Related papers: Multi-entropy from Linking in Chern-Simons Theory

We investigate the generation of multipartite entangled state in a system of N quantum dots embedded in a microcavity and examine the emergence of genuine multipartite entanglement by three different characterizations of entanglement. At…

Quantum correlations are a vital resource in advanced information processing based on quantum phenomena. Remarkably, the vacuum state of a quantum field may act as a key element for the generation of multipartite quantum entanglement. In…

Entanglement in high-dimensional many-body systems plays an increasingly vital role in the foundations and applications of quantum physics. In the present paper, we introduce a theoretical concept which allows to categorize multipartite…

We compute directly the entanglement entropy of spatial regions in Chern-Simons gauge theories in 2+1 dimensions using surgery. We use these results to determine the universal topological piece of the entanglement entropy for Abelian and…

We show how to quantify tri-partite entanglement using entropies derived from experimental correlations. We use a multi-partite generalization of the entanglement of formation that is greater than zero if and only if the state is genuinely…

We classify multipartite entangled states in the 2 x 2 x n (n >= 4) quantum system, for example the 4-qubit system distributed over 3 parties, under local filtering operations. We show that there exist nine essentially different classes of…

Given a finite group G with a bilocal representation, we investigate the bipartite entanglement in the state constructed from the group algebra of G acting on a separable reference state. We find an upper bound for the von Neumann entropy…

Multi-invariants are local-unitary invariants of state replicas introduced as potential probes of multipartite entanglement and correlations in quantum many-body systems. In this paper, we investigate two multi-invariants for tripartite…

We study Chern-Simons theory on 3-manifolds M that are circle-bundles over 2-dimensional orbifolds S by the method of Abelianisation. This method, which completely sidesteps the issue of having to integrate over the moduli space of…

We develop a universal approximation for the Renyi entropies of a pure state at late times in a non-integrable many-body system, which macroscopically resembles an equilibrium density matrix. The resulting expressions are fully determined…

Following the method of Seifert surfaces in knot theory, we define arithmetic linking numbers and height pairings of ideals using arithmetic duality theorems, and compute them in terms of n-th power residue symbols. This formalism leads to…

We present a package of mathematical theorems, which allow to construct multipartite entanglement criteria. Importantly, establishing bounds for certain classes of entanglement does not take an optimization over continuous sets of states.…

We lay down a general framework for how to construct a Topological Quantum Field Theory $Z_A$ defined on shaped triangulations of orientable 3-manifolds from any Pontryagin self-dual locally compact abelian group $A$. The partition function…

Following on our previous work arXiv:2204.07593 and arXiv:2306.01043 studying the orbits of quantum states under Clifford circuits via `reachability graphs', we introduce `contracted graphs' whose vertices represent classes of quantum…

Understanding how complex entanglement structures emerge is a central problem in quantum many-body physics. Recent work by Zhang et al. has considered structured initial states prepared by evolving a product state under a chaotic…

We give an introduction to the theory of multi-partite entanglement. We begin by describing the "coordinate system" of the field: Are we dealing with pure or mixed states, with single or multiple copies, what notion of "locality" is being…

We consider Chern-Simons theory with complex gauge group and present a complete non-perturbative evaluation of the path integral (the partition function and certain expectation values of Wilson loops) on Seifert fibred 3-Manifolds. We use…

Entanglement is a unique nature of quantum theory and has tremendous potential for application. Nevertheless, the complexity of quantum entanglement grows exponentially with an increase in the number of entangled particles. Here we…

With any state of a multipartite quantum system its separability polytope is associated. This is an algebro-topological object (non-trivial only for mixed states) which captures the localisation of entanglement of the state. Particular…

We use the topological quantum field theory description of states in Chern-Simons theory to discuss the relation between spacetime connectivity and entanglement, exploring the paradigm entanglement=topology. We define a special class of…