L-entropy: A new genuine multipartite entanglement measure

TL;DR

This paper introduces L-entropy, a new measure for genuine multipartite entanglement in pure states, applicable to systems with finite and infinite degrees of freedom, and explores its properties and applications in quantum systems and wormholes.

Contribution

It proposes L-entropy as a genuine multipartite entanglement measure, analyzes its properties, and applies it to random states, wormholes, and finite-temperature multipartite systems.

Findings

L-entropy attains maximum for GHZ and 2-uniform states.

L-entropy satisfies all properties of a genuine multipartite entanglement measure.

Random states approximate 2-uniform states with maximal entanglement.

Abstract

We advance ``Latent entropy" (L-entropy) as a novel measure to characterize genuine multipartite entanglement in pure states, applicable to quantum systems with both finite and infinite degrees of freedom. This measure, derived from an upper bound on reflected entropy, attains its maximum for three-party GHZ states and $n=4,5$-party $2$-uniform states. We establish that it satisfies all essential properties of a genuine multipartite entanglement measure, including being a pure-state entanglement monotone. We further obtain an analogue of the Page curve by analyzing the behavior of L-entropy in multiboundary wormholes, emphasizing their connection to multipartite entanglement in random states. Specifically, for $n = 5$, we show that random states approximate $2$-uniform states, exhibiting maximal multipartite entanglement. Extending these ideas to finite temperatures, we introduce the Multipartite Thermal Pure Quantum (MTPQ) state, a generalization of the thermal pure quantum state to multipartite systems, and demonstrate that the entanglement structure in states of the multicopy SYK model exhibits finite-temperature $2$-uniform behavior.