Related papers: Background independent tensor networks
Hierarchical networks actually have many applications in the real world. Firstly, we propose a new class of hierarchical networks with scale-free and fractal structure, which are the networks with triangles compared to traditional…
We construct and analyze holographic superconductors with generalized higher derivative couplings, in single R-charged black hole backgrounds in four and five dimensions. These systems, which we call very general holographic…
In this paper, we present the construction of tensor network states (TNS) for some of the degenerate ground states of 3D stabilizer codes. We then use the TNS formalism to obtain the entanglement spectrum and entropy of these ground-states…
We define bulk/boundary maps corresponding to quantum gravity states in the tensorial group field theory formalism, for quantum geometric models sharing the same type of quantum states of loop quantum gravity. The maps are defined in terms…
We study the holographic properties of a class of quantum geometry states characterized by a superposition of discrete geometric data, in the form of generalised tensor networks. This class specifically includes spin networks, the kinematic…
Quantum entanglement -- correlations of particles that are stronger than any classical analogue -- is the basis for research on the foundations of quantum mechanics and for practical applications such as quantum networks. Traditionally,…
We explore the structure of holographic entropy relations (associated with 'information quantities' given by a linear combination of entanglement entropies of spatial sub-partitions of a CFT state with geometric bulk dual). Such entropy…
We present a general procedure for constructing tensor networks for geometric states in the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence. Given a state in a large-$N$ CFT with a static, semiclassical gravitational dual,…
The hypergraph states are pure multipartite quantum states corresponding to a hypergraph. It is an equal superposition of the states belonging to the computational basis. Given any hypergraph, we can construct a hypergraph state determined…
We develop a strategy for tensor network algorithms that allows to deal very efficiently with lattices of high connectivity. The basic idea is to fine-grain the physical degrees of freedom, i.e., decompose them into more fundamental units…
Inspired by holographic codes and tensor-network decoders, we introduce tensor-network stabilizer codes which come with a natural tensor-network decoder. These codes can correspond to any geometry, but, as a special case, we generalize…
An algorithm is described for the construction of actions for scalar, spinor, and vector gauge fields that remains well-defined when the metric is degenerate and that involve no contravariant tensor fields. These actions produce the…
This dissertation reviews several recent advances at the intersection of quantum information and holography. In holography, properties of quantum systems admit a gravitational interpretation via the AdS/CFT correspondence. For holographic…
This paper discusses ER = EPR, the hypothesis of Susskind and Maldacena that entangled black holes are connected by an Einstein-Rosen bridge, and that more generally, quantum entanglement is accompanied by topological connectivity. Given a…
The many-body entanglement between two finite (size-$d$) disjoint vacuum regions of non-interacting lattice scalar field theory in one spatial dimension -- a $(d_A \times d_B)_{\rm mixed}$ Gaussian continuous variable system -- is locally…
Tensor network states form a variational ansatz class widely used, both analytically and numerically, in the study of quantum many-body systems. It is known that if the underlying graph contains a cycle, e.g. as in projected entangled pair…
Negativity is a measure of entanglement that can be used both in pure and mixed states. The negativity spectrum is the spectrum of eigenvalues of the partially transposed density matrix, and characterizes the degree and "phase" of…
We study the entanglement entropy of a random tensor network (RTN) using tools from free probability theory. Random tensor networks are simple toy models that help the understanding of the entanglement behavior of a boundary region in the…
Large-scale quantum networks, necessary for distributed quantum information processing, are posited to have quantum entangled systems between distant network nodes. The extent and quality of distributed entanglement in a quantum network,…
We provide an explicit connection between the differential generation of entanglement entropy in a tensor network representation of the ground states of two field theories, and a geometric description of these states based on the Fisher…