In this paper, we derive a new generalisation of the strong subadditivity entropy to setting general conditional expectations onto arbitrary finite-dimensional von Neumann algebras. The latter inequality, which call approximate tensorization relative entropy, can be expressed as lower bound for sum entropies between given density and its respective projections two intersecting algebras in terms...

Let G be a group. A subset X of G is a set of pairwise noncommuting elements if xy ̸= yx for any two distinct elements x and y in X. If |X| ≥ |Y | for any other set of pairwise non-commuting elements Y in G, then X is said to be a maximal subset of pairwise non-commuting elements. In this paper we determine the cardinality of a maximal subset of pairwise non-commuting elements in any non-abelian...

This article focuses on optimization of polynomials in noncommuting variables, while taking into account sparsity the input data. A converging hierarchy semidefinite relaxations for eigenvalue and trace is provided. a noncommutative analogue results due to Lasserre [SIAM J. Optim. 17(3) (2006), pp. 822--843] Waki et al. 17(1) 218--242]. The Gelfand-Naimark-Segal (GNS) construction applied extra...

The Clifford spectrum is an elegant way to define the joint of several Hermitian operators. Examples as small a triple 2×2 matrices can have that two-dimensional manifold. To date, there are very few noncommuting examples where has been computed. Our main goal generation various three or four we calculate spectrum. In some cases, our results rigorous, perhaps involving assistance from computer ...