonyHolt (CHSH) inequality [2] for two-particle systems and the Mermin-Ardehali-Belinskii-Klyshko (MABK) inequalities for N particles [4,5,6]. We show that the correlation functions in a standard Bell experiment can be described by a local realistic model if and only if the general Bell inequality is satisfied. Therefore the general Bell inequality is a sufficient and necessary condition for correlation functions, in such an experiment, to be describable within a local realistic model. We also find a necessary and sufficient condition for correlation functions for N qubits in an arbitrary (mixed) quantum state to violate the general Bell inequality in direct measurements. This condition is generalization and reformulation of the one given by the Horodeccy family [11] for two qubits.These results are not only of importance from the fundamental point of view, but also as a research towards identifying ultimate resources for quantum information processing. Recently it was shown [15], that there is a direct lin...

Most working scientists hold fast to the concept of 'realism'--a viewpoint according to which an external reality exists independent of observation. But quantum physics has shattered some of our cornerstone beliefs. According to Bell's theorem, any theory that is based on the joint assumption of realism and locality (meaning that local events cannot be affected by actions in space-like separated regions) is at variance with certain quantum predictions. Experiments with entangled pairs of particles have amply confirmed these quantum predictions, thus rendering local realistic theories untenable. Maintaining realism as a fundamental concept would therefore necessitate the introduction of 'spooky' actions that defy locality. Here we show by both theory and experiment that a broad and rather reasonable class of such non-local realistic theories is incompatible with experimentally observable quantum correlations. In the experiment, we measure previously untested correlations between two entangled photons, and show that these correlations violate an inequality proposed by Leggett for non-local realistic theories. Our result suggests that giving up the concept of locality is not sufficient to be consistent with quantum experiments, unless certain intuitive features of realism are abandoned.

We prove that for every Bell's inequality and for a broad class of protocols, there always exists a multi-party communication complexity problem, for which the protocol assisted by states which violate the inequality is more efficient than any classical protocol. Moreover, for that advantage Bell's inequality violation is a necessary and sufficient criterion. Thus, violation of Bell's inequalities has a significance beyond that of a non-optimal-witness of non-separability.PACS numbers: 3.65 Bz, 42.50 Ar Entanglement is the essential feature, which distinguishes the quantum from the classical [1]. On one hand, entangled states violate Bell inequalities, and thus rule out local realistic explanation of quantum mechanics [2]. On the other hand, they enable certain communication and computation tasks to have an efficiency not achievable by the laws of classical physics [3].Intuition suggests that these two aspects, the fundamental one, and the applicational one, could be intimately linked. Specifically, one could expect, that only the quantum communication protocol which makes use of an entangled state which violates some Bell's inequality can have efficiency larger than any classical protocol. Otherwise one might expect that the efficiency of the protocol could be explainable by a local realistic model, and thus achievable in classical physics. This intuitive reasoning is supported by the result of Ref. [4] where it was shown that violation of Bell's inequality is a condition for the security of quantum key distribution protocols. Here we give another result which supports the intuitive reasoning: the violation of Bell's inequalities is a necessary and sufficient criterion for the quantum communication complexity protocol to be more efficient than any classical one.We shall discuss the following version of the communication complexity problems (such problems were introduced in Ref. [5]). Some input data are distributed over n separated parties. Every party knows the local data, but not the data of the others. The party i obtains an input string z i . The goal is for each of them to determine the value of some function f (z 1 , ..., z n ), while exchanging a restricted amount of information. This restriction, in general, enables the parties to compute the function only with an error. Then the goal for all parties is to compute the function correctly with as high a probability as possible. An execution is considered successful, if the values determined by all parties are correct. Before they start the protocol, the parties are allowed to share (classically) correlated random strings, or any other data, which might improve the success of the protocols. They are allowed to process their data locally in whatever way.The general question is whether and to what extent entanglement can be of advantage for solving such problems. It was shown that entanglement can improve the probability of success in communication complexity protocols beyond the limits which are classically possible [6,7,8,9,10]. Specifically, Buhrman, C...

Multiport beam splitters are shown to be applicable in feasible optical realizations of higher-dimensional EPR correlations, and of tests of local realism involving measurements of nondichotomic variables. These multiports permit optical realizations of any unitary operator in Hilbert spaces of arbitrary finite dimension. Thus it is shown that one is by no means constrained to entangled spin systems, and to Stern-Gerlach apparatuses. In the analysis the concept of generalized Bell numbers is employed, which is more suitable than the standard set of spin eigenvalues. The results presented here move the discussion on entangled higher-than-1 2 spin systems from the realm of gedanken experiments to real experiments. ͓S1050-2947͑97͒07802-5͔