The Pauli channel acting on 2×2 matrices is generalized to an n-level quantum system. When the full matrix algebra Mn is decomposed into pairwise complementary subalgebras, then trace-preserving linear mappings Mn → Mn are constructed such that the restriction to the subalgebras are depolarizing channels. The result is the necessary and sufficient condition of complete positivity. The main exam...

This paper focuses on certain finite dimensional point derivations for the non-selfadjoint operator algebras corresponding to directed graphs. We begin by analyzing the derivations corresponding to full matrix representations of the tensor algebra of a directed graph. We determine when such a derivation is inner, and describe situations that give rise to non-inner derivations. We also analyze t...

We consider left-invariant control affine systems on the matrix Lie group SO (2, 1)0. A classification, under state space equivalence, of all such full-rank control systems is obtained. First, we identify certain subsets on which the group of Lie algebra automorphisms act transitively. We then systematically identify equivalence class representatives (for single-input, two-input and three-input...

I provide a full characterization of the set of absolutely expedient learning rules introduced in Börgers, Morales, and Sarin (2004) [“Expedient and monotone learning rules,” Econometrica, 72, 383–405]. The expected change in the expected payoff can be written as a quadratic form on the vector of relative expected payoffs of the strategies. This permits use of standard linear algebra arguments ...