On quantum information

We investigate the following generalisation of the entropy of quantum measurement. Let H be an infinite-dimensional separable Hilbert space with a 'density' operator ρ, tr ρ = 1. Let I(P) ∈ R be defined for any parti-Q are physically independent). Assuming some continuity properties we give a general form of generalised information I, Theorem 1, formula (1). Throughout the paper we shall use the following notations. H is an infinite dimensional seperable Hilbert space. By ρ we denote a fixed positive trace-class operator with tr ρ = 1. It is convenient to identify ρ with the functional B(H) ∋ A → tr ρA i.e. write ρ(A) for tr ρA. We will also consider