  Quantum private states are the states that represent some amount of perfect
secure key. A simple symmetry of any generalised private quantum state (ie. the
states that represent perfect key but not fully random) is provided and
extended on Devetak-Winter so called ccq (classical-classical-quantum) and cqq
(classical-quantum-quantum) lower bound on secure key. This symmetry is used to
develop a practical method of estimating the Alice measurement that is optimal
form the perspective of single shot Devetak-Witner lower bound on secure key.
The method is particularly good when the noise does not break the symmetry of
the state with respect to the lower bound formula. It suggest a general
paradigm for quick estimation of quantum communication rates under the symmetry
of a given resource like state and/or channel.
