Amplification, Inference, and the Manifestation of Objective Classical Information

Our everyday reality is characterized by objective information—information that is selected and amplified by the environment that interacts with quantum systems. Many observers can accurately infer that information indirectly by making measurements on fragments of the environment. The correlations between the system, [Formula: see text] , and a fragment, [Formula: see text] , of the environment, [Formula: see text] , is often quantified by the quantum mutual information, or the Holevo quantity, which bounds the classical information about [Formula: see text] transmittable by a quantum channel [Formula: see text]. The latter is a quantum mutual information but of a classical-quantum state where measurement has selected outcomes on [Formula: see text]. The measurement generically reflects the influence of the remaining environment, [Formula: see text] , but can also reflect hypothetical questions to deduce the structure of [Formula: see text] correlations. Recently, Touil et al. examined a different Holevo quantity, one from a quantum-classical state (a quantum [Formula: see text] to a measured [Formula: see text]). As shown here, this quantity upper bounds any accessible classical information about [Formula: see text] in [Formula: see text] and can yield a tighter bound than the typical Holevo quantity. When good decoherence is present—when the remaining environment, [Formula: see text] , has effectively measured the pointer states of [Formula: see text] —this accessibility bound is the accessible information. For the specific model of Touil 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, as well as a single-shot framework, to quantify records of the missing, classical information about [Formula: see text].