L-entropy: A new genuine multipartite entanglement measure

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.

💡 Research Summary

The paper introduces “latent entropy” (L‑entropy) as a novel genuine multipartite entanglement (GME) measure for pure quantum states, applicable to both finite‑dimensional systems and those with infinitely many degrees of freedom (e.g., QFTs, CFTs, holography). The construction starts from reflected entropy S_R(A:B), an information‑theoretic quantity defined by purifying a bipartite mixed state on a doubled Hilbert space and taking the von‑Neumann entropy of one of the doubled subsystems. Reflected entropy obeys the bound I(A:B) ≤ S_R(A:B) ≤ min{2S(A), 2S(B)}. The authors define a bipartite “gap”
ℓ_{AB}=min{2S(A), 2S(B)}−S_R(A:B) ≥ 0,
and then aggregate these gaps over all unordered pairs of parties to obtain the multipartite L‑entropy:
ℓ_{A₁…A_n}= (∏{i<j}ℓ{A_iA_j})^{2/