Entanglement Detection in the Stabilizer Formalism

We investigate how stabilizer theory can be used for constructing sufficient conditions for entanglement. First, we show how entanglement witnesses can be derived for a given state, provided some stabilizing operators of the state are known. These witnesses require only a small effort for an experimental implementation and are robust against noise. Second, we demonstrate that also nonlinear criteria based on uncertainty relations can be derived from stabilizing operators. These criteria can sometimes improve the witnesses by adding nonlinear correction terms. All our criteria detect states close to Greenberger-Horne-Zeilinger states, cluster and graph states. We show that similar ideas can be used to derive entanglement conditions for states which do not fit the stabilizer formalism, such as the three-qubit W state. We also discuss connections between the witnesses and some Bell inequalities.Comment: 15 pages including 2 figures, revtex4; typos corrected, presentation improved; to appear in PR

The production of Tsallis entropy in the limit of weak chaos and a new indicator of chaoticity

We study the connection between the appearance of a `metastable' behavior of weakly chaotic orbits, characterized by a constant rate of increase of the Tsallis q-entropy (Tsallis 1988), and the solutions of the variational equations of motion for the same orbits. We demonstrate that the variational equations yield transient solutions, lasting for long time intervals, during which the length of deviation vectors of nearby orbits grows in time almost as a power-law. The associated power exponent can be simply related to the entropic exponent for which the q-entropy exhibits a constant rate of increase. This analysis leads to the definition of a new sensitive indicator distinguishing regular from weakly chaotic orbits, that we call `Average Power Law Exponent' (APLE). We compare the APLE with other established indicators of the literature. In particular, we give examples of application of the APLE in a) a thin separatrix layer of the standard map, b) the stickiness region around an island of stability in the same map, and c) the web of resonances of a 4D symplectic map. In all these cases we identify weakly chaotic orbits exhibiting the `metastable' behavior associated with the Tsallis q-entropy.Comment: 19 pages, 12 figures, accepted for publication by Physica

Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System

Peer reviewedPublisher PD

F-formation Detection: Individuating Free-standing Conversational Groups in Images

Detection of groups of interacting people is a very interesting and useful task in many modern technologies, with application fields spanning from video-surveillance to social robotics. In this paper we first furnish a rigorous definition of group considering the background of the social sciences: this allows us to specify many kinds of group, so far neglected in the Computer Vision literature. On top of this taxonomy, we present a detailed state of the art on the group detection algorithms. Then, as a main contribution, we present a brand new method for the automatic detection of groups in still images, which is based on a graph-cuts framework for clustering individuals; in particular we are able to codify in a computational sense the sociological definition of F-formation, that is very useful to encode a group having only proxemic information: position and orientation of people. We call the proposed method Graph-Cuts for F-formation (GCFF). We show how GCFF definitely outperforms all the state of the art methods in terms of different accuracy measures (some of them are brand new), demonstrating also a strong robustness to noise and versatility in recognizing groups of various cardinality.Comment: 32 pages, submitted to PLOS On

Concise Security Bounds for Practical Decoy-State Quantum Key Distribution

Due to its ability to tolerate high channel loss, decoy-state quantum key distribution (QKD) has been one of the main focuses within the QKD community. Notably, several experimental groups have demonstrated that it is secure and feasible under real-world conditions. Crucially, however, the security and feasibility claims made by most of these experiments were obtained under the assumption that the eavesdropper is restricted to particular types of attacks or that the finite-key effects are neglected. Unfortunately, such assumptions are not possible to guarantee in practice. In this work, we provide concise and tight finite-key security bounds for practical decoy-state QKD that are valid against general attacks.Comment: 5+3 pages and 2 figure