A New Genuine Multipartite Entanglement Measure: from Qubits to Multiboundary Wormholes

Abstract We introduce the latent entropy (L-entropy) as a novel measure to characterize the genuine multipartite entanglement in quantum systems. Our measure leverages the upper bound of reflected entropy and its maximal values attained by 2-uniform states for n-party ($n= 4,5$) and by the GHZ state for 3-party quantum systems. We demonstrate that the measure is a nonnegative, local unitary invariant function that vanishes for separable states. We then analyze its interesting characteristics in spin chain models and the Sachdev–Ye–Kitaev (SYK) model. Subsequently, we explore its implications for holography by deriving a Page-like curve for the L-entropy in the conformal field theory (CFT) dual to a multiboundary wormhole model. Furthermore, we examine the behavior of L-entropy in Haar random states, deriving analytical expressions and validating them against numerical results. In particular, we show that for $n =5$, random states approximate 2-uniform states with maximal multipartite entanglement. Furthermore, we propose a potential connection between random states and multiboundary wormhole geometries. Extending to finite-temperature systems, we introduce the multipartite thermal pure quantum (MTPQ) state, a multipartite generalization of the thermal pure quantum state, and explore its entanglement properties. By incorporating the state-dependent construction of the MTPQ state, we resolve the factorization issue in the random average of the MTPQ state, ensuring consistency with the correlation functions in the holographic dual multiboundary wormhole. Finally, we apply this construction to the multicopy SYK model and examine its multipartite entanglement structure.