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Non-Markovian effects can speed up the dynamics of quantum systems while thelimits of the evolution time can be derived by quantifiers of quantumstatistical speed. We introduce a witness for characterizing thenon-Markovianity of quantum evolutions through the Hilbert-Schmidt speed (HSS),which is a special type of quantum statistical speed. This witness has theadvantage of not requiring diagonalization of evolved density matrix. Itssensitivity is investigated by considering several paradigmatic instances ofopen quantum systems, such as one qubit subject to phase-covariant noise andPauli channel, two independent qubits locally interacting with leaky cavities,V-type and $\Lambda $-type three-level atom (qutrit) in a dissipative cavity.We show that the proposed HSS-based non-Markovianity witness detects memoryeffects in agreement with the well-established trace distance-based witness,being sensitive to system-environment information backflows.

Witnessing non-Markovian effects of quantum processes through Hilbert-Schmidt speed