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 $\mathcal{S}$.

arXiv comment8 pages, 1 figure

References in corpus (41)

• Monogamy of entanglement and other correlations
• Quantum Darwinism
• The Quantum Chernoff Bound
• Asymptotic Error Rates in Quantum Hypothesis Testing
• Objective properties from subjective quantum states: Environment as a witness
• Quantum Darwinism: Entanglement, branches, and the emergent classicality of redundantly stored quantum information
• Distinguishability and Accessible Information in Quantum Theory
• The Chernoff lower bound for symmetric quantum hypothesis testing
• Generic emergence of classical features in quantum Darwinism
• Environment as a Witness: Selective Proliferation of Information and Emergence of Objectivity in a Quantum Universe
• Accessible information and optimal strategies for real symmetrical quantum sources
• Quantum origins of objectivity
• A simple example of "Quantum Darwinism": Redundant information storage in many-spin environments
• Quantum Darwinism in an Everyday Environment: Huge Redundancy in Scattered Photons
• Quantum Darwinism in a hazy environment
• Quantum Darwinism in quantum Brownian motion: the vacuum as a witness
• Objectivity in the Photonic Environment Through State Information Broadcasting
• The Rise and Fall of Redundancy in Decoherence and Quantum Darwinism
• Quantum Darwinism, Classical Reality, and the Randomness of Quantum Jumps
• Revealing the emergence of classicality in nitrogen-vacancy centers
• Quantum Darwinism in non-ideal environments
• Redundancy of classical and quantum correlations during decoherence
• Relative States and the Environment: Einselection, Envariance, Quantum Darwinism, and the Existential Interpretation
• Redundant Information from Thermal Illumination: Quantum Darwinism in Scattered Photons
• Experimental signature of Quantum Darwinism in photonic cluster states
• Roads to objectivity: Quantum Darwinism, Spectrum Broadcast Structures, and Strong quantum Darwinism -- a review
• Discriminating quantum states: the multiple Chernoff distance
• Eavesdropping on the Decohering Environment: Quantum Darwinism, Amplification, and the Origin of Objective Classical Reality
• Amplification, Redundancy, and the Quantum Chernoff Information
• Collisional unfolding of quantum Darwinism
• The role of information back-flow in the emergence of quantum Darwinism
• Generic emergence of objectivity of observables in infinite dimensions
• Amplification, Decoherence, and the Acquisition of Information by Spin Environments
• Quantum Darwinism and non-Markovian dissipative dynamics from quantum phases of the spin-1/2 XX model
• Decoherence without entanglement and Quantum Darwinism
• Redundancy of einselected information in quantum Darwinism: The irrelevance of irrelevant environment bits
• Quantum Darwinism in a structured spin environment
• Entanglement and objectivity in pure dephasing models
• (Anti-)Zeno-based dynamical control of the unfolding of quantum Darwinism
• Dissipation, dephasing and quantum Darwinism in qubit systems with random unitary interactions
• Appearance of objectivity for NV centers interacting with dynamically polarized nuclear environment

Cited by in corpus (4)

• Quantum Theory of the Classical: Einselection, Envariance, Quantum Darwinism and Extantons
• Branching States as The Emergent Structure of a Quantum Universe
• On the relation between quantum Darwinism and approximate quantum Markovianity
• Holevo bound and objectivity in the boson-spin model