Bounds on quantum entanglement from Random Matrix Theory

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  • 27 March 2002
Abstract
Recent results [A. Lakshminarayan, Phys. Rev. E, vol.64, Page no. 036207 (2001)] indicate that it is not easy to dynamically create maximally entangled states. Chaos can lead to substantial entropy production thereby maximizing dynamical entanglement, which still falls short of maximality. We show that this dynamical bound is universal and depends only on the dimensions of the Hilbert spaces involved. This entails pointing out the universal distribution of the eigenvalues of the reduced density matrices that one can expect from a Random Matrix Theory (RMT) modeling of composite quantum chaotic systems. This distribution provides a statistical upper bound for the entanglement of formation of arbitrary time evolving and stationary states. We substantiate these conclusions with the help of a quantized chaotic coupled kicked top model.

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