The Local Orthogonality between Quantum States and Entanglement
Year: 2014
Type: preprint
Abstract: For a quantum state $\rho$, let $E_{f}(\rho)$ be the entanglement of formation. Professors Horodecki proved the following important results: If $\rho$ is composed of the locally orthogonal pure state ensemble $\{\out{\psi_{i}}{\psi_{i}}\}_{i=1}^K$ with probability distribution $p=(p_i)$ such that $\rho =\sum_{i=1}^{K}p_{i}\out{\psi_{i}}{\psi_{i}}$, then $$E_{f}(\rho) = \sum_{i}p_{i}E_{f}(\out{\psi_{i}}{\psi_{i}}).$$ In this paper, we generalize the conclusion to quantum state $\rho$ which is composed of locally orthogonal quantum state ensemble $\{\rho_{a}\}_{a\in\Sigma}$. Finally, we present an interesting example to show that the conditions of these conclusions are existence.
Source: arXiv (Cornell University)
Authors: Sunho Kim, Junde Wu, Lin Zhang, Minhyung Cho
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2962754719