Accessible information and optimal strategies for real symmetrical quantumsources

We study the problem of optimizing the Shannon mutual information for sourc es of real quantum states, i.e., sources for which there is a basis in whic h all of the states have only real components. We consider in detail the so urces epsilon(M) of M equiprobable quantum bit (qubit) states lying symmetr ically around the great circle of real states on the Bloch sphere and give a variety of explicit optimal strategies. We also consider general real gro up-covariant sources for which the group acts irreducibly on the subset of all real states and prove the existence of a real group-covariant optimal s trategy, extending a theorem of Davies [E. B. Davies, IEEE. Inf. Theory IT- 24, 596 (1978)]. Finally, we propose an optical scheme to implement our opt imal strategies, simple enough to be realized with present technology. [S10 50-2947(99)11005-9].