Different measures have been presented to depict the deviation of quantum time evolution in open systems from Markovian processes. We demonstrate that the measure proposed by Breuer, Laine, and Piilo [Phys. Rev. Lett. 103, 210401 (2009)] and the two measures proposed by Rivas, Huelga, and Plenio [Phys. Rev. Lett. 105, 050403 (2010)] have exactly the same non-Markovian time-evolution intervals and thus are really equivalent to each other when they are applied to open two-level systems coupled to environments via the Jaynes-Cummings or dephasing models. This equivalence implies that the three measures, in different ways, capture the intrinsic character of the non-Markovianity of quantum evolutional processes. We also show that the maximization in the definition of the first measure can be actually removed for the considered models without influencing the sensibility of the measure to detect non-Markovianity.

• Received 21 March 2011

DOI:https://doi.org/10.1103/PhysRevA.84.032118