Joint separable numerical range and bipartite entanglement witness
arXiv:2007.02717 · doi:10.1088/1751-8121/abb511
Abstract
In 2017 an idea considering a pair of Hermitian operators of product form was published, which is called ultrafine entanglement witnessing. In 2018 some rigorous results were given. Here we improve their work. First we point this idea can be directly derived from an earlier concept named joint separable numerical range and explain how it works as a series of witnesses. Second by a simple method we present a sufficient condition for an effective pair. Finally we prove this condition is necessary for optimization.
arXiv commentLinear algebra
References in corpus (11)
- Separability of Mixed States: Necessary and Sufficient Conditions
- Optimization of entanglement witnesses
- Entanglement witnesses: construction, analysis and classification
- Covariance matrices and the separability problem
- Entanglement Detection by Local Orthogonal Observables
- Restricted numerical range: a versatile tool in the theory of quantum information
- Classification of joint numerical ranges of three hermitian matrices of size three
- Ultrafine Entanglement Witnessing
- Product numerical range in a space with tensor product structure
- Physical origins of ruled surfaces on the reduced density matrices geometry
- The structure of ultrafine entanglement witnesses