  The accessible information acc(E) of an ensemble E is the maximum mutual
information between a random variable encoded into quantum states, and the
probabilistic outcome of a quantum measurement of the encoding. Accessible
information is extremely difficult to characterize analytically; even bounds on
it are hard to place. The celebrated Holevo bound states that accessible
information cannot exceed chi(E), the quantum mutual information between the
random variable and its encoding. However, for general ensembles, the gap
between the acc(E) and chi(E) may be arbitrarily large.
  We consider the special case of a binary random variable, which often serves
as a stepping stone towards other results in information theory and
communication complexity. We give explicit lower bounds on the the accessible
information acc(E) of an ensemble E = {(p, rho_0), (1-p, rho_1)}, with 0 <= p
<= 1, as functions of p and chi(E). The bounds are incomparable in the sense
that they surpass each other in different parameter regimes.
  Our bounds arise by measuring the ensemble according to a complete orthogonal
measurement that preserves the fidelity of the states rho_0,rho_1. As an
intermediate step, therefore, we give new relations between the two quantities
acc(E), chi(E) and the fidelity B(rho_0,rho_1).

Quantum Physics