Accessible information and optimal strategies for real symmetrical quantum sources

Abstract

We study the problem of optimizing the Shannon mutual information for sources of real quantum states i.e. sources for which there is a basis in which all the states have only real components. We consider in detail the sources EM of M equiprobable qubit states lying symmetrically around the great circle of real states on the Bloch sphere and give a variety of explicit optimal strategies. We also consider general real group-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 strategy, extending a theorem of Davies (E. B. Davies, IEEE. Inf. Theory IT-24, 596 (1978)). Finally we propose an optical scheme to implement our optimal strategies, simple enough to be realized with present technology.

Highly symmetric POVMs and their informational power

“…The problem of maximization of I (E, Π) consists of two dual aspects [7,63,65]: maximization over all possible measurements, providing the ensemble E is given, see, e.g., [39,60,101,114], and (less explored) maximization over all ensembles, when the POVM Π is fixed [6,90]. In the former case, the maximum is called accessible information.…”

Minimum-error discrimination between symmetric mixed quantum states

“…The theory of quantum information and communication is a well-developed field of research [1][2][3]. It concerns the transmission of information using quantum states and channels.…”

Maximum Confidence Quantum Measurements

“…Unambiguous discrimination can be extended to higher dimensions [13], but it is only applicable to sets of linearly independent states [14]. Other figures of merit include the mutual information shared by the transmitting and receiving parties [15,16] and the fidelity between the state received and one transmitted on the basis of the measurement result [17,18]. Examples of optimal minimum error, mutual information and unambiguous discrimination measurement strategies have been demonstrated in experiments on optical polarisation [19,20,21,22,23,24].…”