Non-Markovian quantum repeated interactions and measurements

2009/03/23 by C Pellegrini, F Petruccione · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Markov process #Master equation #Open quantum system #Operator (biology) #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum operation #Quantum probability #Quantum process #Quantum system #Spectral Theory in Mathematical Physics #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1088/1751-8113/42/42/425304

22 pages

arxiv created 2009/03/23 · openalex publication_date 2009/09/30 · arxiv updated 2015/05/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06

Abstract

A non-Markovian model of quantum repeated interactions between a small quantum system and an infinite chain of quantum systems is presented. By adapting and applying usual projection operator techniques in this context, discrete versions of the integro-differential and time-convolutionless master equations for the reduced system are derived. Next, an intuitive and rigorous description of the indirect quantum measurement principle is developed and a discrete non-Markovian stochastic master equation for the open system is obtained. Finally, the question of unravelling in a particular model of non-Markovian quantum interactions is discussed.

Citations

• Non-Markovian Quantum State Diffusion
• Monte Carlo wave-function method in quantum optics
• Stochastic wave-function method for non-Markovian quantum master equations
• Pure-State Quantum Trajectories for General Non-Markovian Systems Do Not Exist
• Completely positive dynamical semigroups of N-level systems
• Open System Dynamics with Non-Markovian Quantum Trajectories
• Non-Markovian generalization of the Lindblad theory of open quantum systems

Cited by

• Simulating quantum collision models with Hamiltonian simulations using early fault-tolerant quantum computers
• Quantum-memory-enhanced dissipative entanglement creation in nonequilibrium steady states

Related

• Stochastic limits of Quantum repeated measurements
• Repeated interactions in open quantum systems
• System of stochastic interacting wave functions that model quantum measurements
• Physical Reduced Stochastic Equations for Continuously Monitored Non-Markovian Quantum Systems with a Markovian Embedding
• Non-Commutative Markov Chains and Multi-Analytic Operators