Multipartite correlations in quantum collision models

Abstract

Quantum collision models have proved to be useful for a clear and concise description of many physical phenomena in the field of open quantum systems: thermalization, decoherence, homogenization, nonequilibrium steady state, entanglement generation, simulation of many-body dynamics, quantum thermometry. A challenge in the standard collision model, where the system and many ancillas are all initially uncorrelated, is how to describe quantum correlations among ancillas induced by successive system-ancilla interactions. Another challenge is how to deal with initially correlated ancillas. Here we develop a tensor network formalism to address both challenges. We show that the induced correlations in the standard collision model are well captured by a matrix product state (a matrix product density operator) if the colliding particles are in pure (mixed) states. In the case of the initially correlated ancillas, we construct a general tensor diagram for the system dynamics and derive a memory-kernel master equation. Analyzing the perturbation series for the memory kernel, we go beyond the recent results concerning the leading role of two-point correlations and consider multipoint correlations (Waldenfelds cumulants) that become relevant in the higher order stroboscopic limits. These results open an avenue for a further analysis of memory effects in the collisional quantum dynamics.

arXiv comment21 pages, 10 figures

References in corpus (91)

• The density-matrix renormalization group in the age of matrix product states
• Efficient classical simulation of slightly entangled quantum computations
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
• Tensor networks for complex quantum systems
• On the degree of non-Markovianity of quantum evolution
• Concepts of quantum non-Markovianity: a hierarchy
• Non-Markovian quantum processes: complete framework and efficient characterisation
• IBM Q Experience as a versatile experimental testbed for simulating open quantum systems
• Thermalizing Quantum Machines: Dissipation and Entanglement
• Operational Markov condition for quantum processes
• Quantum collision models: open system dynamics from repeated interactions
• Non-Markovian quantum dynamics: local versus non-local
• Quantum Channels with Memory
• Photonic Quantum Circuits with Time Delays
• Collision-model-based approach to non-Markovian quantum dynamics
• Open Quantum Random Walks
• N-Photon wave packets interacting with an arbitrary quantum system
• Demonstration of non-Markovian process characterisation and control on a quantum processor
• Master equations for correlated quantum channels
• Sequential generation of linear cluster states from a single photon emitter
• Collision model for non-Markovian quantum dynamics
• Composite quantum collision models
• Collisional quantum thermometry
• All (qubit) decoherences: Complete characterization and physical implementation
• Collision models can efficiently simulate any multipartite Markovian quantum dynamics
• Qubit models of weak continuous measurements
• Simulation of indivisible qubit channels in collision models
• Machine learning non-Markovian quantum dynamics
• System-environment correlations and Markovian embedding of quantum non-Markovian dynamics
• Nakajima-Zwanzig versus time-convolutionless master equation for the non-Markovian dynamics of a two-level system
• Collision models in open system dynamics: A versatile tool for deeper insights?
• Divisibility of quantum dynamical maps and collision models
• Repeated interactions and quantum stochastic thermodynamics at strong coupling
• Spin chains and channels with memory
• Simulation complexity of open quantum dynamics: Connection with tensor networks
• Realizing a Deterministic Source of Multipartite-Entangled Photonic Qubits
• Open Quantum Walks on Graphs
• Collisional picture of quantum optics with giant emitters
• The Structure of Quantum Stochastic Processes with Finite Markov Order
• Repeated interactions in open quantum systems
• Scattering into one-dimensional waveguides from a coherently-driven quantum-optical system
• Delayed Coherent Quantum Feedback from a Scattering Theory and a Matrix Product State Perspective
• High-fidelity multi-photon-entangled cluster state with solid-state quantum emitters in photonic nanostructures
• Photon-number entanglement generated by sequential excitation of a two-level atom
• Riemannian geometry and automatic differentiation for optimization problems of quantum physics and quantum technologies
• A quantum non-Markovian collision model: incoherent swap case
• Robust multipartite entanglement generation via a collision model
• Non Markovian Quantum Repeated Interactions and Measurements
• Pronounced non-Markovian features in multiply-excited, multiple-emitter waveguide-QED: Retardation-induced anomalous population trappin
• Tensor network states in time-bin quantum optics
• Phase covariant qubit dynamics and divisibility
• Proposal for Quantum Simulation via All-Optically Generated Tensor Network States
• Open dynamics under rapid repeated interaction
• Master equation for cascade quantum channels: a collisional approach
• Quantum evolution in the stroboscopic limit of repeated measurements
• Enhanced steady-state coherence via repeated system-bath interactions
• Wick's theorem for matrix product states
• QGOpt: Riemannian optimization for quantum technologies
• Locally accurate MPS approximations for ground states of one-dimensional gapped local Hamiltonians
• Random repeated interaction quantum systems
• Many body physics and the capacity of quantum channels with memory
• Two-qubit entanglement generation through non-Hermitian Hamiltonians induced by repeated measurements on an ancilla
• Random repeated quantum interactions and random invariant states
• Generation of Photonic Matrix Product States with Rydberg Atomic Arrays
• Microscopic derivation of Open Quantum Walks
• Quantum master equations for entangled qubit environments
• Time deformations of master equations
• Steady states of continuous-time open quantum walks
• Open system dynamics of simple collision models
• Quantum master equations for a system interacting with quantum gas in the low density limit and for the semiclassical collision model
• From a posteriori to a priori solutions for a two-level system interacting with a single-photon wavepacket
• Memory Effects in Quantum Processes
• Exact dynamics of moments and correlation functions for fermionic Poisson-type GKSL equations
• Closed-System Solution of the 1D Atom from Collision Model
• Non-equilibrium states of a photon cavity pumped by an atomic beam
• Transfer-tensor description of memory effects in open-system dynamics and multi-time statistics
• Correlations break homogenization
• Quantum non-Markovian collision models from colored-noise baths
• Dynamics of an Open System for Repeated Harmonic Perturbation
• Matrix Product Density Operators: when do they have a local parent Hamiltonian?
• Repeated Interaction Quantum Systems: van Hove Limits and Asymptotic States
• The multi-time correlation functions, free white noise, and the generalized Poisson statistics in the low density limit
• Collisional open quantum dynamics with a generally correlated environment: Exact solvability in tensor networks
• Repeatable quantum memory channels
• Process estimation in presence of time-invariant memory effects
• Hitting statistics from quantum jumps
• Constructing k-local parent Lindbladians for matrix product density operators

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