| （英） |
The qubit state space is a beautiful sphere, but the high-dimensional one is increasingly asymmetric in proportion to the dimension. Similar observations also apply to classical systems. Here, we investigate this phenomenon in the light of general probabilistic theory, and conclude “the asymmetry is caused by the increase of contained information.” To start, we introduce total detection probability $N$ of a set of states, and show it nicely quantifies asymmetry of the state space. Next, information theoretic meaning of $N$ is investigated. Almost by definition, $N$ is not less than the number of distinguishable states, and by application of $N$ to the set of the receiver's states of a channel, we obtain the (maximized) product of the number of messages and the success probability of decode. In quantum mechanical systems, $N$ is written using Renner's max-relative entropy, and an upper bound to the channel capacity by $N$ is compared with Holevo's bound. |