Symmetric distinguishability as a quantum resource

We develop a resource theory of symmetric distinguishability, the fundamental objects which are elementary quantum information sources, i.e., sources that emit one two possible states with given prior probabilities. Such source can be represented by classical-quantum state composite system $XA$, corresponding to an ensemble states, $X$ being classical and $A$ quantum. study for different classes free operations: $(i)$ ${\rm{CPTP}}_A$, consists channels acting only on $A$, $(ii)$ conditional doubly stochastic (CDS) maps $XA$. introduce notion distinguishability prove it is monotone under both these operations. tasks distillation dilution in one-shot asymptotic regimes. regime, optimal rate converting another equal ratio their Chernoff divergences, This imparts new operational interpretation divergence. also obtain interesting interpretations Thompson metric, context distinguishability.