# Does the quantum Jensen-Shannon divergence appear in any quantum algorithms or texts on quantum computing?

The generalization of probability distributions on density matrices allows to define quantum Jensen–Shannon divergence (QJSD), which uses von Neumann entropy. Does QJSD appear in any quantum algorithms or texts on quantum computing?

• It looks/behaves like a mutual information defined between the classical and quantum parts of an ensemble. If I "tag" each member of a quantum ensemble with a classical bit of information - $\rho = \sum_i p_i |i \rangle \langle i |_C \otimes \rho_{i, Q}$ I can write the joint entropy of this classical-quantum system as $H(C, Q) = H(C) + \sum_i p_i S(\rho_{i, Q})$, the first term being entropy over classical distribution $(p_i, |i\rangle \langle i|)$. Then define $\chi$ as $S(C:Q) \equiv H(C) + S(\rho) - H(C, Q)$ to recover Holevo information. Nov 4 '20 at 20:22
• but its more intuitive to think of $\chi$ as the upper bound to accessible information, which really is just mutual information between an (optimal) measurement and the input state $\rho$. Nov 4 '20 at 20:24