Distinguishability, Ensemble Steering, and the No-Signaling Principle

Joonwoo Bae
(Center for Quantum Technologies, National University of Singapore, Singapore 117543)

We consider a fundamental operational task, distinguishing systems in different states, in the framework of generalized probabilistic theories and provide a general formalism of minimum-error discrimination of states in convex optimization. With the formalism established, we show that the distinguishability is generally a global property assigned to the ensemble of given states rather than other details of a given state space or pairwise relations of given states. Then, we consider bipartite systems where ensemble steering is possible, and show that show that with two operational tasks, ensemble steering and the no-signaling condition, the distinguishability is tightly determined. The result is independent to the structure of the state space. This concludes that the distinguishability is generally determined by the compatibility between two tasks, ensemble steering on states and the non-signaling principle on probability distributions of outcomes.

In Bob Coecke and Matty Hoban: Proceedings of the 10th International Workshop on Quantum Physics and Logic (QPL 2013), Castelldefels (Barcelona), Spain, 17th to 19th July 2013, Electronic Proceedings in Theoretical Computer Science 171, pp. 26–32.
Published: 27th December 2014.

ArXived at: https://dx.doi.org/10.4204/EPTCS.171.3 bibtex PDF
References in reconstructed bibtex, XML and HTML format (approximated).
Comments and questions to: eptcs@eptcs.org
For website issues: webmaster@eptcs.org