Tensor eigenvalues and entanglement of symmetric states
arXiv:1608.03537 · doi:10.1103/PhysRevA.94.042324
Abstract
Tensor eigenvalues and eigenvectors have been introduced in the recent mathematical literature as a generalization of the usual matrix eigenvalues and eigenvectors. We apply this formalism to a tensor that describes a multipartite symmetric state or a spin state, and we investigate to what extent the corresponding tensor eigenvalues contain information about the multipartite entanglement (or, equivalently, the classicality) of the state. This extends previous results connecting entanglement to spectral properties related to the state. While for spin-1 states the positivity of the smallest tensor eigenvalue is equivalent to separability, we show that for higher values of the angular momentum there is a correlation between entanglement and the value of the smallest tensor eigenvalue.
arXiv comment9 pages, 5 figures
References in corpus (22)
- A computable measure of entanglement
- Positive Wigner functions render classical simulation of quantum computation efficient
- Universal Quantum Estimator
- Direct estimations of linear and non-linear functionals of a quantum state
- Largest separable balls around the maximally mixed bipartite quantum state
- Maximally entangled mixed states of two qubits
- Geometry of entangled states
- Generating random density matrices
- Entanglement and permutational symmetry
- The geometric measure of entanglement for symmetric states
- Detection of multipartite entanglement in the vicinity of symmetric Dicke states
- Multiqubit symmetric states with high geometric entanglement
- The maximally entangled symmetric state in terms of the geometric measure
- Classicality of spin states
- Quantifying Quantumness and the Quest for Queens of Quantum
- Characterizing multiparticle entanglement in symmetric N-qubit states via negativity of covariance matrices
- Separability from Spectrum for Qubit-Qudit States
- PPT from spectra
- Tensor Representation of Spin States
- Witness of mixed separable states useful for entanglement creation
- Quantumness of spin-1 states
- Determining eigenvalues of a density matrix with minimal information in a single experimental setting