相关论文: Highly entangled tensors
We study the entanglement of a two-qubit one dimensional XYZ Heisenberg chain in thermal equilibrium at temperature T. We obtain an analytical expression for the entanglement of formation for this system in terms of the parameters of the…
We study the entanglement properties of a higher-integer-spin Affleck-Kennedy-Lieb-Tasaki model with quantum group symmetry in the periodic boundary condition. We exactly calculate the finite size correction terms of the entanglement…
We propose the definition of the geometric measure of entanglement for continuous variable states. On the basis of this definition we examine entanglement of the graph states obtained as a result of action of a unitary operator on the…
Let $L$ be a holomorphic line bundle on a compact complex manifold $X$ of dimension $n,$ and let $e^{-\phi}$ be a continuous metric on $L.$ Fixing a measure $d\mu$ on $X$ gives a sequence of Hilbert spaces consisting of holomorphic sections…
What is the relation between spin squeezing and entanglement? To clarify this, we derive the full set of generalized spin squeezing inequalities for the detection of entanglement. These are inequalities for the mean values and variances of…
The geometric measure of entanglement $E$ of an $m$ qubit quantum state takes maximal possible value $m$. In previous work of Gross, Flammia, and Eisert, it was shown that $E \ge m-O(\log m)$ with high probability as $m\to\infty$. They…
Entropic entanglement measures of a two-dimensional system of two Coulombically interacting particles confined in an anisotropic harmonic potential are discussed in dependence on the anisotropy and the interaction strength. The harmonic…
The rank of a tensor is analyzed in context of quantum entanglement. A pure quantum state $\bf v$ of a composite system consisting of $d$ subsystems with $n$ levels each is viewed as a vector in the $d$-fold tensor product of…
We study the detection of continuous-variable entanglement, for which most of the existing methods designed so far require a full specification of the devices, and we present protocols for entanglement detection in a scenario where the…
Despite significant progress in experimental quantum sciences, measuring entanglement entropy remains challenging. Through a geometric perspective, we reveal the intrinsic anti-symmetric nature of entanglement. We prove that most…
The entanglement entropy of a generic $d$-dimensional conformal field theory receives a regulator independent contribution when the entangling region contains a (hyper)conical singularity of opening angle $\Omega$, codified in a function…
We propose a simple generalization of the matrix resolvent to a resolvent for real symmetric tensors $T\in \otimes^p \mathbb{R}^N$ of order $p\ge 3$. The tensor resolvent yields an integral representation for a class of tensor invariants…
In this paper we present the novel qualities of entanglement of formation for general (so also infinite dimensional) quantum systems. A major benefit of our presentation is a rigorous description of entanglement of formation. In particular,…
By analogy with conjectures for random matrices, Fyodorov-Hiary-Keating and Fyodorov-Keating proposed precise asymptotics for the maximum of the Riemann zeta function in a typical short interval on the critical line. In this paper, we…
We report about the state of the art on complex and real generic identifiability of tensors, we describe some of our recent results obtained in [6] and we present perspectives on the subject.
We calculate one, two and three point functions of the holographic stress tensor for any bulk Lagrangian of the form ${\mathcal{L}}(g^{ab}, R_{abcd}, \nabla_e R_{abcd})$. Using the first law of entanglement, a simple method has recently…
We study the Von Neumann and R\'enyi entanglement entropy of long-range harmonic oscillators (LRHO) by both theoretical and numerical means. We show that the entanglement entropy in massless harmonic oscillators increases logarithmically…
The class of local invertible operations is defined and the invariance of entanglement under such operations is established. For the quantification of entanglement, universal entanglement measures are defined, which are invariant under…
Entanglement, which is an essential characteristic of quantum mechanics, is the key element in potential practical quantum information and quantum communication systems. However, there are many open and fundamental questions (relating to…
This paper studies nuclear norms of symmetric tensors. As recently shown by Friedland and Lim, the nuclear norm of a symmetric tensor can be achieved at a symmetric decomposition. We discuss how to compute symmetric tensor nuclear norms,…