Non-Markovian dephasing and depolarizing channels
arXiv:1805.11411 · doi:10.1103/PhysRevA.98.032328
Abstract
We introduce a method to construct non-Markovian variants of completely positive (CP) dynamical maps, particularly, qubit Pauli channels. We identify non-Markovianity with the breakdown in CP-divisibility of the map, i.e., appearance of a not-completely-positive (NCP) intermediate map. In particular, we consider the case of non-Markovian dephasing in detail. The eigenvalues of the Choi matrix of the intermediate map crossover at a point which corresponds to a singularity in the canonical decoherence rate of the corresponding master equation, and thus to a momentary non-invertibility of the map. Thereafter, the rate becomes negative, indicating non-Markovianity. We quantify the non-Markovianity by two methods, one based on CP-divisibility (Hall et al., PRA 89, 042120, 2014), which doesn't require optimization but requires normalization to handle the singularity, and another method, based on distinguishability (Breuer et al. PRL 103, 210401, 2009), which requires optimization but is insensitive to the singularity.
arXiv commentAccepted for publication in Physical Review A; 8 pages, 6 figures
References in corpus (18)
- 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
- Canonical form of master equations and characterization of non-Markovianity
- Concepts of quantum non-Markovianity: a hierarchy
- On measures of non-Markovianity: divisibility vs. backflow of information
- Completely positive maps with memory
- Markovian and non-Markovian dynamics in quantum and classical systems
- Dynamics of initially entangled open quantum systems
- Finding the Kraus decomposition from a master equation and vice versa
- Kraus representation of quantum evolution and fidelity as manifestations of Markovian and non-Markovian avataras
- Choi's Proof and Quantum Process Tomography
- Non-unital non-Markovianity of quantum dynamics
- Geometric Phase of a qubit interacting with a squeezed-thermal bath
- A classical appraisal of quantum definitions of non-Markovian dynamics
- Dissipative and Non-dissipative Single-Qubit Channels: Dynamics and Geometry
- The operator sum-difference representation for quantum maps: application to the two-qubit amplitude damping channel
Cited by in corpus (42)
- Temporal self-similarity of quantum dynamical maps as a concept of memorylessness
- Facets of quantum information under non-Markovian evolution
- All-photonic architectural roadmap for scalable quantum computing using Greenberger-Horne-Zeilinger states
- Quantum non-Markovianity: Overview and recent developments
- Experimental investigation of Markovian and non-Markovian channel addition
- Constructive Feedback of Non-Markovianity on Resources in Random Quantum States
- Hierarchy of quantum correlations under non-Markovian dynamics
- Quantum correlations and speed limit of central spin system
- Quantum causal correlations and non-Markovianity of quantum evolution
- Characterizing qubit channels in the context of quantum teleportation
- Impact of non-Markovian evolution on characterizations of quantum thermodynamics
- Qudit States in Noisy Quantum Channels
- Singularities, mixing and non-Markovianity of Pauli dynamical maps
- Quantum speed limit time: role of coherence
- The effect of quantum memory on quantum speed limit time for CP-(in)divisible channels
- Dynamics of two central spins immersed in spin baths
- Measure of not-completely-positive qubit maps: the general case
- Harnessing quantumness of states using discrete Wigner functions under (non)-Markovian quantum channels
- Attainable and usable coherence in X states over Markovian and non-Markovian channels
- A study of coherence based measure of quantumness in (non) Markovian channels
- Phase covariant channel: Quantum speed limit of evolution
- Towards realization of universal quantum teleportation using weak measurements
- Facets of correlated non-Markovian channels
- Interplay between nonclassicality and symmetry in an effective two level system with open system effects
- Quantumness of channels
- (Thermo-)dynamics of the spin-boson model in the weak coupling regime: Application as a quantum battery
- Superiority in dense coding through non-Markovian stochasticity
- Controlling gain with loss: Bounds on localizable entanglement in multi-qubit systems
- Exploring the Non-Markovian Dynamics in Depolarizing Maps
- Non-Hermitian quantum walks and non-Markovianity: the coin-position interaction
- Detecting Non-Markovianity via Linear Entropy of Choi State
- Localizing genuine multiparty entanglement in noisy stabilizer states
- Collective attack free controlled quantum key agreement without quantum memory
- Digital simulation of convex mixtures of Markovian and non-Markovian single qubit Pauli channels on NISQ devices
- On the non-Markovianity of quantum semi-Markov processes
- Non-Markovianity in Discrete-Time Open Quantum Random Walk on Arbitrary Graphs
- Superclassical non-Markovian open quantum dynamics
- Distinguishing environment-induced non-Markovianity from subsystem dynamics
- Model Order Reduction for Open Quantum Systems Based on Measurement-adapted Time-coarse Graining
- Evolution of Entanglement Witness of Dicke State under Noise and Error Mitigation
- Quantum state transfer and periodicity in discrete-time quantum walks under non--Markovian dephasing noise
- Non-Markovian steady states of a driven two-level system