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A<sc>bstract</sc> We propose a generalized protocol for constructing a dual free bulk theory from any boundary model of generalized free fields (GFFs). To construct the bulk operators, we employ a linear ansatz similar to the Hamilton-Kabat-Liftschytz-Lowe (HKLL) construction. However, unlike the HKLL construction, our protocol relies only on boundary data with no presupposed form for the bulk equations of motion, so our reconstructed bulk is fully emergent. For a (1+1)d bulk, imposing the bulk operator algebra as well as a causal structure is sufficient to determine the bulk operators and dynamics uniquely up to an unimportant local basis choice. We study the bulk construction for several two-sided SYK models with and without coupling between the two sides, and find good agreement with known results in the low-temperature conformal limit. In particular, we find bulk features consistent with the presence of a black hole horizon for the TFD state, and characterize the infalling fermion modes. We are also able to extract bulk quantities such as the curvature and bulk state correlators in terms of boundary quantities. In the presence of coupling between the two SYK models, we are able to observe evidence of the shockwave geometry and the traversable wormhole geometry using the two-sided mutual information between the reconstructed bulk operators. Our results show evidence that features of the geometric bulk can survive away from the low temperature conformal limit. Furthermore, the generality of the protocol allows it to be applied to other boundary theories with no canonical holographic bulk. 

This study presents a comprehensive analysis of three types of multimodal data‐response accuracy, response times, and eye‐tracking data‐derived from a computer‐based spatial rotation test. To tackle the complexity of high‐dimensional data analysis challenges, we have developed a methodological framework incorporating various statistical and machine learning methods. The results of our study reveal that hidden state transition probabilities, based on eye‐tracking features, may be contingent on skill mastery estimated from the fluency CDM model. The hidden state trajectory offers additional diagnostic insights into spatial rotation problem‐solving, surpassing the information provided by the fluency CDM alone. Furthermore, the distribution of participants across different hidden states reflects the intricate nature of visualizing objects in each item, adding a nuanced dimension to the characterization of item features. This complements the information obtained from item parameters in the fluency CDM model, which relies on response accuracy and response time. Our findings have the potential to pave the way for the development of new psychometric and statistical models capable of seamlessly integrating various types of multimodal data. This integrated approach promises more meaningful and interpretable results, with implications for advancing the understanding of cognitive processes involved in spatial rotation tests. 

A<sc>bstract</sc> The mutual information characterizes correlations between spatially separated regions of a system. Yet, in experiments we often measure dynamical correlations, which involve probing operators that are also separated in time. Here, we introduce a space-time generalization of mutual information which, by construction, satisfies several natural properties of the mutual information and at the same time characterizes correlations across subsystems that are separated in time. In particular, this quantity, that we call thespace-time mutual information, bounds all dynamical correlations. We construct this quantity based on the idea of the quantum hypothesis testing. As a by-product, our definition provides a transparent interpretation in terms of an experimentally accessible setup. We draw connections with other notions in quantum information theory, such as quantum channel discrimination. Finally, we study the behavior of the space-time mutual information in several settings and contrast its long-time behavior in many-body localizing and thermalizing systems. 

A bstract Holevo information is an upper bound for the accessible classical information of an ensemble of quantum states. In this work, we use Holevo information to investigate the ensemble theory interpretation of quantum gravity. We study the Holevo information in random tensor network states, where the random parameters are the random tensors at each vertex. Based on the results in random tensor network models, we propose a conjecture on the holographic bulk formula of the Holevo information in the gravity case. As concrete examples of holographic systems, we compute the Holevo information in the ensemble of thermal states and thermo-field double states in the Sachdev-Ye-Kitaev model. The results are consistent with our conjecture. 

A bstract Since the work of Ryu and Takayanagi, deep connections between quantum entanglement and spacetime geometry have been revealed. The negative eigenvalues of the partial transpose of a bipartite density operator is a useful diagnostic of entanglement. In this paper, we discuss the properties of the associated entanglement negativity and its Rényi generalizations in holographic duality. We first review the definition of the Rényi negativities, which contain the familiar logarithmic negativity as a special case. We then study these quantities in the random tensor network model and rigorously derive their large bond dimension asymptotics. Finally, we study entanglement negativity in holographic theories with a gravity dual, where we find that Rényi negativities are often dominated by bulk solutions that break the replica symmetry. From these replica symmetry breaking solutions, we derive general expressions for Rényi negativities and their special limits including the logarithmic negativity. In fixed-area states, these general expressions simplify dramatically and agree precisely with our results in the random tensor network model. This provides a concrete setting for further studying the implications of replica symmetry breaking in holography. 

A bstract The study of quantum gravity in the form of the holographic duality has uncovered and motivated the detailed investigation of various diagnostics of quantum chaos. One such measure is the operator size distribution, which characterizes the size of the support region of an operator and its evolution under Heisenberg evolution. In this work, we examine the role of the operator size distribution in holographic duality for the Sachdev-Ye-Kitaev (SYK) model. Using an explicit construction of AdS 2 bulk fermion operators in a putative dual of the low temperature SYK model, we study the operator size distribution of the boundary and bulk fermions. Our result provides a direct derivation of the relationship between (effective) operator size of both the boundary and bulk fermions and bulk SL(2; ℝ) generators.