Singularity of dynamical maps

Abstract

For a dynamical map $\Lambda (t,0)$, which sends a state $\rho (0)$ of quantum open system to a state $\rho (t)=\Lambda (t,0)\rho (0)$, the decomposition law $\Lambda (t,0)=\Lambda (t,t_c)\Lambda (t_c,0)$ may break down at a specific time $t_c$. In this paper, we present a method to find the singular points $t_c$ and propose a measure for the singularity of the dynamical map. Two examples are portrayed to illustrate the method, the measure of singularity for these singular points is calculated and discussed. An extension to high-dimensional system is presented.

6 pages, no figure

References in corpus (8)

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Cited by in corpus (16)

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• Non-Markovian random unitary qubit dynamics
• Non-Markovianity through flow of information between a system and an environment
• Equivalence between divisibility and monotonic decrease of information in classical and quantum stochastic processes
• Non-Markovianity, coherence and system-environment correlations in a long-range collision model
• Non-Markovianity and memory effects in quantum open systems
• Witnessing non-Markovianity of quantum evolution
• Quantum causal correlations and non-Markovianity of quantum evolution
• Singularities, mixing and non-Markovianity of Pauli dynamical maps
• Measure of invertible dynamical maps under convex combinations of noninvertible dynamical maps
• Noninvertibility as a requirement for creating a semigroup under convex combinations of channels
• Noninvertibility and non-Markovianity of quantum dynamical maps
• The role of the total entropy production in dynamics of open quantum systems in detection of non-Markovianity
• Non-Markovian dynamics for a two-atom-coupled system interacting with local reservoir at finite temperature
• Eternally non-Markovian dynamics of a qubit interacting with a single-photon wavepacket
• Open quantum dynamics with singularities: Master equations and degree of non-Markovianity