Information storing yields a point-asymmetry of state space in general probabilistic theories

Understand

It is known that the high-dimensional quantum state space is notoriously complicated in contrast with the beautiful Bloch ball of the qubit.

• We examined the mechanism behind this fact in the frame work of general probabilistic theory (GPT), and found rather general quantitative relations between the geometry of the state space and its information storing capability.
• The main result is the information-asymmetry identity, which (up to the constant term) equates the {\it Minkowski measure of asymmetry} with the {\it information storability} which, in addition to its own operational meaning, serves as an upper bound to common information measures such as semi-classical capacity.
• As a consequence, the asymmetry measure is lower-bounded by information storing capability of the state space, so the increase in the latter enhances the former.