Entanglement of random vectors

Abstract

We analytically calculate the average value of i-th largest Schmidt coefficient for random pure quantum states. Schmidt coefficients, i.e., eigenvalues of the reduced density matrix, are expressed in the limit of large Hilbert space size and for arbitrary bipartite splitting as an implicit function of index i.

8 pages

References in corpus (14)

• Efficient classical simulation of slightly entangled quantum computations
• Level-Spacing Distributions and the Airy Kernel
• Average Entropy of a Subsystem
• On Orthogonal and Symplectic Matrix Ensembles
• Induced measures in the space of mixed quantum states
• Aspects of generic entanglement
• Random Quantum Circuits and Pseudo-Random Operators: Theory and Applications
• Average Entropy of a Subsystem
• Is efficiency of classical simulations of quantum dynamics related to integrability?
• Statistical properties of random density matrices
• Efficient Generation of Generic Entanglement
• Convergence Conditions for Random Quantum Circuits
• Bounds on entanglement in qudit subsystems
• Entanglement Generation of Nearly-Random Operators

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