Generating random quantum channels

Abstract

Several techniques of generating random quantum channels, which act on the set of $d$-dimensional quantum states, are investigated. We present three approaches to the problem of sampling of quantum channels and show under which conditions they become mathematically equivalent, and lead to the uniform, Lebesgue measure on the convex set of quantum operations. We compare their advantages and computational complexity and demonstrate which of them is particularly suitable for numerical investigations. Additional results focus on the spectral gap and other spectral properties of random quantum channels and their invariant states. We compute mean values of several quantities characterizing a given quantum channel, including its unitarity, the average output purity and the $2$-norm coherence of a channel, averaged over the entire set of the quantum channels with respect to the uniform measure. An ensemble of classical stochastic matrices obtained due to super-decoherence of random quantum stochastic maps is analyzed and their spectral properties are studied using the Bloch representation of a classical probability vector.

arXiv comment29 pages, 7 figures

References in corpus (48)

• Quantum entanglement
• Integration with respect to the Haar measure on unitary, orthogonal and symplectic group
• Superadditivity of communication capacity using entangled inputs
• Induced measures in the space of mixed quantum states
• The problem of equilibration and the computation of correlation functions on a quantum computer
• Estimating the Coherence of Noise
• Generating random density matrices
• How to generate random matrices from the classical compact groups
• Local environment can enhance fidelity of quantum teleportation
• Truncations of random unitary matrices
• Statistical properties of random density matrices
• A Brief History of the GKLS Equation
• Composed ensembles of random unitary matrices
• Random matrix techniques in quantum information theory
• Random Unitaries Give Quantum Expanders
• Random Quantum Operations
• On Random Unitary Channels
• Random quantum channels I: graphical calculus and the Bell state phenomenon
• Random unistochastic matrices
• Simulating Open Quantum Systems with Hamiltonian Ensembles and the Nonclassicality of the Dynamics
• The structures of state space concerning Quantum Dynamical Semigroups
• Unitary quantum gates, perfect entanglers and unistochastic maps
• Coherifying quantum channels
• Distinguishability of generic quantum states
• Circular Law Theorem for Random Markov Matrices
• Spectral transitions and universal steady states in random Kraus maps and circuits
• Quantifying the nonclassicality of pure dephasing
• Random generators of Markovian evolution: A quantum-classical transition by superdecoherence
• Geometry of sets of quantum maps: a generic positive map acting on a high-dimensional system is not completely positive
• A universal set of qubit quantum channels
• Almost all quantum channels are equidistant
• The Dirichlet Markov Ensemble
• Correlation length in random MPS and PEPS
• Volume of the set of unistochastic matrices of order 3 and the mean Jarlskog invariant
• QuantumInformation.jl---a Julia package for numerical computation in quantum information theory
• Bipartite unitary gates and billiard dynamics in the Weyl chamber
• RTNI - A symbolic integrator for Haar-random tensor networks
• Universality of spectra for interacting quantum chaotic systems
• Realigning random states
• Spectral density of generalized Wishart matrices and free multiplicative convolution
• The absolute positive partial transpose property for random induced states
• Simulating a single qubit channel using a mixed state environment
• Random positive operator valued measures
• The ensemble of random Markov matrices
• Quasi inversion of qubit channels
• Volume of the space of qubit-qubit channels and state transformations under random quantum channels
• Distinguishing classically indistinguishable states and channels
• On the spectral gap of random quantum channels

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• Variational certification of quantum devices
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• Estimation of correlations and non-separability in quantum channels via unitarity benchmarking
• Deployed quantum link characterization via Bayesian ancilla-assisted process tomography
• Matrix product states and the decay of quantum conditional mutual information
• Approximate Petz recovery from the geometry of density operators
• What can unitary sequences tell us about multi-time physics?
• Quantum-Dynamical Semigroups and the Church of the Larger Hilbert Space
• Probing the limits of quantum theory with quantum information at subnuclear scales
• Random covariant quantum channels
• Coherent information of a quantum channel or its complement is generically positive
• Relating entropies of quantum channels
• Random Lindblad operators obeying detailed balance
• Certifying nonlocal properties of noisy quantum operations
• Generating random Gaussian states
• Thermodynamic criteria for signaling in quantum channels
• Fidelity and Entanglement of Random Bipartite Pure States: Insights and Applications
• Enhancement of non-Stabilizerness within Indefinite Causal Order
• Quantum Advantage in Storage and Retrieval of Isometry Channels
• Quantum-aware Transformer model for state classification
• Typicality of Contextuality
• Scaling Laws of Quantum Information Lifetime in Monitored Quantum Dynamics
• In situ quantum verification of polarization-stabilized optical channels
• Summing free unitary Brownian motions with applications to quantum information
• Moments of Quantum Channel Ensembles
• Accessible maps in a group of classical or quantum channels
• Qudit non-Clifford interleaved benchmarking