Entanglement measures and the Hilbert-Schmidt distance
By Masanao Ozawa. 2000
151 citations recorded by the source corpus.
Abstract In order to construct a measure of entanglement on the basis of a `distance' between two states, it is one of desirable properties that the `distance' is nonincreasing under every completely positive trace preserving map. Contrary to a recent claim, this letter shows that the Hilbert–Schmidt distance does not have this property.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/2f11151377a18e93817d7277ac1a3ba8b3fc4bc5
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
- Nicolas Sangouard
- Karol Zyczkowski
- Ingemar Bengtsson
- Nicolas Gisin
- F. Frowis
- Pavel Sekatski
- Wolfgang Dür
In Atomic and Molecular Physics, and Optics
- Nicolas Sangouard
- Karol Zyczkowski
- Ingemar Bengtsson
- Nicolas Gisin
- F. Frowis
- Pavel Sekatski
- Wolfgang Dür
In Mathematical Physics
Citations in the corpus
- Geometry of Quantum States: Index (2007, background): “Since the Hilbert–Schmidt metric is not monotone [712] it is not at all clear whether the minimal HS distance is an entanglement monotone [925].”
- Macroscopic quantum states: Measures, fragility, and implementations (2017, background): “…operations because of a problematic connection to 29 Fröwis and Dür (2012b); Lee and Jeong (2011); Park et al. (2016); Shimizu and Miyadera (2002) the Hilbert-Schmidt norm, which is known to be not contractive under trace-preserving operations (Ozawa, 2000; Piani, 2012; Yadin and Vedral, 2016).”