R. Alicki, M. Fannes
We prove continuity of quantum conditional information $S(ρ^{12}| ρ^2)$ with respect to the uniform convergence of states and obtain a bound which is independent of the dimension of the second party. This can, e.g., be used to prove the continuity of squashed entanglement.
This paper contains 2 theorems, 18 equations.
Theorem 1
Take any two states $\rho^{12}$ and $\sigma^{12}$ on $\mathfrak{H}^{12} = \mathfrak{H}^1 \otimes \mathfrak{H}^2$ such that $\epsilon := \|\rho^{12}-\sigma^{12}\| < 1$ and let $d_1$ be the dimension of $\mathfrak{H}^1$, then the following estimate holds In particular, the right-hand side of (th1.1) does not explicitly depend on the dimension of $\mathfrak{H}^2$.
