We present a precise characterization of the onset of classicality that combines the formalism of quantum Darwinism with the tools from quantum metrology. We show that the quantum Fisher information provides a useful metric for assessing the rate at which classical objectivity emerges. Furthermore, our formalism allows us to explore how the choice of measurement impacts the precision with which an observer can determine the state of the system. For a paradigmatic example of the spin-star model, we demonstrate that optimal measurements lead to the emergence of classicality at an exponential rate. Although other measurements necessarily lead to slower emergence, we importantly show that suboptimal measurements can still saturate the Cramér-Rao bound. By recasting emergent classicality as an information acquisition protocol, our framework provides a precise operational description of quantum Darwinism.
We present a precise characterization of the onset of classicality that combines the formalism of quantum Darwinism with the tools from quantum metrology. We show that the quantum Fisher information provides a useful metric for assessing the rate at which classical objectivity emerges. Furthermore, our formalism allows us to explore how the choice of measurement impacts the precision with which an observer can determine the state of the system. For a paradigmatic example of the spin-star model, we demonstrate that optimal measurements lead to the emergence of classicality at an exponential rate. Although other measurements necessarily lead to slower emergence, we importantly show that suboptimal measurements can still saturate the Cramér-Rao bound. By recasting emergent classicality as an information acquisition protocol, our framework provides a precise operational description of quantum Darwinism.
Abstract Classical objectivity arises when many independent observers can retrieve the same information about a quantum system without disturbing it. Quantum Darwinism (QD) explains this by treating the environment as a communication channel that redundantly broadcasts information about pointer observables. We develop an operational framework for quantifying this redundancy through the lens of functional information. By introducing a one-sided adequacy criterion based on the Holevo bound, we measure the \emph{abundance} of environment fragments that individually contain nearly all classically accessible pointer information. Using a heterogeneous pure–dephasing model, we sample fragments to extract onset statistics and apply isotonic regression to obtain stable estimates of redundancy and its functional-information counterpart FIQD=log2Rδ. The results reveal a generic onset–plateau structure: redundancy grows rapidly at early times, then saturates at a capacity-limited ceiling, universally across adequacy tolerances. We further connect FIQD to thermodynamic bounds, showing that each additional bit of redundancy implies exponentially increasing minimal heat costs for record stabilization. This approach provides a conservative, model-agnostic measure of emergent classicality, suitable for both theoretical analysis and experimental probing.
Quantum Darwinism extends the decoherence formalism to explain how objectivity emerges from quantum mechanics. However, existing approaches often capture only partial aspects of objectivity. By connecting quantum Darwinism to operator algebra quantum error correction, we show that the emergence of objectivity can be identified with the algebraic local recoverability of quantum codes. Applying this algebraic framework to stabilizer codes, we show that it yields a far more precise characterization of classicality and redundancy, unifies the traditional measures of objectivity, enables efficient classification via coding-theoretic tools, and supports large-scale Clifford simulations of decoherence dynamics.
Critical metrology relies on the precise preparation of a system in its ground state near a quantum phase transition point where quantum correlations get very strong. Typically, this increases the quantum Fisher information with respect to changes in system parameters and thus improves the optimally possible measurement precision limited by the Cramér-Rao bound. Hence critical metrology involves encoding information about the unknown parameter in changes of the system's ground state. Conversely, in conventional metrology methods like Ramsey interferometry, the eigenstates of the system remain unchanged, and information about the unknown parameter is encoded in the relative phases that excited system states accumulate during their time evolution. Here we introduce an approach combining these two methodologies into a unified protocol applicable to closed and driven-dissipative systems. We show that the quantum Fisher information in this case exhibits an additional interference term originating from the interplay between eigenstate and relative phase changes. We provide analytical expressions for the quantum and classical Fisher information in such a setup, elucidating as well a straightforward measurement approach that nearly attains the maximum precision permissible under the Cramér-Rao bound. We showcase these results by focusing on the squeezing Hamiltonian, which characterizes the thermodynamic limit of Dicke and Lipkin-Meshkov-Glick Hamiltonians.
Quantum mechanics describes the smallest systems, whilst classical physics describes macroscopic scales. However, the quantum-to-classical transition is a major unsolved problem. In this thesis, we develop further understanding of the transition through the concept of objectivity. The objects we perceive in our everyday world are objective: they exist regardless of observation, and their properties are independent of observers. This is because information about everyday objects came be found, for example, in the surrounding photon environment. Quantum Darwinism is a conceptual and theoretical framework that describes the emergence of objectivity. The “Darwinistic” part refers to how certain types of information tends to spread at the expense of others. The thesis addresses the quantitative description of objectivity, the dynamics of emergent objectivity, and the analysis of non-objectivity in experimental and biology-inspired systems. Firstly, we propose two new mathematical frameworks to describe objectivity, Strong Quantum Darwinism and invariant spectrum broadcast structure. Then we unite them with the pre-existing frameworks, Zurek's Quantum Darwinism and spectrum broadcast structure, by identifying their deep connections and differences. These conditions highlight how Each framework considers varying amounts of objectivity in the system and environments and together, they create a hierarchy of objectivity. We then analyse objectivity in a scenario where system-environment interactions are strong and non-Markovian, highlighting some practical differences between the Quantum Darwinism frameworks. Next, we describe the quantum channels that create objective states, leading us to discuss the contribution of non-Markovianity to the emergence of objectivity. Then, we introduce a witnessing scheme that simplifies the detection of non-objectivity to promote further experimental testing of Quantum Darwinism with larger environments. Finally, we examine the contribution of quantum coherence and non-objectivity to the performance of a biological-inspired quantum magnetic sensor that operates close to the quantum-classical boundary. We find that the sensor operates in a non-objective regime, and that quantum coherence is necessary for the sensor's performance. The quantum-to-classical transition is a longstanding open question: these findings deepen our knowledge of how objectivity emerges, and contributes to and the types of interactions that keep systems quantum, which is relevant for understanding quantum biological systems and exploiting environment effects in novel quantum technologies. While the quantum-to-classical transition remains unsolved, Quantum Darwinism and its frameworks contribute to the understanding of emergent objectivity and have much potential to further explore aspects of the transition within the structure of quantum mechanics.
Quantum Darwinism posits that only specific information about a quantum system that is redundantly proliferated to many parts of its environment becomes accessible and objective, leading to the emergence of classical reality. However, it is not clear under what conditions this mechanism holds true. Here we prove that the emergence of classical features along the lines of quantum Darwinism is a general feature of any quantum dynamics: observers who acquire information indirectly through the environment have effective access at most to classical information about one and the same measurement of the quantum system. Our analysis does not rely on a strict conceptual splitting between a system-of-interest and its environment, and allows one to interpret any system as part of the environment of any other system. Finally, our approach leads to a full operational characterization of quantum discord in terms of local redistribution of correlations. Quantum Darwinism provides an explanation for the emergence of classical reality from the underlying quantum world, as information proliferates in the environment and becomes objective. Here, the authors show how some aspects of this mechanism is generic and classicality emerges for any quantum dynamics.
For a given quantum state used in sensing, the quantum Cramér-Rao bound (QCRB) sets a fundamental limit on the precision achievable by an unbiased estimator of an unknown parameter, determined by the inverse of the quantum Fisher information (QFI). The QFI serves as an upper bound on the classical Fisher information (CFI), representing the maximum extractable information about the unknown parameter from measurements on a physical system. Thus, a central goal in quantum parameter estimation is to find a measurement, described by a POVM, that saturates the QFI (achieves maximum CFI), and thereby achieves the QCRB. In the idealization that one uses pure states and unitary encodings for sensing, discontinuities can appear in the CFI but not the QFI. In this article, we demonstrate that these discontinuities are important features, quantifying how much Fisher information is lost in the presence of noise. We refer to this as the Fisher information "fragility". We present a simple framework for understanding how discontinuities increase fragility through Jensen's inequality, and demonstrate how one can use this framework to design more robust POVMs for quantum advantage in metrology.