Catalytic Conversion Probabilities for Bipartite Pure States

For two given bipartite-entangled pure states, an expression is obtained for the least upper bound of conversion probabilities using catalysis. The attainability of the upper bound can also be decided if that bound is less than one.Comment: 4 pages; comments appreciated; the article is a modified version of this preprint combined with arXiv:0707.044

Cellular automata on regular rooted trees

We study cellular automata on regular rooted trees. This includes the characterization of sofic tree shifts in terms of unrestricted Rabin automata and the decidability of the surjectivity problem for cellular automata between sofic tree shifts

On almost randomizing channels with a short Kraus decomposition

For large d, we study quantum channels on C^d obtained by selecting randomly N independent Kraus operators according to a probability measure mu on the unitary group U(d). When mu is the Haar measure, we show that for N>d/epsilon^2$, such a channel is epsilon-randomizing with high probability, which means that it maps every state within distance epsilon/d (in operator norm) of the maximally mixed state. This slightly improves on a result by Hayden, Leung, Shor and Winter by optimizing their discretization argument. Moreover, for general mu, we obtain a epsilon-randomizing channel provided N > d (\log d)^6/epsilon^2$. For d=2^k (k qubits), this includes Kraus operators obtained by tensoring k random Pauli matrices. The proof uses recent results on empirical processes in Banach spaces.Comment: We added some background on geometry of Banach space

Hastings' additivity counterexample via Dvoretzky's theorem

The goal of this note is to show that Hastings' counterexample to the additivity of minimal output von Neumann entropy can be readily deduced from a sharp version of Dvoretzky's theorem on almost spherical sections of convex bodies.Comment: 12 pages; v.2: added references, Appendix A expanded to make the paper essentially self-containe

How often is a random quantum state k-entangled?

The set of trace preserving, positive maps acting on density matrices of size d forms a convex body. We investigate its nested subsets consisting of k-positive maps, where k=2,...,d. Working with the measure induced by the Hilbert-Schmidt distance we derive asymptotically tight bounds for the volumes of these sets. Our results strongly suggest that the inner set of (k+1)-positive maps forms a small fraction of the outer set of k-positive maps. These results are related to analogous bounds for the relative volume of the sets of k-entangled states describing a bipartite d X d system.Comment: 19 pages in latex, 1 figure include

Decision with Bayesian network in the concurrent faults event

The purpose of this article is to present a new method for process diagnosis with Bayesian network. The interest of this method is to propose a new structure of Bayesian network allowing to diagnose a system with the model-based framework or with the data-driven framework. A particular interest of the proposed approach is the use of continuous nodes in the network in order to evaluate the status of the process. The effectiveness and performances of the method are illustrated on a heating water process corrupted by various faults

Non-additivity of Renyi entropy and Dvoretzky's Theorem

The goal of this note is to show that the analysis of the minimum output p-Renyi entropy of a typical quantum channel essentially amounts to applying Milman's version of Dvoretzky's Theorem about almost Euclidean sections of high-dimensional convex bodies. This conceptually simplifies the (nonconstructive) argument by Hayden-Winter disproving the additivity conjecture for the minimal output p-Renyi entropy (for p>1).Comment: 8 pages, LaTeX; v2: added and updated references, minor editorial changes, no content change

Using Bayesian networks for decision in the simultaneous faults case

The purpose of this article is to present a new method for process diagnosis with Bayesian network. The interest of this method is to propose a new structure of Bayesian network allowing to diagnose a system with the model-based framework or with the data-driven framework. A particular interest of the proposed approach is the use of continuous nodes in the network in order to evaluate the status of the process. The effectiveness and performances of the method are illustrated on a heating water process corrupted by various faults

Fracture properties characterization of nuclear fuel using micro-cantilever bending

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