Schmidt measure as a tool for quantifying multiparticle entanglement

By Jens Eisert, Hans J. Briegel. 2000

209 citations recorded by the source corpus.

We present a measure of quantum entanglement which is capable of quantifying the degree of entanglement of a multi-partite quantum system. This measure, which is based on a generalization of the Schmidt rank of a pure state, is defined on the full state space and is shown to be an entanglement monotone, that is, it cannot increase under local quantum operations with classical communication and under mixing. For a large class of mixed states this measure of entanglement can be calculated exactly, and it provides a detailed classification of mixed states.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/beb0f00bbe6569f77513df2b5305ba86b2e55570

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Otfried Gühne
2. Géza Tóth
3. Marcus Huber
4. Xiaoguang Wang
5. Nicolai Friis
6. Mehul Malik
7. Giuseppe Vitagliano

In Atomic and Molecular Physics, and Optics

1. Otfried Gühne
2. Géza Tóth
3. Marcus Huber
4. Xiaoguang Wang
5. Nicolai Friis
6. Mehul Malik
7. Giuseppe Vitagliano

Citations in the corpus

• Geometry of Quantum States: Index (2007, unknown): “80) is pure, ρb = |φb〉〈φb|, the weight is a monotone [288], so the quantity (1− )E1(φb) works as a measure of entanglement [595, 957].”
• Entanglement detection (2008, background): “Other approaches try to identify different classes via a generalization of the Schmidt rank [196] or tensor ranks [197], but there it is difficult to determine in which class a pure state lies.”