Suppose you are given an n-qubit quantum channel defined

Question

Suppose you are given an n-qubit quantum channel defined as ε(ρ) = _iΣ Π X_i ρ X_i^t , where X_i denotes an n-fold tensor product of Pauli matrices and {P_i} is a probability distribution. The Holevo-Schumacher-Westmoreland capacity of the channel is defined by χ(ε) = _{{qj, pj}}max [S (_jΣ q_jp_j) - _jΣ q_j S (p_j)], where S denotes the von Neumann entropy of a density matrix. Is it known how to calculate this number as a function of p_i and n?