Strong bound between trace distance and Hilbert-Schmidt distance for low-rank states
Strong bound between trace distance and Hilbert-Schmidt distance for low-rank states
The trace distance between two quantum states, $\ensuremath{\rho}$ and $\ensuremath{\sigma}$, is an operationally meaningful quantity in quantum information theory. However, in general it is difficult to compute, involving the diagonalization of $\ensuremath{\rho}\ensuremath{-}\ensuremath{\sigma}$. In contrast, the Hilbert-Schmidt distance can be computed without diagonalization, although it is less operationally significant. Here, we …