Random matrix techniques in quantum information theory

Abstract

The purpose of this review article is to present some of the latest developments using random techniques, and in particular, random matrix techniques in quantum information theory. Our review is a blend of a rather exhaustive review, combined with more detailed examples -- coming from research projects in which the authors were involved. We focus on two main topics, random quantum states and random quantum channels. We present results related to entropic quantities, entanglement of typical states, entanglement thresholds, the output set of quantum channels, and violations of the minimum output entropy of random channels.

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• The Weingarten Calculus
• Generating random quantum channels
• Random generators of Markovian evolution: A quantum-classical transition by superdecoherence
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• Observation of entanglement negativity transition of pseudo-random mixed states
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• A graphical calculus for integration over random diagonal unitary matrices
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• Random density matrices: Analytical results for mean root fidelity and mean square Bures distance
• Single-Particle Universality of the Many-Body Spectral Form Factor
• Free Independence and the Noncrossing Partition Lattice in Dual-Unitary Quantum Circuits
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• On the spectral gap of random quantum channels
• Random density matrices: Analytical results for mean fidelity and variance of squared Bures distance
• On the joint distribution of the marginals of multipartite random quantum states
• Complete diagrammatics of the single ring theorem
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• Thesis: Tensor networks for dynamic spacetimes
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• Moment Methods on compact groups: Weingarten calculus and its applications
• Nearly query-optimal classical shadow estimation of unitary channels
• Generating random Gaussian states
• Uncorrelated problem-specific samples of quantum states from zero-mean Wishart distributions
• Onset of universality in the dynamical mixing of a pure state
• Bridging Classical and Quantum Information Scrambling with the Operator Entanglement Spectrum
• Markov Gap and Bound Entanglement in Haar Random State
• Critical Dynamics of the Anderson Transition on Small-World Graphs
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• Estimating the entanglement of random multipartite quantum states
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• Asymptotic resolvents of a product of two marginals of a random tensor
• Gelfand-Tsetlin polytopes and random contractions away from the limiting shapes
• Quantum Skyrmions in Mixed States of Light and Their Nested Topology
• Crystalline Spectral Form Factors
• Moments of Quantum Channel Ensembles
• Van Hove singularities in stabilizer entropy densities