Abstract
A witness of non-Markovianity based on the Hilbert–Schmidt speed (HSS), a special type of quantum statistical speed, has been recently introduced for low-dimensional quantum systems. Such a non-Markovianity witness is particularly useful, being easily computable since no diagonalization of the system density matrix is required. We investigate the sensitivity of this HSS-based witness to detect non-Markovianity in various high-dimensional and multipartite open quantum systems with finite Hilbert spaces. We find that the time behaviors of the HSS-based witness are always in agreement with those of quantum negativity or quantum correlation measure. These results show that the HSS-based witness is a faithful identifier of the memory effects appearing in the quantum evolution of a high-dimensional system with a finite Hilbert space.
Highlights
Hilbert–Schmidt Speed-BasedThe unavoidable interaction of quantum systems with their environments induces decoherence and dissipation of energy
The Hilbert–Schmidt speed (HSS)-based witness, a quantifier of quantum statistical speed which has the advantage of avoiding the diagonalization of the evolved density matrix, has been introduced as a trustful witness of non-Markovianity in low-dimensional systems [61]
We have generalized this result showing that the proposed witness is a bonafide identifier of non-Markovianity for high-dimensional and multipartite open quantum systems with finite Hilbert spaces
Summary
The unavoidable interaction of quantum systems with their environments induces decoherence and dissipation of energy. Hilbert–Schmidt speed (HSS) [60], a measure of quantum statistical speed which has the advantage of avoiding diagonalization of the evolved density matrix, has been proposed and employed as a faithful witness of non-Markovianity in Hermitian systems [61–64] and an efficient tool in quantum metrology [65,66]. These studies are so far especially limited to low-dimensional systems, while high-dimensional ones have not been investigated in detail.
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