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.
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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.
is often used too, for example in Chap. Author information
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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
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DOI: https://doi.org/10.1007/978-3-319-21891-5_5
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-319-21891-5
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