TY - GEN
T1 - Min-Entropic Quantities Induced by Cones
T2 - 2024 IEEE International Symposium on Information Theory, ISIT 2024
AU - George, Ian
AU - Chitambar, Eric
N1 - Publisher Copyright:
© 2024 IEEE.
PY - 2024
Y1 - 2024
N2 - In one-shot and zero-error information theory, the conditional min-entropy is a fundamental tool. It may be expressed as a conic program over the positive semidefinite cone. Recently, Chitambar et al. showed that the same conic program altered to be over the separable cone is a measure of transmitting classical communication over a quantum channel called the 'communication value.' In this work, we extend this idea to a broad class of convex cones to induce new families of entropic quantities. We show this methodology has operational relevance by characterizing a generalized notion of communication value and relating a class of cone-restricted entropies to a partial ordering on converting quantum channels via bistochastic preprocessing. We also show regularized smooth versions of these entropic quantities do not in general converge to the von Neumann entropy, which shows tasks characterized by these quantities are not equivalent even in an asymptotic i.i.d. fashion.
AB - In one-shot and zero-error information theory, the conditional min-entropy is a fundamental tool. It may be expressed as a conic program over the positive semidefinite cone. Recently, Chitambar et al. showed that the same conic program altered to be over the separable cone is a measure of transmitting classical communication over a quantum channel called the 'communication value.' In this work, we extend this idea to a broad class of convex cones to induce new families of entropic quantities. We show this methodology has operational relevance by characterizing a generalized notion of communication value and relating a class of cone-restricted entropies to a partial ordering on converting quantum channels via bistochastic preprocessing. We also show regularized smooth versions of these entropic quantities do not in general converge to the von Neumann entropy, which shows tasks characterized by these quantities are not equivalent even in an asymptotic i.i.d. fashion.
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U2 - 10.1109/ISIT57864.2024.10619525
DO - 10.1109/ISIT57864.2024.10619525
M3 - Conference contribution
AN - SCOPUS:85202840405
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 1005
EP - 1010
BT - 2024 IEEE International Symposium on Information Theory, ISIT 2024 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 7 July 2024 through 12 July 2024
ER -