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

Abstract

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

Ohmic reservoir-based non-Markovianity and Quantum Speed Limit Time

“…The non-Markovian effect in the dynamics process can be described by the non-Markovianity. Many efforts have been made to define non-Markovianity, to measure it, and to take advantage of it [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. For examples, the non-markovianity was quantified by correlations in [10], the authors in [21,12] studied the measurement of non-Markovianity and Paternostro's team studied geometrical characterization of non-Markovianity [17].…”

“…Many efforts have been made to define non-Markovianity, to measure it, and to take advantage of it [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. For examples, the non-markovianity was quantified by correlations in [10], the authors in [21,12] studied the measurement of non-Markovianity and Paternostro's team studied geometrical characterization of non-Markovianity [17]. In recent years, the research on non-Markovianity in the dynamics process of the open system has attracted the attention of the community, both theoretically and experimentally [25][26][27][28].…”