Quantum information processing is the study of methods and efficiency in storage, manipulation and conversion of information represented by quantum states. Many quantum information theoretic concepts are closely related to geometry. For instance, trace distance and fidelity, which come out of the study of distinguishability between quantum states, are closely linked with Bures and Fubini-Study ...

The anchored hyperplane location problem is to locate a hyperplane passing through some given points P ⊆ IR and minimizing either the sum of weighted distances (median problem), or the maximum weighted distance (center problem) to some other points Q ⊆ IR. This problem of computational geometry is analyzed by using nonlinear programming techniques. If the distances are measured by a norm, it wi...

In this paper we use a particular type of mutual information norm — the cepstral information norm — for anomaly detection at the router level in the Internet. We combine the cepstral norm with a state space Kalman filter to define two distance metrics to capture anomalous behaviour. These metrics are implemented using a subspace-based model-free paradigm to aid realtime analysis. We infer a top...

In this paper we study the dual codes of a wide family of evaluation codes on norm-trace curves. We explicitly find out their minimum distance and give a lower bound for the number of their minimum-weight codewords. A general geometric approach is performed and applied to study in particular the dual codes of onepoint and two-point codes arising from norm-trace curves through Goppa’s constructi...

We show that 2-norm pseudospectra ofm-by-nmatrices have no more than 2m(4m−1) connected components. Such bounds are pertinent for computing the distance to uncontrollability of a control system, since this distance is the minimum value of a function whose level sets are pseudospectra. We also discuss algorithms for computing this distance, including a trisection variant of Gu’s recent algorithm...

The stability radius of an n×n matrix A (or distance to instability) is a well-known measure of robustness of stability of the linear stable dynamical system ẋ = Ax. Such a distance is commonly measured either in the 2-norm or in the Frobenius norm. Even if the matrix A is real, the distance to instability is most often considered with respect to complex valued matrices (in such case the two no...