Efficient estimation of the quantum Chernoff bound

The quantum Chernoff bound is a famous result about discriminating two different states in a setting where large numbers of copies are available, which gives the analytic asymptotic rate at which the minimal error probability decays to zero exponentially. It is however a challenging task to calculate the quantum Chernoff bound exactly in practical scenarios. In this paper, from the viewpoint of differential geometry, we demonstrate a remarkable link between the quantum Chernoff bound and Wigner-Yanase skew information. As a result, the quantum Chernoff bound can be estimated efficiently by virtue of the skew information. We present several examples to illustrate the efficiency of estimation about the quantum Chernoff bound via Wigner-Yanase skew information.