Relative entropy of steering: on its definition and properties. (23rd October 2017)

• Record Type: Journal Article
• Authors: Kaur, Eneet; Wilde, Mark M
• Is Part Of: Journal of physics. Volume 50:Number 46(2017)
• Publication Date: 2017-10-23
• Subjects: relative entropy of steering -- steering monotone -- resource theory of steering; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aa907b
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: In Gallego and Aolita (2015 Phys. Rev . X5 041008), the authors proposed a definition for the relative entropy of steering and showed that the resulting quantity is a convex steering monotone. Here we advocate for a different definition for relative entropy of steering, based on well grounded concerns coming from quantum Shannon theory. We prove that this modified relative entropy of steering is a convex steering monotone. Furthermore, we establish that it is uniformly continuous and faithful, in both cases giving quantitative bounds that should be useful in applications. We also consider a restricted relative entropy of steering which is relevant for the case in which the free operations in the resource theory of steering have a more restricted form (the restricted operations could be more relevant in practical scenarios). The restricted relative entropy of steering is convex, monotone with respect to these restricted operations, uniformly continuous, and faithful.