Quantum mechanical entropy

Generalized relative entropy

Generalized relative entropy (-relative entropy) is a measure of dissimilarity between two quantum states. It is a "one-shot" analogue of quantum relative entropy and shares many properties of the latter quantity. In the study of quantum information theory, we typically assume that information processing tasks are repeated multiple times, independently. The corresponding information-theoretic notions are therefore defined in the asymptotic limit. The quintessential entropy measure, von Neumann entropy, is one such notion. In contrast, the study of one-shot quantum information theory is concerned with information processing when a task is conducted only once. New entropic measures emerge in this scenario, as traditional notions cease to give a precise characterization of resource requirements. -relative entropy is one such particularly interesting measure. In the asymptotic scenario, relative entropy acts as a parent quantity for other measures besides being an important measure itself. Similarly, -relative entropy functions as a parent quantity for other measures in the one-shot scenario. (Wikipedia).

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Anna Vershynina: "Quasi-relative entropy: the closest separable state & reversed Pinsker inequality"

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From playlist Entropy Inequalities, Quantum Information and Quantum Physics 2021

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Now that you know what Density means, it would be quite easy for you to understand what Relative Density means. Watch this video to know more. ✅To learn more about Relative Density enroll in our full course now: https://infinitylearn.com/microcourses?utm_source=youtube&utm_medium=Soical&

From playlist Physics

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From playlist Seminar Series

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From playlist Information theory and Coding

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From playlist Statistics

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From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester

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From playlist Information theory and Coding

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Related pages

Quantum channel | Entropic value at risk | Hilbert space | Strong subadditivity of quantum entropy | Mutual information | Quantum relative entropy | Trace distance | Min-entropy | Von Neumann entropy | POVM | Information theory