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After a brief introduction to the concept of entanglement in quantum systems, I apply these ideas to many-body systems and show that the von Neumann entropy is an effective way of characterising the entanglement between the degrees of…
Topological order comes in different forms, and its classification and detection is an important field of modern research. In this work, we show that the Disconnected Entanglement Entropy, a measure originally introduced to identify…
The entanglement entropy of the incompressible states of a realistic quantum Hall system in the second Landau level are studied by direct diagonalization. The subdominant term to the area law, the topological entanglement entropy, which is…
We define a notion of target space entanglement entropy. Rather than partitioning the base space on which the theory is defined, we consider partitions of the target space. This is the physical case of interest for first-quantized theories,…
In gravitational theories with boundaries, diffeomorphisms can become physical and acquire a non-vanishing Noether charge. Using the covariant phase space formalism, on shell of the gravitational constraints, the latter localizes on…
Motivated to understand how entanglement resources can be distributed in quantum networks, we introduce threshold entanglement (TE) states. These are multipartite quantum states whose entanglement across bipartitions forces all marginals of…
In this article we consider physical states in the hypercuboidal truncation of the EPRL-FK spin foam quantum gravity model. In particular, these states are defined on graphs which allow considering the entanglement entropy (EE) associated…
The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement is explored for bi-partite and multi-partite pure and mixed states.…
The properties of the entanglement entropy (EE) of a clean Cayley tree (CT) are studied. The EE shows a completely different behaviour depending on the way the CT is partitioned into two regions and whether we consider the ground-state or…
Quantum systems with short range interactions are known to respect an area law for the entanglement entropy: the von Neumann entropy $S$ associated to a bipartition scales with the boundary $p$ between the two parts. Here we study the case…
The entanglement entropy of a pure quantum state of a bipartite system $A \cup B$ is defined as the von Neumann entropy of the reduced density matrix obtained by tracing over one of the two parts. Critical ground states of local…
The non-Abelian topological order has attracted a lot of attention for its fundamental importance and exciting prospect of topological quantum computation. However, explicit demonstration or identification of the non-Abelian states and the…
We elaborate on a previous proposal by Hartman and Maldacena on a tensor network which accounts for the scaling of the entanglement entropy in a system at a finite temperature. In this construction, the ordinary entanglement renormalization…
We perform a comprehensive analysis of the symmetry-resolved (SR) entanglement entropy (EE) for one single interval in the ground state of a $1+1$D conformal field theory (CFT), that is invariant under an arbitrary finite or compact Lie…
Quantum entanglement of pure states of a bipartite system is defined as the amount of local or marginal ({\em i.e.}referring to the subsystems) entropy. For mixed states this identification vanishes, since the global loss of information…
We investigate the diagonal entropy for ground states of the extended Kitaev chains with extensive pairing and hopping terms. The systems contain rich topological phases equivalently represented by topological invariant winding numbers and…
Entanglement entropy (EE) is widely used to quantify quantum correlations in field theory, with the well-known result in two-dimensional conformal field theory (CFT) predicting a logarithmic divergence with the ultraviolet (UV) cutoff.…
We define a new complex-valued measure of information called the timelike entanglement entropy (EE) which in the boundary theory can be viewed as a Wick rotation that changes a spacelike boundary subregion to a timelike one. An explicit…
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…
We show that the entropy of entanglement is sensitive to the coherent quantum phase transition between normal and super-radiant regions of a system of a finite number of three-level atoms interacting in a dipolar approximation with a…