Related papers: Quantum complexity and generalized area law in ful…
The area law for entanglement provides one of the most important connections between information theory and quantum many-body physics. It is not only related to the universality of quantum phases, but also to efficient numerical simulations…
It is commonly believed that area laws for entanglement entropies imply that a quantum many-body state can be faithfully represented by efficient tensor network states - a conjecture frequently stated in the context of numerical simulations…
Random pure states of multi-partite quantum systems, associated with arbitrary graphs, are investigated. Each vertex of the graph represents a generic interaction between subsystems, described by a random unitary matrix distributed…
Physical interactions in quantum many-body systems are typically local: Individual constituents interact mainly with their few nearest neighbors. This locality of interactions is inherited by a decay of correlation functions, but also…
The entanglement entropy of the ground state of a quantum lattice model with local interactions usually satisfies an area law. However, in 1D systems some violations may appear in inhomogeneous systems or in random systems. In our…
Area laws describe how entanglement entropy scales and thus provide important necessary conditions for efficient quantum many-body simulation, but they do not, by themselves, yield a direct measure of computational complexity. Here we…
In this work, we make a connection between two seemingly different problems. The first problem involves characterizing the properties of entanglement in the ground state of gapped local Hamiltonians, which is a central topic in quantum…
Suppose we would like to approximate all local properties of a quantum many-body state to accuracy $\delta$. In one dimension, we prove that an area law for the Renyi entanglement entropy $R_\alpha$ with index $\alpha<1$ implies a matrix…
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…
The area law-like scaling of local quantum entropies is the central characteristic of the entanglement inherent in quantum fields, many-body systems, and spacetime. Whilst the area law is primarily associated with the entanglement structure…
Entanglement entropy quantifies the amount of uncertainty of a quantum state. For quantum fields in curved space, entanglement entropy of the quantum field theory degrees of freedom is well-defined for a fixed background geometry. In this…
We demonstrate that the entropy of entanglement and the distillable entanglement of regions with respect to the rest of a general harmonic lattice system in the ground or a thermal state scale at most as the boundary area of the region.…
We consider the relationship between correlations and entanglement in gapped quantum systems, with application to matrix product state representations. We prove that there exist gapped one-dimensional local Hamiltonians such that the…
An area law is proved for the Renyi entanglement entropy of possibly degenerate ground states in one-dimensional gapped quantum systems. Suppose in a chain of $n$ spins the ground states of a local Hamiltonian with energy gap $\epsilon$ are…
We give a detailed physical argument for the area law for entanglement entropy in gapped phases of matter arising from local Hamiltonians. Our approach is based on renormalization group (RG) ideas and takes a resource oriented perspective.…
Quantum Hamiltonian complexity studies computational complexity aspects of local Hamiltonians and ground states; these questions can be viewed as generalizations of classical computational complexity problems related to local constraint…
This review focuses on the field of quantum entanglement applied to condensed matter physics systems with strong correlations, a domain which has rapidly grown over the last decade. By tracing out part of the degrees of freedom of…
For pure states of multi-dimensional quantum lattice systems, which in a convenient computational basis have amplitude and phase structure of sufficiently rapid decorrelation, we construct high fidelity approximations of relatively low…
A general geometrical structure of the entanglement entropy for spatial partition of a relativistic QFT system is established by using methods of the effective gravity action and the spectral geometry. A special attention is payed to the…
The entanglement area law is a universal principle that characterizes the information structure in quantum many-body systems and serves as the foundation for modern algorithms based on tensor network representations. Historically, the area…