Amplification, inference, and the manifestation of objective classical information

Abstract

Our everyday reality is characterized by objective information$\unicode{x2013}$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, $\mathcal{S}$, and a fragment, $\mathcal{F}$, of the environment, $\mathcal{E}$, is often quantified by the quantum mutual information or the Holevo quantity that bounds the classical information about $\mathcal{S}$ transmittable by a quantum channel $\mathcal{F}$. The latter is a quantum mutual information but of a classical-quantum state where measurement has selected outcomes on $\mathcal{S}$. The measurement generically reflects the influence of the remaining environment, $\mathcal{E}/\mathcal{F}$, but can also reflect hypothetical questions to deduce the structure of $\mathcal{S}\mathcal{F}$ correlations. Recently, Touil et al. examined a different Holevo quantity, one from a quantum-classical state (a quantum $\mathcal{S}$ to a measured $\mathcal{F}$). As shown here, this quantity upper bounds any accessible classical information about $\mathcal{S}$ in $\mathcal{F}$ and can yield a tighter bound than the typical Holevo quantity. When good decoherence is present$\unicode{x2013}$when the remaining environment, $\mathcal{E}/\mathcal{F}$, has effectively measured the pointer states of $\mathcal{S}$$\unicode{x2013}$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 $\mathcal{S}$.