Entangling power of the quantum baker's map

Abstract

We investigate entanglement production in a class of quantum baker's maps. The dynamics of these maps is constructed using strings of qubits, providing a natural tensor-product structure for application of various entanglement measures. We find that, in general, the quantum baker's maps are good at generating entanglement, producing multipartite entanglement amongst the qubits close to that expected in random states. We investigate the evolution of several entanglement measures: the subsystem linear entropy, the concurrence to characterize entanglement between pairs of qubits, and two proposals for a measure of multipartite entanglement. Also derived are some new analytical formulae describing the levels of entanglement expected in random pure states.

22 pages, 11 figures

References in corpus (29)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Mixed State Entanglement and Quantum Error Correction
• Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
• Entanglement of a Pair of Quantum Bits
• Distributed Entanglement
• Random Matrix Theories in Quantum Physics: Common Concepts
• Quantifying Entanglement
• Average Entropy of a Subsystem
• Entanglement Measures and Purification Procedures
• Global entanglement in multiparticle systems
• Thermodynamics and the Measure of Entanglement
• Induced measures in the space of mixed quantum states
• On the Entangling Power of Quantum Evolutions
• Average Entropy of a Subsystem
• Testing statistical bounds on entanglement using quantum chaos
• Entangling power of quantized chaotic systems
• Composed ensembles of random unitary matrices
• Dynamical aspects of quantum entanglement for weakly coupled kicked tops
• Quantum Approach to a Derivation of the Second Law of Thermodynamics
• Using a quantum computer to investigate quantum chaos
• Entanglement sharing in one-particle states
• Saturation of the production of quantum entanglement between weakly coupled mapping systems in strongly chaotic region
• Typical entanglement in multi-qubit systems
• Realizing the quantum baker's map on an NMR quantum computer
• Entanglement versus relaxation and decoherence in a quantum algorithm for quantum chaos
• Classical limit in terms of symbolic dynamics for the quantum baker's map
• The classical limit for a class of quantum baker's maps
• Quantum baker map on the sphere
• A Canonical Quantization of the Baker's Map

Cited by in corpus (101)

• Dynamics of Loschmidt echoes and fidelity decay
• Entanglement and the Power of One Qubit
• Multipartite entanglement, quantum-error-correcting codes, and entangling power of quantum evolutions
• Random Quantum Circuits and Pseudo-Random Operators: Theory and Applications
• Entanglement as a signature of quantum chaos
• Decoherence, Entanglement and Irreversibility in Quantum Dynamical Systems with Few Degrees of Freedom
• Maximally multipartite entangled states
• Entanglement and Entropy in a Spin-Boson Quantum Phase Transition
• Entanglement production in coupled chaotic systems : Case of the Kicked Tops
• A simple example of "Quantum Darwinism": Redundant information storage in many-spin environments
• Entanglement, avoided crossings and quantum chaos in an Ising model with a tilted magnetic field
• Phase transitions of bipartite entanglement
• Chaos, entanglement and decoherence in the quantum kicked top
• Multipartite Entanglement in a One-Dimensional Time Dependent Ising Model
• Information Scrambling over Bipartitions: Equilibration, Entropy Production, and Typicality
• Semiclassical time-evolution of the reduced density matrix and dynamically assisted generation of entanglement for bipartite quantum systems
• Entanglement Across a Transition to Quantum Chaos
• Quantum Chaos, Delocalization, and Entanglement in Disordered Heisenberg Models
• Entangling power of time-evolution operators in integrable and nonintegrable many-body systems
• Tripartite mutual information, entanglement, and scrambling in permutation symmetric systems with an application to quantum chaos
• Random pure states: quantifying bipartite entanglement beyond the linear statistics
• Entanglement dynamics in chaotic systems
• Probability density function characterization of multipartite entanglement
• Unitary quantum gates, perfect entanglers and unistochastic maps
• Quantum ergodicity and entanglement in kicked coupled-tops
• Phase transitions and metastability in the distribution of the bipartite entanglement of a large quantum system
• Out-of-time-ordered correlator in the quantum bakers map and truncated unitary matrices
• Distribution of bipartite entanglement for random pure states
• Entanglement Generation of Nearly-Random Operators
• A Brief Overview of Bipartite and Multipartite Entanglement Measures
• Decoherence induced by a chaotic environment: A quantum walker with a complex coin
• Quantum coherence as a signature of chaos
• Generalized entanglement as a framework for complex quantum systems: Purity vs delocalization measures
• Multipartite Entanglement and Frustration
• Almost Markovian processes from closed dynamics
• Signatures of chaos in the dynamics of quantum discord
• Optimal two-qubit gate for generation of random bipartite entanglement
• Random unitary maps for quantum state reconstruction
• Parameters of Pseudo-Random Quantum Circuits
• Local entanglement structure across a many-body localization transition
• Random Matrix Theory of the Isospectral twirling
• Relaxation due to random collisions with a many-qudit environment
• Classical Statistical Mechanics Approach to Multipartite Entanglement
• Matrix realignment and partial transpose approach to entangling power of quantum evolutions
• Quantum correlations as probes of chaos and ergodicity
• Entanglement dynamics and relaxation in a few qubit system interacting with random collisions
• Quantum signatures of chaos, thermalization and tunneling in the exactly solvable few body kicked top
• Quantum chaos, thermalization and tunneling in an exactly solvable few body system
• Signatures of bifurcation on quantum correlations: Case of the quantum kicked top
• Statistical distribution of the local purity in a large quantum system
• Statistical mechanics of multipartite entanglement
• Entanglement of localized states
• Typicality in Ensembles of Quantum States: Monte Carlo Sampling versus Analytical Approximations
• Detecting entanglement of random states with an entanglement witness
• Almost all four-particle pure states are determined by their two-body marginals
• Hypersensitivity and chaos signatures in the quantum baker's maps
• Classical bifurcations and entanglement in smooth Hamiltonian system
• Matrix Element Distribution as a Signature of Entanglement Generation
• Multipartite entanglement generation and fidelity decay in disordered qubit systems
• Quantum dynamical entropy and decoherence rate
• Generalized Entanglement as a Natural Framework for Exploring Quantum Chaos
• Quantum-classical correspondence in entanglement production: Entropy and classical tori
• Entanglement-screening by nonlinear resonances
• Entanglement and Stabilizer entropies of random bipartite pure quantum states
• Time Reversal and n-qubit Canonical Decompositions
• Emergence of equilibrium thermodynamic properties in quantum pure states. I. Theory
• Entangling power of baker's map: Role of symmetries
• On the negativity of random pure states
• Generalized Quantum Baker Maps as perturbations of a simple kernel
• Characterizing and measuring multipartite Entanglement
• Average skew information-based coherence and its typicality for random quantum states
• Super-sharp resonances in chaotic wave scattering
• Quenching and generation of random states in a kicked Ising model
• Comment on "Entanglement and chaos in the kicked top"
• Multipartite entanglement characterization of a quantum phase transition
• Robust and efficient generator of almost maximal multipartite entanglement
• Intermediate quantum maps for quantum computation
• Entanglement Echoes in Quantum Computation
• Characterizing and Quantifying Quantum Chaos with Quantum Tomography
• Typical Entanglement
• Transition from pure-state to mixed-state entanglement by random scattering
• Statistical bounds on the dynamical production of entanglement
• Quantum Cellular Automata Pseudo-Random Maps
• Entanglement transitions in random definite particle states
• Polarized ensembles of random pure states
• Dynamically localized systems: entanglement exponential sensitivity and efficient quantum simulations
• Universality in Dynamical Formation of Entanglement for Quantum Chaos
• Pseudo-random operators of the circular ensembles
• Characterizing randomness in parameterized quantum circuits through expressibility and average entanglement
• Quantum tomography with random diagonal unitary maps and statistical bounds on information generation using random matrix theory
• The modular multiplication operator and the quantized bakers maps
• Quantum Chaos: Reduced Density Matrix Fluctuations in Coupled Systems
• Quantum baker maps with controlled-NOT coupling
• Probability measure generated by the superfidelity
• Persistent entanglement in a class of eigenstates of quantum Heisenberg spin glasses
• Entanglement production in a chaotic quantum dot
• Entangling power of symmetric multiqubit systems: a geometrical approach
• Simulating typical entanglement with many-body Hamiltonian dynamics
• Eigenstates and spectral projection for quantized baker's map
• Multipartite entanglement and few-body Hamiltonians
• Entanglement production in the Sachdev-Ye-Kitaev Model and its variants