Maximum entropy and approximate descriptions of pure states

N. Canosa, Angelo Plastino, R. Rossignoli

N. Canosa, R. Rossignoli, Angel Ricardo Plastino

Angel Ricardo Plastino, M. Casas, Angel Ricardo Plastino +1 more

Arguments of the Jaynes maximum entropy sort have proved to be surprisingly successful in providing one with approximate descriptions of pure states in a variety of scenarios, entirely bypassing any consideration of Schr\"odinger's equation. Thus far, however, the algorithm has been unable to incorporate input information concerning expectation values of complementary observables. We discuss here how to overcome this difficulty by recourse to diagonal hypervirial theorems.

A. K. Rajagopal, S. Teitler

Jaydeep Kumar Basak, Vinay Malvimat, Junggi Yoon

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.

N. Canosa, R. Rossignoli, Angelo Plastino