On the eternal non-Markovianity of non-unital quantum channels

Abstract

The eternally non-Markovian Pauli channel is an example of a unital channel characterized by a negative decay rate for all time $t>0$. Here we consider the problem of constructing an analogous non-unital channel, and show in particular that a $d$-dimensional generalized amplitude damping (GAD) channel cannot be eternally non-Markovian when the non-Markovianity originates solely from the non-unital part of the channel. We study specific ramifications of this result for qubit GAD. Specifically, we construct a quasi-eternally non-Markovian qubit GAD channel, characterized by a time $t^{\ast }>0$, such that the channel is non-Markovian only and for all time $t>t^{\ast }$. We further point out that our negative result for the qudit GAD channel, namely the impossibility of the eternal non-Markovian property, does not hold for a general qubit or higher-dimensional non-unital channel.

arXiv comment13 pages, 2 figures; Accepted in International Journal of Quantum Information

References in corpus (34)

• Measure for the Degree of Non-Markovian Behavior of Quantum Processes in Open Systems
• Non-Markovian dynamics in open quantum systems
• Entanglement and non-Markovianity of quantum evolutions
• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Assessing non-Markovian dynamics
• Canonical form of master equations and characterization of non-Markovianity
• Concepts of quantum non-Markovianity: a hierarchy
• Non-Markovian quantum processes: complete framework and efficient characterisation
• Operational Markov condition for quantum processes
• Geometrical characterization of non-Markovianity
• Markovian and non-Markovian dynamics in quantum and classical systems
• Completely Positive Divisibility Does Not Mean Markovianity
• Kraus representation of quantum evolution and fidelity as manifestations of Markovian and non-Markovian avataras
• The squeezed generalized amplitude damping channel
• Quantifying Non-Markovianity with Temporal Steering
• Non-Markovian random unitary qubit dynamics
• High-dimensional quantum teleportation under noisy environments
• Non-Markovianity degree for random unitary evolution
• Eternal non-Markovianity: from random unitary to Markov chain realisations
• Divisibility and Information Flow Notions of Quantum Markovianity for Noninvertible Dynamical Maps
• Non-Markovian evolution: a quantum walk perspective
• Non-unital non-Markovianity of quantum dynamics
• Temporal self-similarity of quantum dynamical maps as a concept of memorylessness
• Quantum non-Markovian processes break conditional past-future independence
• Phase covariant qubit dynamics and divisibility
• Conditional past-future correlation induced by non-Markovian dephasing reservoirs
• Quantum non-Markovianity: Overview and recent developments
• Entropic bounds on information backflow
• Symmetry-noise interplay in quantum walk on an n-cycle
• Markovian semigroup from non-Markovian evolutions
• Hierarchy of quantum correlations under non-Markovian dynamics
• Non-Markovian channel from the reduced dynamics of coin in quantum walk
• Simple criteria for noise resistance of two qudit entanglement
• Quantum causal correlations and non-Markovianity of quantum evolution