Trace norm quantum discord for two qubits: the complete solution revisited and applications

We have significantly improved the previous analysis of Lugiewicz et al. (Quantum Inf Process 18:185, 2019) in terms of several key issues. By emphasizing geometric arguments, for the first time we give a mathematically complete proof of the principle of three large circles on the unit sphere. This principle is one of the key ingredients of the whole reasoning on which our results are based. In addition, due to the elimination of difficult to use auxiliary special functions that were introduced earlier, we present now simplified formulae for the one-sided trace norm discord of any state of two qubits. We give applications of the new result in study of the state space. In particular, we propose an alternative classification of states, distinguish between self-adhered states, and discuss the complete description of the new class of states.