A brief journey through collision models for multipartite open quantum dynamics

Abstract

The quantum collision models are a useful method to describe the dynamics of an open quantum system by means of repeated interactions between the system and some particles of the environment, which are usually termed "ancillas". In this paper, we review the main collision models for the dynamics of multipartite open quantum systems, which are composed of several subsystems. In particular, we are interested in models that are based on elementary collisions between the subsystems and the ancillas, and that simulate global and/or local Markovian master equations in the limit of infinitesimal timestep. After discussing the mathematical details of the derivation of a generic collision-based master equation, we provide the general ideas at the basis of the collision models for multipartite systems, we discuss their strengths and limitations, and we show how they may be simulated on a quantum computer. Moreover, we analyze some properties of a collision model based on entangled ancillas, derive the master equation it generates for small timesteps, and prove that the coefficients of this master equation are subject to a constraint that limits their generality. Finally, we present an example of this collision model with two bosonic ancillas entangled in a two-mode squeezed thermal state.

arXiv commentAccepted version in the special issue of Open Syst. Inf. Dyn. devoted to the memory of Prof. A. Kossakowski. We have added the current Appendix A, new references, and additional discussions on the cascade master equation

References in corpus (48)

• An Open-System Quantum Simulator with Trapped Ions
• IBM Q Experience as a versatile experimental testbed for simulating open quantum systems
• Decoherence-Free Subspaces and Subsystems
• On the Local and Global Approaches to Quantum Transport and Violation of the Second-law of Thermodynamics
• Markovian master equations for quantum thermal machines: local vs global approach
• Quantum collision models: open system dynamics from repeated interactions
• Reconciliation of quantum local master equations with thermodynamics
• Finding Exponential Product Formulas of Higher Orders
• Detecting crosstalk errors in quantum information processors
• Testing the validity of the local and global GKLS master equations on an exactly solvable model
• Gaussian states in continuous variable quantum information
• Collision-model-based approach to non-Markovian quantum dynamics
• Local vs global master equation with common and separate baths: superiority of the global approach in partial secular approximation
• The thermodynamic cost of driving quantum systems by their boundaries
• Perturbative treatment of inter-site couplings in the local description of open quantum networks
• A Brief History of the GKLS Equation
• Master equations for correlated quantum channels
• Mechanism of decoherence-free coupling between giant atoms
• Landauer's principle in multipartite open quantum system dynamics
• Collision model for non-Markovian quantum dynamics
• Composite quantum collision models
• Collision models can efficiently simulate any multipartite Markovian quantum dynamics
• Machine learning non-Markovian quantum dynamics
• System-environment correlations and Markovian embedding of quantum non-Markovian dynamics
• Collision models in open system dynamics: A versatile tool for deeper insights?
• Collisional picture of quantum optics with giant emitters
• Collective effects and quantum coherence in dissipative charging of quantum batteries
• Quantum thermodynamically consistent local master equations
• Heat flux dynamics in dissipative cascaded systems
• Three-qubit refrigerator with two-body interactions
• Quantum synchronization in a collision model
• Quantum machines powered by correlated baths
• Robust multipartite entanglement generation via a collision model
• Synchronization and Non-Markovianity in open quantum systems
• Local master equations bypass the secular approximation
• General structure of quantum collisional models
• Master equation for cascade quantum channels: a collisional approach
• Bath-induced collective phenomena on superconducting qubits: synchronization, subradiance, and entanglement generation
• Thermalization of finite many-body systems by a collision model
• Quantum Darwinism in a composite system: Objectivity versus classicality
• Quantum master equations for entangled qubit environments
• Quantum Rayleigh problem and thermocoherent Onsager relations
• Master equations and quantum trajectories for squeezed wave packets
• Interferometric Quantum Cascade Systems
• Interferometric modulation of quantum cascade interactions
• Asynchronism and nonequilibrium phase transitions in $(1+1)$D quantum cellular automata
• Effect of inter-system coupling on heat transport in a microscopic collision model
• Collisional-model quantum trajectories for entangled qubit environments

Cited by in corpus (16)

• Charging a quantum battery in a non-Markovian environment: a collisional model approach
• Quantum simulation of dissipative collective effects on noisy quantum computers
• Embedding Quantum Many-Body Scars into Decoherence-Free Subspaces
• Quantum non-stationary phenomena of spin systems in collision models
• Experimental simulation of daemonic work extraction in open quantum batteries on a digital quantum computer
• Long-range interacting systems are locally non-interacting
• Structured quantum collision models: generating coherence with thermal resources
• Simulating quantum transport via collisional models on a digital quantum computer
• Dissipative quantum many-body dynamics in (1+1)D quantum cellular automata and quantum neural networks
• Queued quantum collision models
• Space-time correlations in monitored kinetically constrained discrete-time quantum dynamics
• Non-linear classification capability of quantum neural networks due to emergent quantum metastability
• Continuous Variable Structured Collision Models
• Current circulation near additional energy degeneracy points in quadratic Fermionic networks
• Strong symmetries in collision models and physical dilations of covariant quantum maps
• Revealing emergent many-body phenomena by analyzing large-scale space-time records of monitored quantum systems