Cambridge University Press eBooks

The Asymptotic Regime

Gilad Gour

Published Apr 10, 2025• 0 citations

Abstract

Chapter 8 explores the asymptotic regime of quantum information processing, beginning with quantum typicality, which illustrates the convergence of quantum states toward a typical form with increasing copies. This leads to the asymptotic equipartition property (AEP), indicating that with a high number of copies, probability vectors become uniformly distributed. The method of types is introduced next, a tool from classical information theory that classifies sequences based on their statistical properties. This is crucial for understanding the behavior of large quantum systems and has implications for quantum data compression. Advancing to quantum hypothesis testing, the chapter outlines efficient strategies for distinguishing between two quantum states through repeated measurements. Central to this is the Quantum Stein’s lemma, which asserts the exponential decline in the error probability of hypothesis testing as the sample size of quantum systems increases. The chapter highlights the deep interplay between typicality, statistical methods, and hypothesis testing, laying the groundwork for asymptotic interconversion of quantum resources.

DOI: 10.1017/9781009560870.008

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