On the universal constraints for relaxation rates for quantum dynamical semigroup

Abstract

A conjecture for the universal constraints for relaxation rates of a quantum dynamical semigroup is proposed. It is shown that it holds for several interesting classes of semigroups, e.g. unital semigroups and semigroups derived in the weak coupling limit from the proper microscopic model. Moreover, proposed conjecture is supported by numerical analysis. This conjecture has several important implications: it allows to provide universal constraints for spectra of quantum channels and provides necessary condition to decide whether a given channel is consistent with Markovian evolution.

arXiv comment9 pages, 1 figure

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Cited by in corpus (15)

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• Bounds on the breaking time for entanglement-breaking channels
• Number of steady states of quantum evolutions
• One parameter generalization of BW inequality and its application to open quantum dynamics
• Quantum versus classical $P$-divisibility
• Böttcher-Wenzel inequality for weighted Frobenius norms and its application to quantum physics
• Understanding and Generalizing Unique Decompositions of Generators of Dynamical Semigroups
• Uncertainty relations based on state-dependent norm of commutator
• Random Lindblad operators obeying detailed balance
• Eternally non-Markovian dynamics of a qubit interacting with a single-photon wavepacket
• Asymptotic dynamics in the Heisenberg picture: attractor subspace and Choi-Effros product
• A universal constraint for relaxation rates for quantum Markov generators: complete positivity and beyond
• Universal Bound on the Eigenvalues of 2-Positive Trace-Preserving Maps
• Unital Kadison-Schwarz Maps
• Constraints for the spectra of generators of quantum dynamical semigroups