A Characterization of Entangled Two‐Qubit States via Partial‐Transpose‐Moments. Issue 11 (10th September 2022)

• Record Type: Journal Article
• Authors: Zhang, Lin; Zhao, Ming‐Jing; Chen, Lin; Xiang, Hua; Shen, Yi
• Is Part Of: Annalen der Physik. Volume 534:Issue 11(2022)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2022-09-10
• Subjects: partial‐transpose‐moments -- two‐qubit entangled states; Physics -- Periodicals; Chemistry -- Periodicals; 530.05
• DOI: 10.1002/andp.202200289
• Languages: English
• ISSNs: 0003-3804

Abstract

Abstract: Although quantum entanglement is an important resource, its characterization is quite challenging. The partial transposition is a common method to detect bipartite entanglement. In this paper, the authors study the partial‐transpose(PT)‐moments of two‐qubit states, and completely describe the whole region, composed of the second and third PT‐moments, for all two‐qubit states. Furthermore, they determine the accurate region corresponding to all entangled two‐qubit states. The states corresponding to those boundary points of the whole region, and to the border lines between separable and entangled states are analyzed. As an application, they characterize the entangled region of PT‐moments for the two families of Werner states and Bell‐diagonal states. The relations between entanglement and the pairs of PT‐moments are revealed from these typical examples. They also numerically plot the whole region of possible PT‐moments for all two‐qubit X ‐states, and find that this region is almost the same as the whole region of PT‐moments for all two‐qubit states. Moreover, they extend their results to detect the entanglement of multiqubit states. By utilizing the PT‐moment‐based method to characterize the entanglement of the multiqubit states mixed by the GHZ and W states, they propose an operational way of verifying the genuine entanglement in such states. Abstract : The measurability of PT‐moments (partial‐transpose‐moments) bridges the practical limitations of the PPT (positive‐partial‐transpose) criterion. This work describes the whole region composed of the second and third PT‐moments, for all two‐qubit states, and determines the entangled region. It provides an experimentally efficient separability criterion of two‐qubit states. This criterion is also applied to several widely used states to characterize their entanglement.