Stronger Entanglement Criteria Based on Quantum Fisher Information

Ao-Xiang Liu, Ma-Cheng Yang, Cong‐Feng Qiao

Nan Li, Shunlong Luo

We propose an entanglement criterion in terms of quantum Fisher information, which complements the criterion based on variance and local uncertainty relations [H. F. Hofmann and S. Takeuchi, Phys. Rev. A 68, 032103 (2003)]. We illustrate the significance of this criterion by showing that it can reveal entanglement undetectable by the variance method. The dual relation between the criterion based on quantum Fisher information and that based on variance are highlighted. The combination of these two criteria leads to a refined method for entanglement detection, which is stronger than when either one is used alone.

A.‐S. F. Obada, S. Abdel‐Khalek

Szilárd Szalay, Géza Tóth

We work out the general theory of one-parameter families of partial entanglement properties and the resulting entanglement depth-like quantities. Special cases of these are the depth of partitionability, the depth of producibility (or simply entanglement depth) and the depth of stretchability, which are based on one-parameter families of partial entanglement properties known earlier. We also construct some further physically meaningful properties, for instance the squareability, the toughness, the degree of freedom, and also several ones of entropic motivation. Metrological multipartite entanglement criteria with the quantum Fisher information fit naturally into this framework. Here we formulate these for the depth of squareability, which therefore turns out to be the natural choice, leading to stronger bounds than the usual entanglement depth. Namely, the quantum Fisher information turns out to provide a lower bound not only on the maximal size of entangled subsystems, but also on the average size of entangled subsystems for a random choice of elementary subsystems. We also formulate criteria with convex quantities for both cases, which are much stronger than the original ones. In particular, the quantum Fisher information puts a lower bound on the average size of entangled subsystems. We also argue that one-parameter partial entanglement properties, which carry entropic meaning, are more suitable for the purpose of defining metrological bounds.

Yan Hong, Shunlong Luo, Hongting Song

The $k$-nonseparability is a kind of multipartite quantum correlation which can be used to characterize some aspects of multipartite entanglement. In this paper, we discuss the detection of $k$-nonseparability of $n$-partite quantum states from an information perspective and obtain some $k$-nonseparability criteria in terms of quantum Fisher information. These criteria can identify many $k$-nonseparable states, and their advantages over an important and well-known $k$-nonseparability criterion [M. Huber et al., Phys. Rev. A 88, 042328 (2013)] are illustrated by several typical examples.

Zain Saleem