We consider two quantum cryptographic schemes relying on encoding the key into qudits, i.e., quantum states in a d-dimensional Hilbert space. The first cryptosystem uses two mutually unbiased bases (thereby extending the BB84 scheme), while the second exploits all d 1 1 available such bases (extending the six-state protocol for qubits). We derive the information gained by a potential eavesdropper applying a cloning-based individual attack, along with an upper bound on the error rate that ensures unconditional security against coherent attacks.

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We present the experimental detection of genuine multipartite entanglement using entanglement witness operators. To this aim we introduce a canonical way of constructing and decomposing witness operators so that they can be directly implemented with present technology. We apply this method to three-and four-qubit entangled states of polarized photons, giving experimental evidence that the considered states contain true multipartite entanglement. [3,4] as it gives a simple sufficient and necessary condition for entanglement. Yet, the situation is much more complicated for higher dimensional and multipartite systems, where simple necessary and sufficient conditions are not known [5].In the analysis of multipartite systems, it is important to distinguish between genuine multipartite entanglement and biseparable (triseparable, etc.) entanglement. Genuine multipartite entangled pure states cannot be created without participation of all parties. Conversely, for pure biseparable states of n parties a group of m < n parties can be found which are entangled among each other, but not with any member of the other group of n − m parties [6]. Distinction and detection of genuine multipartite entanglement poses an important challenge in quantum information science. Bell inequalities are not suited to this aim in general. Multiseparable and biseparable states violate known Bell inequalities less than npartite Greenberger-Horne-Zeilinger (GHZ) states. However, for n > 3 there exist even pure n-partite entangled states with a lower violation than biseparable states [7]. Only recently, significant progress in classifying multipartite entanglement has been achieved using entanglement witnesses [4,8]. These observables can always be used to detect various forms of multipartite entanglement, when some a priori knowledge about the states under investigation is provided [9]; they are in this sense more powerful than Bell inequalities.A witness of genuine n-partite entanglement is an observable which has a positive expectation value on states with n − 1 partite entanglement and a negative expectation value on some n-partite entangled states. The latter states and their entanglement, respectively, are said to be detected by W. Witnesses provide sufficient criteria for entanglement and for distinguishing the various classes of genuine multipartite entangled states.The goal of this Letter is twofold. First, we introduce a general scheme for the construction of multipartite witness operators and their decomposition into locally measurable observables. In this way, we demonstrate how witness operators can be implemented experimentally in a straightforward way by using local projective measurements, even for multipartite systems [10]. Then, we apply this scheme to certain states and perform the experimental detection of their multipartite entanglement, which could not be revealed by known Bell inequalities. In particular, we use this method for the characterization of the three-qubit W state [11], and the four-qubit state |Ψ (4) [12]. A wit...

We present an experimental state-independent violation of an inequality for noncontextual theories on single particles. We show that 20 different single-photon states violate an inequality which involves correlations between results of sequential compatible measurements by at least 419 standard deviations. Our results show that, for any physical system, even for a single system, and independent of its state, there is a universal set of tests whose results do not admit a noncontextual interpretation. This sheds new light on the role of quantum mechanics in quantum information processing.