Random Quantum Operations
arXiv:0804.2361 · doi:10.1016/j.physleta.2008.11.043
Abstract
We define a natural ensemble of trace preserving, completely positive quantum maps and present algorithms to generate them at random. Spectral properties of the superoperator Phi associated with a given quantum map are investigated and a quantum analogue of the Frobenius-Perron theorem is proved. We derive a general formula for the density of eigenvalues of Phi and show the connection with the Ginibre ensemble of real non-symmetric random matrices. Numerical investigations of the spectral gap imply that a generic state of the system iterated several times by a fixed generic map converges exponentially to an invariant state.
References in corpus (12)
- Induced measures in the space of mixed quantum states
- The problem of equilibration and the computation of correlation functions on a quantum computer
- Quantum Process Tomography of the Quantum Fourier Transform
- Eigenvalue statistics of the real Ginibre ensemble
- Truncations of random unitary matrices
- Statistical properties of random density matrices
- Convergence Conditions for Random Quantum Circuits
- On Random Unitary Channels
- Random unistochastic matrices
- General Eigenvalue Correlations for the Real Ginibre Ensemble
- Quantum pseudo-randomness from cluster-state quantum computation
- Irreversible Quantum Baker Map
Cited by in corpus (71)
- Estimating the Coherence of Noise
- Generating random density matrices
- Universal spectra of random Lindblad operators
- Practical Bayesian Tomography
- Symmetry Classification and Universality in Non-Hermitian Many-Body Quantum Chaos by the Sachdev-Ye-Kitaev Model
- Quantum process tomography of unitary and near-unitary maps
- Quantum process tomography via completely positive and trace-preserving projection
- Asymptotic Floquet states of open quantum systems: The role of interaction
- Quantum circuits for measuring weak values, Kirkwood--Dirac quasiprobability distributions, and state spectra
- Random Lindblad Dynamics
- Geometric measures of quantum correlations: characterization, quantification, and comparison by distances and operations
- Induced Ginibre ensemble of random matrices and quantum operations
- Channel capacity enhancement with indefinite causal order
- Optimal Strategies of Quantum Metrology with a Strict Hierarchy
- Generating random quantum channels
- Dysonian dynamics of the Ginibre ensemble
- Coherifying quantum channels
- Integrable nonunitary open quantum circuits
- Spectral transitions and universal steady states in random Kraus maps and circuits
- QInfer: Statistical inference software for quantum applications
- Statistical properties of random matrix product states
- Generating and using truly random quantum states in Mathematica
- Random generators of Markovian evolution: A quantum-classical transition by superdecoherence
- A principle of maximum ignorance for semiclassical gravity
- Asymptotic Evolution of Random Unitary Operations
- Almost all quantum channels are equidistant
- Quantum Markovianity as a supervised learning task
- Random repeated quantum interactions and random invariant states
- Entropic trade-off relations for quantum operations
- QuantumInformation.jl---a Julia package for numerical computation in quantum information theory
- Quantum bifurcation diagrams
- Universality of spectra for interacting quantum chaotic systems
- Asymptotic properties of quantum Markov chains
- Universal Emergence of PageRank
- Fidelity induced distance measures for quantum states
- Quantum leakage detection using a model-independent dimension witness
- Gauge invariant information concerning quantum channels
- The ensemble of random Markov matrices
- On limiting distributions of quantum Markov chains
- Theory of Ergodic Quantum Processes
- Experimentally feasible measures of distance between quantum operations
- Quantum Chaos and Coherence: Random Parametric Quantum Channels
- Single qubit decoherence under a separable coupling to a random matrix environment
- Convergence of quantum random walks with decoherence
- Multi-frequency control and measurement of a spin-7/2 system encoded in a transmon qudit
- Operational, gauge-free quantum tomography
- Enhancing pseudo-telepathy in the Magic Square game
- SchWARMA: A model-based approach for time-correlated noise in quantum circuits
- Quantum-correlation breaking channels, quantum conditional probability and Perron-Frobenius theory
- Time periodicity from randomness in quantum systems
- Exponential Families for Bayesian Quantum Process Tomography
- Direct estimation of minimum gate fidelity
- A Thermodynamic Formalism for density matrices in Quantum Information
- Schur function averages for the real Ginibre ensemble
- On the probabilistic quantum error correction
- Volume of the space of qubit-qubit channels and state transformations under random quantum channels
- Fuzzy measurements and coarse graining in quantum many-body systems
- Variational certification of quantum devices
- Estimation of correlations and non-separability in quantum channels via unitarity benchmarking
- Complementary Resource Relation of Concurrence and Roughness for atwo Qubits State
- What can unitary sequences tell us about multi-time physics?
- User-specified random sampling of quantum channels and its applications
- A model for quantum queue
- Random covariant quantum channels
- Geometry of symmetric and non-invertible Pauli channels
- Random Lindblad operators obeying detailed balance
- Complex symmetric, self-dual, and Ginibre random matrices: Analytical results for three classes of bulk and edge statistics
- Effective dynamics of qubit networks via phase-covariant quantum ensembles
- Hacking Quantum Networks: Extraction and Installation of Quantum Data
- Typicality of Contextuality
- Moments of Quantum Channel Ensembles