A fundamental resource in any communication and computation task is the amount of information that can be transmitted and processed. The classical information encoded in a set of states is limited by the number of distinguishable states or classical dimension d(c) of the set. The sets used in quantum communication and information processing contain states that are neither identical nor distinguishable, and the quantum dimension d(q) of the set is the dimension of the Hilbert space spanned by these states. An important challenge is to assess the (classical or quantum) dimension of a set of states in a device-independent way, that is, without referring to the internal working of the device generating the states. Here we experimentally test dimension witnesses designed to efficiently determine the minimum dimension of sets of (three or four) photonic states from the correlations originated from measurements on them, and distinguish between classical and quantum sets of states.

A simple geometrical criterion gives experimentally friendly sufficient conditions for entanglement. Its generalization gives a necessary and sufficient condition. It is linked with a family of entanglement identifiers, which is strictly richer than the family of entanglement witnesses.

The separability problem is formulated in terms of a characterization of a single entanglement witness. More specifically, we show that any (in general multipartite) state rho is separable if and only if a specially constructed entanglement witness W-rho is weakly optimal, i.e., its expectation value vanishes on at least one product vector. Interestingly, the witness can always be chosen to be decomposable. Our result changes the conceptual aspect of the separability problem and raises some questions about the properties of positive maps.

We show that the state-independent violation of inequalities for noncontextual hidden variable theories introduced in [Phys. Rev. Lett. 101, 210401 (2008)] is universal, i.e., occurs for any quantum mechanical system in which noncontextuality is meaningful. We describe a method to obtain state-independent violations for any system of dimension d >= 3. This universality proves that, according to quantum mechanics, there are no "classical'' states.

Contextuality and nonlocality are two fundamental properties of nature. Hardy's proof is considered the simplest proof of nonlocality and can also be seen as a particular violation of the simplest Bell inequality. A fundamental question is: Which is the simplest proof of contextuality? We show that there is a Hardy-like proof of contextuality that can also be seen as a particular violation of the simplest noncontextuality inequality. Interestingly, this new proof connects this inequality with the proof of the Kochen-Specker theorem, providing the missing link between these two fundamental results, and can be extended to an arbitrary odd number n of settings, an extension that can be seen as a particular violation of the n-cycle inequality.

Stockholm University, Faculty of Science, Department of Physics.

Badziag, Piotr

Stockholm University, Faculty of Science, Department of Physics.

Bourennane, Mohamed

Stockholm University, Faculty of Science, Department of Physics.

Cabello, Adán

Stockholm University, Faculty of Science, Department of Physics. Universidad de Sevilla, Spain.

Bell inequalities for the simplest exclusivity graph2013In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 87, no 1, article id 012128Article in journal (Refereed)

Abstract [en]

Which is the simplest logical structure for which there is quantum nonlocality? We show that there are only three bipartite Bell inequalities with quantum violation associated with the simplest graph of relationships of exclusivitywith a quantum-classical gap. These are the most elementary logical Bell inequalities. We showthat the quantum violation of some well-known Bell inequalities is related to them. We test the three Bell inequalities with pairs of polarization-entangled photons and report violations in good agreement with the quantum predictions. Unlike other experiments testing noncontextuality inequalities with pentagonal exclusivity, the ones reported here are free of the compatibility loophole. DOI: 10.1103/PhysRevA.87.012128

Extending Bell inequalities to more parties2008In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 77, no 3, p. 32105-Article in journal (Refereed)

Abstract [en]

We describe a method of extending Bell inequalities from n to n+ 1 parties and formulate sufficient conditions for our method to produce tight inequalities from tight inequalities. The method is nontrivial in the sense that the inequalities produced by it, when applied to entangled quantum states may be violated stronger than the original inequalities. In other words, the method is capable of generating inequalities which are more powerful indicators of nonclassical correlations than the original inequalities.

We construct a simple algorithm to generate any Clauser-Horne-Shimony-Holt- (CHSH-) type Bell inequality involving a party with two local binary measurements from two CHSH-type inequalities without this party. The algorithm readily generalizes to situations where the additional observer uses three measurement settings. There, each inequality involving the additional party is constructed from three inequalities with this party excluded. With this generalization at hand, we construct and analyze a class of symmetric inequalities for four observers and three experimental settings per observer.