Abstract
Conditional Entropies are measures of the uncertainty inherent in a system from the perspective of an observer who is given side information on the system. The system as well as the side information can be either classical or a quantum. The goal in this chapter is to define conditional Rényi entropies that are operationally significant measures of this uncertainty, and to explore their properties. Unconditional entropies are then simply a special case of conditional entropies where the side information is uncorrelated with the system under observation.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The notation \(H_{\min }(A|B)_{\rho |\rho } \equiv \widetilde{H}_{\infty }^{\scriptscriptstyle \,\downarrow }(A|B)_{\rho }\) and \(H_{\min }(A|B)_{\rho } \equiv \widetilde{H}_{\infty }^{\scriptscriptstyle \,\uparrow }(A|B)_{\rho }\) is widely used. The alternative notation is often used too, for example in Chap. 6.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2016 The Author(s)
About this chapter
Cite this chapter
Tomamichel, M. (2016). Conditional Rényi Entropy. In: Quantum Information Processing with Finite Resources. SpringerBriefs in Mathematical Physics, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-21891-5_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-21891-5_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-21890-8
Online ISBN: 978-3-319-21891-5
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)