Detecting non-Markovianity via uncertainty relations

We present a formalism for detection of non-Markovianity (NM) through uncertainty relations. We show that when there is an information back-flow to the system from its environment through CP-divisibility breaking, the Choi-states corresponding to the reduced system evolution contain at least one negative eigenvalue. The consequent break down of uncertainty relations for such states can be used to witness non-Markovian dynamics. We present some relevant examples of the phenomenon for qubit channels. We further prove that square of the variance of a suitable Hermitian operator can act as a non-linear witness of NM. We finally show that NM is necessary in order to decrease the uncertainty of the states undergoing unital dynamics for qubits. This provides another method of certifying NM. (paper)