A New Genuine Multipartite Entanglement Measure from Reflected Entropy
ABSTRACT
Bipartite entanglement has been extensively studied using measures such as entanglement entropy and entanglement negativity. In contrast, the notion of multipartite entanglement remains a more intricate and nuanced concept, and holds immense significance for quantum teleportation and quantum communication. Existing measures in the literature are often limited in scope, primarily applicable to systems with a small number of qubits. In this talk, I will introduce a novel measure, termed Latent Entropy (L-entropy), designed to characterize genuine multipartite entanglement. This measure offers broad applicability, extending to many-body systems, quantum field theories, and holography. Leveraging the upper bound of reflected entropy, L-entropy attains maximal values for GHZ states in 3-party systems and 2-uniform states in the n-party systems ( for n≥4 ). I will demonstrate how L-entropy serves as a robust multipartite pure state entanglement monotone and discuss its potential extension to mixed multipartite states. Additionally, I will explore its intriguing properties in spin chain models, Haar random states, and the Sachdev-Ye-Kitaev (SYK) model, highlighting its relevance to complex quantum systems.The talk will conclude with the implications of L-entropy in holography, emphasizing its role in uncovering the multipartite entanglement structure of conformal field theories (CFTs) dual to multi-boundary wormholes.