Operator traces

Nazakat Ullah

It is shown that angular momentum operator identities between ladder operators and rotation operators can be used to study the trace problem. Using an explicit representation of the rotation matrices, the author evaluates the trace of the operator ${J}_{\ensuremath{-}}^{k}{J}_{+}^{k}$ in closed form. The identities are found to be particularly useful in providing checks for the sum of the traces.

A E Rastegin

In the present paper, the trace distance is exposed within the quantum operations formalism. The definition of the trace distance in terms of a maximum over all quantum operations is given. It is shown that for any pair of different states there are an uncountably infinite number of maximizing quantum operations. Conversely, for any operation of the described type, there are an uncountably infinite number of those pairs of states that the maximum is reached by the operation. The behaviour of the trace distance under considered operations is studied. Relations and distinctions between the trace distance and the sine distance are discussed.

Norman K. Glendenning

Josep Planelles

Formulae are derived for traces of symmetry-adapted reduced density operators in a finite-dimensional, antisymmetric and spin-adapted space. The traces are expressed in terms of traces of products of the orbital occupation number operators.