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Entanglement detection is an important problem in quantum information theory because quantum entanglement is a key resource in quantum information processing. Realignment criteria is a powerful tool for detection of entangled states in…
We introduce a generalized two-dimensional orbital compass model, which interpolates continuously from the classical Ising model to the orbital compass model with frustrated quantum interactions, and investigate it using the multiscale…
Special approximation technique for analysis of different characteristics of states of multipartite infinite-dimensional quantum systems is proposed and applied to study of the relative entropy of entanglement and its regularisation. We…
The 1-form symmetry, manifesting as loop-like symmetries, has gained prominence in the study of quantum phases, deepening our understanding of symmetry. However, the role of 1-form symmetries in Projected Entangled-Pair States (PEPS),…
Projected Entangled Pair States (PEPS) are used in practice as an efficient parametrization of the set of ground states of quantum many body systems. The aim of this paper is to present, for a broad mathematical audience, some mathematical…
In recent years, tensor network states have emerged as a very useful conceptual and simulation framework to study quantum many-body systems at low energies. In this paper, we describe a particular way in which any given tensor network can…
The Minimally Entangled Typical Thermal States (METTS) are an ensemble of pure states, equivalent to the Gibbs thermal state, that can be efficiently represented by tensor networks. In this article, we use the Projected Entangled Pair…
We study entanglement and other correlation properties of random states in high-dimensional bipartite systems. These correlations are quantified by parameters that are subject to the "concentration of measure" phenomenon, meaning that on a…
(Presented at conference on Fundamental Problems in Physics - UMBC - June 1994) It is shown that among the orthogonal sets of EPR (completely entangled) states there is a unique basis (up to equivalence) that is a also a perfectly resolved…
Quantum systems prepared in pure states evolve into mixtures under environmental action. Physically realizable ensembles are the pure state decompositions of those mixtures that can be generated in time through continuous measurements of…
We have discussed the tensor-network representation of classical statistical or interacting quantum lattice models, and given a comprehensive introduction to the numerical methods we recently proposed for studying the tensor-network…
A remarkable feature of typical ground states of strongly-correlated many-body systems is that the entanglement entropy is not an extensive quantity. In one dimension, there exists a proof that a finite correlation length sets a constant…
A natural way to generalise tensor network variational classes to quantum field systems is via a continuous tensor contraction. This approach is first illustrated for the class of quantum field states known as continuous matrix-product…
Absolutely maximally entangled (AME) states are typically defined in homogeneous systems. However, the quantum system is more likely to be heterogeneous in a practical setup. In this work we pay attention to the construction of AME states…
We reconstruct a matrix product state (MPS) in reduced spaces using density matrix. This scheme applies to a MPS built on a blocked quantum lattice. Each block contains $N$ physical sites that have a local space of rank $R$. The simulation…
The norms or expectation values of infinite projected entangled-pair states (PEPS) cannot be computed exactly, and approximation algorithms have to be applied. In the last years, many efficient algorithms have been devised -- the corner…
In the holographic correspondence of quantum gravity, a global onsite symmetry at the boundary generally translates to a local gauge symmetry in the bulk. We describe one way how the global boundary onsite symmetries can be gauged within…
The advent of quantum computers promises exponential speed ups in the execution of various computational tasks. While their capabilities are hindered by quantum decoherence, they can be exactly simulated on classical hardware at the cost of…
We consider the entanglement marginal problem, which consists of deciding whether a number of reduced density matrices are compatible with an overall separable quantum state. To tackle this problem, we propose hierarchies of semidefinite…
Every Maximally Entangled State (MES) of two d-dimensional particles is shown to be a product state of suitably chosen collective coordinates. The state may be viewed as defining a "point" in a "phase space" like d^2 array representing d^2…