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Quantum private states are the states that represent some amount of perfectsecure key. A simple symmetry of any generalised private quantum state (ie. thestates that represent perfect key but not fully random) is provided andextended on Devetak-Winter so called ccq (classical-classical-quantum) and cqq(classical-quantum-quantum) lower bound on secure key. This symmetry is used todevelop a practical method of estimating the Alice measurement that is optimalform 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 ofthe state with respect to the lower bound formula. It suggest a generalparadigm for quick estimation of quantum communication rates under the symmetryof a given resource like state and/or channel.

Symmetry-based estimation of lower bound on secure key rate of noisy private states