Induced Ginibre ensemble of random matrices and quantum operations

Abstract

A generalisation of the Ginibre ensemble of non-Hermitian random square matrices is introduced. The corresponding probability measure is induced by the ensemble of rectangular Gaussian matrices via a quadratisation procedure. We derive the joint probability density of eigenvalues for such induced Ginibre ensemble and study various spectral correlation functions for complex and real matrices, and analyse universal behaviour in the limit of large dimensions. In this limit the eigenvalues of the induced Ginibre ensemble cover uniformly a ring in the complex plane. The real induced Ginibre ensemble is shown to be useful to describe statistical properties of evolution operators associated with random quantum operations, for which the dimensions of the input state and the output state do differ.

2nd version, 34 pages, 5 figures

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• Products of Independent Quaternion Ginibre Matrices and their Correlation Functions
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• Analogies between random matrix ensembles and the one-component plasma in two-dimensions
• Probing non-orthogonality of eigenvectors in non-Hermitian matrix models: diagrammatic approach
• Characteristic polynomials of complex random matrices and Painlevé transcendents
• Statistical limits of dictionary learning: random matrix theory and the spectral replica method
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• Dropping the independence: singular values for products of two coupled random matrices
• Multiplicative Convolution of Real Asymmetric and Real Antisymmetric Matrices
• Skew-orthogonal polynomials in the complex plane and their Bergman-like kernels
• Universality of the number variance in rotational invariant two-dimensional Coulomb gases
• The Probability That All Eigenvalues are Real for Products of Truncated Real Orthogonal Random Matrices
• Quantum Chaos and Coherence: Random Parametric Quantum Channels
• Exponential moments for disk counting statistics of random normal matrices in the critical regime
• Universal eigenvector correlations in quaternionic Ginibre ensembles
• Scaling Limits of Planar Symplectic Ensembles
• Wronskian structures of planar symplectic ensembles
• Skew orthogonal polynomials for the real and quaternion real Ginibre ensembles and generalizations
• Singular values for products of two coupled random matrices: hard edge phase transition
• Spherical Induced Ensembles with Symplectic Symmetry
• Products of random matrices from fixed trace and induced Ginibre ensembles
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• Universal spectral correlations in ensembles of random normal matrices
• Product matrix processes for coupled multi-matrix models and their hard edge scaling limits
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• Universality for products of random matrices I: Ginibre and truncated unitary cases
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