Norihiro Iizuka

We study genuine multientropy as a diagnostic of multipartite entanglement in the toric code, which provides a controlled setting for probing multipartite structures in topologically ordered states. Our main question is whether genuine multientropy captures information that is not reducible to conventional lower-party entropic data, such as topological entanglement entropy. We first analyze toric-code ground states that admit a stabilizer-state description, where the relevant quantities can be evaluated exactly. We conjecture that, for stabilizer states and q ≥ 4 , the q -partite genuine multientropy at replica index n < q collapses to a linear combination of multientropies involving at most q − 2 parties. We establish this pattern explicitly for q = 4 in the toric code stabilizer sector: for n = 2 , 3, the genuine multientropy is proportional to the tripartite information I 3 and, for the Kitaev-Preskill partition, contains no independent genuine four-partite information beyond that captured by the topological entanglement entropy. At n = 4 , however, this reduction breaks down: the genuine multientropy is no longer proportional to I 3 , but remains a topological invariant of the toric-code stabilizer ground states under Kitaev-Preskill-preserving deformations that do not change whether the numbers of vertex- and plaquette-type junctions coincide. For generic nonstabilizer superpositions within the ground-state manifold and for coherent superpositions of local excitations, the low- n reduction also fails. These results show that genuine multientropy probes multipartite entanglement structure beyond the tripartite information, and hence beyond the topological entanglement entropy in the Kitaev-Preskill partition, whereas for stabilizer states at low replica index it reduces to lower-partite entropic data.

A bstract: We investigate how the junction law for multipartite entanglement is realized in confining holographic backgrounds, using genuine multi-entropy (GM) as our main diagnostic. We first study an AdS ₃ hard-wall toy model as an analytic benchmark, where multi-way cuts and junction geometries can be analyzed explicitly. In this setup, we classify the relevant saddles, determine the dominant phases, and show that the genuinely multipartite contribution diagnosed by GM is localized near the junction. We also examine how this structure depends on subsystem sizes, asymmetry, and the confinement scale, including phase transitions between competing saddles. We then move beyond the hard-wall benchmark to smooth confining geometries, focusing on the D4-soliton and D3-soliton backgrounds and formulating the corresponding framework also for the Klebanov-Strassler background. In the smooth-cap examples, we find that the junction picture persists, while the detailed phase structure differs from the hard-wall case: in particular, the hard-wall plateau does not survive, and GM instead decreases monotonically and vanishes at a finite critical scale. We also find that the short-distance behavior is background-dependent, with GM ⁽³⁾ ~ L ⁻⁴ in the D4-soliton background, GM ⁽³⁾ ~ L ⁻² in the D3-soliton background, and GM ⁽³⁾ ~ L ⁻² (log L ) ² in the Klebanov-Strassler background. These results clarify which features of the junction-law picture are robust in confining holography and which features of the phase structure and short-distance scaling are background-dependent.

We study the symmetry-resolved genuine multientropy, a measure that captures genuine multipartite entanglement, in Haar random states and random graph states in the presence of a conserved quantity. For Haar random states, we derive explicit formulas for the genuine multientropy under a global U ( 1 ) symmetry in the thermodynamic limit, and find that its dependence on subsystem sizes closely resembles that of fully Haar random states without a conserved charge. We also perform numerical analyses, focusing on spin systems for both Haar random and graph states. For random graph states, our numerical analyses reveal distinctive features of their multipartite entanglement structure and we contrast them with the Haar random case.

A bstract: The Markov gap, defined as the difference between reflected entropy and mutual information, serves as a diagnostic for quantum recoverability and multipartite entanglement. In holographic settings, it admits a geometric interpretation as the deviation between entanglement wedge cross-sections and RT surfaces. Motivated by this holographic perspective, we propose a generalization of the Markov gap to multipartite systems by using a reflected multi-entropy. The resulting Multipartite Markov gap can capture geometric obstructions to bulk reconstruction. We investigate the properties of this quantity from both information-theoretic and holographic viewpoints, and examine its potential operational significance through candidate recovery maps. We further introduce the genuine reflected multi-entropy, which is designed to vanish for states containing only lower-partite entanglement. Together, these quantities offer complementary probes of recoverability and multipartite structure in holographic quantum systems.

By generalizing the construction of genuine multientropy GM ( q ) for genuine multipartite entanglement proposed in the previous paper [Genuine multi-entropy and holography, .], we give a prescription on how to construct GM ( q ) systematically for any q . The crucial point is that our construction naturally fits to the partition number p ( a ) of integer a . For general q , GM ( q ) contains N ( q ) = p ( q ) − p ( q − 1 ) − 1 number of free parameters. Furthermore, these give N ( q ) + 1 number of new diagnostics for genuine q -partite entanglement. Especially for q = 4 case, this reproduces not only the known diagnostics pointed out by Balasubramanian [Multiboundary wormholes and holographic entanglement, .], but also a new diagnostics for quadripartite entanglement. We also study these GM ( q ) for q = 4 , 5 in holography and show that these are of the order of O ( 1 / G N ) both analytically and numerically. Our results give evidence that genuine multipartite entanglement is ubiquitous in holography. We discuss the connection to quantum error correction and the role of genuine multipartite entanglement in bulk reconstruction.

We explore a centaur geometry in Jackiw-Teitelboim gravity, which is an asymptotically anti–de Sitter (AdS) spacetime but in the IR admits a de Sitter (dS) bubble, with another AdS geometry in the deep IR. Thus, this geometry admits a holographic dual in the sense that it is asymptotically AdS. In an attempt to understand this geometry, we calculate the density of states of the putative boundary dual for such mixed geometries by evaluating the on-shell action. We compute the density of states analytically in the classical limit. The resultant density of states suggests that the degrees of freedom in the IR are reduced in such a putative boundary theory due to the IR modification corresponding to the dS bubble.

In quantum field theories that admit gravity dual, specific inequalities involving entanglement entropy between arbitrary disjoint spatial regions hold. An example is the negativity of tripartite information. Inspired by this, we investigate the analogous entropy inequalities in Sachdev-Ye-Kitaev (SYK) and sparse SYK models, which involve the entanglement among different flavors of Majorana fermions rather than spatial entanglement. Sparse SYK models are models where some of the SYK couplings are set to zero. Since these models have been argued to admit gravity duals up to a certain sparseness, it is interesting to see whether the multipartite entanglement structure changes in a sparseness-dependent manner. In the parameter space explored by our numerical analysis, which we performed upto five parties, we find that all entropy inequalities are satisfied for any temperature and degree of sparseness for an arbitrary choice of flavor subregions. In addition, if we plot the multipartite entanglement entropy in terms of purity, the only significant effect of sparseness is to change the range of purity. Thus, we conclude that multipartite information is almost unaffected by sparseness. As a counterexample, we also show that in a vector model of N-flavored Majorana fermions which contains no random variables, choices of subregions exist for which the entropy inequalities are violated.

We investigate the multi-partite entanglement structure of an evaporating black hole and its Hawking radiation by dividing the radiation into finer subsystems. We approximate an evaporating black hole and its radiation with a Haar-random state for this purpose. Using the multi-entropy of these configurations, we define a black hole multi-entropy curve, which describes how the multi-entropy changes during the black hole evaporation. This black hole multi-entropy curve is a natural generalization of the Page curve since the multi-entropy reduces to the entanglement entropy for the bi-partite case. The multi-entropy curve keeps increasing in the early time. It reaches the maximum value at the multi-entropy time, which is later than the Page time, and starts to decrease. However, it does not decrease to zero at the end of the black hole evaporation. This non-zero value of the multi-entropy represents the secret entanglement between Hawking particles.

We consider the thermal behavior of a large number of matrix degrees of freedom in the planar limit. We work in 0 + 1 dimensions, with D matrices, and use 1 / D as an expansion parameter. This can be thought of as a noncommutative large- D vector model, with two independent quartic couplings for the two different orderings of the matrices. We compute a thermal two-point correlator to O ( 1 / D ) and find that the degeneracy present at large D is lifted, with energy levels split by an amount ∼ 1 / D . This implies a timescale for thermal dissipation ∼ D . At high temperatures dissipation is predominantly due to one of the two quartic couplings. Published by the American Physical Society 2025

We explore a Centaur geometry in JT gravity, which is an asymptotically AdS spacetime but in the IR admits a dS bubble with another AdS geometry in the deep IR. Thus, this geometry admits a holographic dual in the sense that it is asymptotically AdS. In an attempt to understand this geometry, we calculate the density of states of the putative boundary dual for such mixed geometries by evaluating the on-shell action. We compute the density of states analytically in the classical limit. The resultant density of states suggest that the degrees of freedom in the IR are reduced in such a putative boundary theory due to the IR modification corresponding to the dS bubble.