Generalized Entanglement Entropies of Quantum Designs - Kölner UniversitätsPublikationsServer

Liu, Zi-Wen, Lloyd, Seth, Zhu, Elton Yechao and Zhu, Huangjun (2018). Generalized Entanglement Entropies of Quantum Designs. Phys. Rev. Lett., 120 (13). COLLEGE PK: AMER PHYSICAL SOC. ISSN 1079-7114

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DOI:10.1103/PhysRevLett.120.130502

Abstract

The entanglement properties of random quantum states or dynamics are important to the study of a broad spectrum of disciplines of physics, ranging from quantum information to high energy and many-body physics. This Letter investigates the interplay between the degrees of entanglement and randomness in pure states and unitary channels. We reveal strong connections between designs (distributions of states or unitaries that match certain moments of the uniform Haar measure) and generalized entropies (entropic functions that depend on certain powers of the density operator), by showing that Renyi entanglement entropies averaged over designs of the same order are almost maximal. This strengthens the celebrated Page's theorem. Moreover, we find that designs of an order that is logarithmic in the dimension maximize all Renyi entanglement entropies and so are completely random in terms of the entanglement spectrum. Our results relate the behaviors of Renyi entanglement entropies to the complexity of scrambling and quantum chaos in terms of the degree of randomness, and suggest a generalization of the fast scrambling conjecture.

Item Type:

Journal Article

Creators:

Creators	Email	ORCID	ORCID Put Code
Liu, Zi-Wen	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED
Lloyd, Seth	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED
Zhu, Elton Yechao	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED
Zhu, Huangjun	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED