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Amplification, inference, and the manifestation of objective classical information



Michael Zwolak


Abstract Quantum systems are generally open to a large environment composed of, e.g., photons or phonons. The environment can make measurements on those systems, amplifying and transmitting select information about them. Other systems or observers can then learn about that select information indirectly by making measurements on fragments of the environment. The correlations between the system, S, and a fragment, F, of the environment, E, is often quantified by the quantum mutual information or the Holevo quantity that bounds the classical information about S transmittable by a quantum channel F. The latter is a quantum mutual information but of a classical-quantum state where measurement has selected outcomes on S. The measurement generically reflects the influence of the remaining environment, E/F, but can also reflect hypothetical questions to deduce the structure of SF correlations. Recently, Akram et al. examined a different Holevo quantity, one from a quantum-classical state (a quantum S to a measured F). As shown here, this quantity upper bounds any accessible classical information about S in F and can yield a tighter bound than the typical Holevo quantity. When good decoherence is present—when the remaining environment, E/F, has effectively measured the pointer states of S—this accessibility bound is the accessible information. For the specific model considered by Akram et al., the accessible information is related to the error probability for optimal detection and, thus, has the same behavior as the quantum Chernoff bound. The latter reflects amplification and provides a universal approach to quantify records of the missing, classical information about S.


decoherence, amplification, inference, Holevo, quantum Chernoff bound


Zwolak, M. (2022), Amplification, inference, and the manifestation of objective classical information, Entropy, [online],, (Accessed May 29, 2024)


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Created June 1, 2022, Updated November 29, 2022