Non-Markovian dynamics of a qubit

2005/09/30 by Sabrina Maniscalco, Francesco Petruccione · 4 citations
Computer Science · Mathematics · Physics and Astronomy · #Applied mathematics #Discrete mathematics #Dynamics (music) #Kernel (algebra) #Markov process #Master equation #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum mechanics #Qubit #Spectroscopy and Quantum Chemical Studies #Statistical physics #Statistics #quant-ph

paper · pdf · doi:10.1103/physreva.73.012111

published as Phys. Rev. A 73,012111 (2006) · Replaced with published version (minor changes)

openalex publication_date 2006/01/24 · arxiv created 2006/02/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this paper we investigate the non-Markovian dynamics of a qubit by comparing two generalized master equations with memory. In the case of a thermal bath, we derive the solution of the recently proposed post-Markovian master equation [A. Shabani and D. A. Lidar, Phys. Rev. A 71, 020101(R) (2005)] and we study the dynamics for an exponentially decaying memory kernel. We compare the solution of the post-Markovian master equation with the solution of the typical memory kernel master equation. Our results lead to a new physical interpretation of the reservoir correlation function and bring to light the limits of usability of master equations with memory for the system under consideration.

Citations

• Depolarizing channel as a completely positive map with memory
• Genuine quantum trajectories for non-Markovian processes
• Optimal strategy for a single-qubit gate and the trade-off between opposite types of decoherence
• Completely positive post-Markovian master equation via a measurement approach
• Completely positive dynamical semigroups of N-level systems
• Fault-tolerant quantum computation for local non-Markovian noise

Cited by

• Recovering the lost steerability of quantum states within non-Markovian environments by utilizing quantum partially collapsing measurements
• Open system dynamics from thermodynamic compatibility
• A quantum non-Markovian collision model: incoherent swap case
• Simple non-Markovian microscopic models for the depolarizing channel of a single qubit
• Perturbative dynamics of open quantum systems by renormalization group method