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Europhysics Letters (EPL)

Emergence of classical realism under successive noncommuting measurements

D. M. Fucci, Lucas Fanderuff Gaissler, R. M. Angelo

Published Mar 24, 2025• 2 citations
Publisher

Abstract

Abstract The problem of emergence of classicality from quantum mechanics has been addressed over time through numerous frameworks, from Bohr's correspondence principle to quantum Darwinism. Traditional approaches associate the emergence of classicality with the decoherence process induced by large reservoirs on the system's state. In this work, we present an effective mechanism by which classicality emerges through the establishment of elements of reality. This involves the process of successive monitoring of noncommuting observables. To assess physical reality, we employ the realism criterion introduced by Bilobran and Angelo (see Bilobran A. L. O. and Angelo R. M., EPL , 112 (2015) 40005), as well as their quantifier for the violations of this criterion. With these tools, we formally demonstrate, for generic systems, that a quasi-classical regime can always be reached with a sufficiently large number of incompatible measurements. Thus, instead of diagnosing the emergence of the classical regime in terms of the resulting algebraic characteristics for the density operator under the action of large reservoirs, our results reveal that classicality can emerge, at the level of physical elements of reality, from the coupling of the system with environments of a few degrees of freedom.

DOI
10.1209/0295-5075/adc481

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Abstract The problem of emergence of classicality from quantum mechanics has been addressed over time through numerous frameworks, from Bohr's correspondence principle to quantum Darwinism. Traditional approaches associate the emergence of classicality with the decoherence process induced by large reservoirs on the system's state. In this work, we present an effective mechanism by which classicality emerges through the establishment of elements of reality. This involves the process of successive monitoring of noncommuting observables. To assess physical reality, we employ the realism criterion introduced by Bilobran and Angelo (see Bilobran A. L. O. and Angelo R. M., EPL , 112 (2015) 40005), as well as their quantifier for the violations of this criterion. With these tools, we formally demonstrate, for generic systems, that a quasi-classical regime can always be reached with a sufficiently large number of incompatible measurements. Thus, instead of diagnosing the emergence of the classical regime in terms of the resulting algebraic characteristics for the density operator under the action of large reservoirs, our results reveal that classicality can emerge, at the level of physical elements of reality, from the coupling of the system with environments of a few degrees of freedom.
The problem of emergence of classicality from quantum mechanics has been addressed over time through numerous frameworks, from Bohr's correspondence principle to quantum Darwinism. Traditional approaches associate the emergence of classicality with the decoherence process induced by large reservoirs on the system's state. In this work, we present an effective mechanism by which classicality emerges through the establishment of elements of reality. This involves the process of successive monitoring of noncommuting observables. To assess physical reality, we employ the realism criterion introduced by Bilobran and Angelo [EPL, 112 (2015) 40005], as well as their quantifier for the violations of this criterion. With these tools, we formally demonstrate, for generic systems, that a quasi-classical regime can always be reached with a sufficiently large number of incompatible measurements. Thus, instead of diagnosing the emergence of the classical regime in terms of the resulting algebraic characteristics for the density operator under the action of large reservoirs, our results reveal that classicality can emerge, at the level of physical elements of reality, from the coupling of the system with environments of a few degrees of freedom.
This study offers a comprehensive technical analysis of the mechanisms through which classical behavior emerges from the dynamics of quantum measurement. Beginning with unitary evolution and the principles of measurement, we construct the framework of environment-induced decoherence, the selection of pointer states, and the reduction of interference. Our examination focuses on how effective classicality emerges through reduced density matrices, quantum Darwinism, and consistent histories, highlighting the importance of system-environment interactions in determining stable observables. The review investigates into mathematical constructs such as spectral theory, completely positive maps, and quantum trajectories, linking them to experimental observations in mesoscopic systems, optomechanics, and superconducting circuits. We explore the constraints of decoherence in addressing the outcome problem and review interpretational models that tackle the remaining issues. The discussion emphasizes applications in quantum information, metrology, and tests of macroscopic superpositions. The article favors physical insights and mathematical guidance over exhaustive proofs, making it suitable for researchers in quantum foundations and quantum technologies.
Correlation is the basic mechanism of every measurement model, as one never accesses the measured system directly. Instead, correlations are created, codifying information about the measurable property into the environment. Here, we address the problem of the emergence of physical reality from the quantum world by introducing a model that interpolates between weak and strong nonselective measurements for qudits. By utilizing Heisenberg-Weyl operators, our model suggests that independently of the interaction intensity between the system and the environment, full information about the observable of interest can always be obtained by making the system interact with many environmental qudits, following a quantum Darwinism framework.
The emergence of classical behavior in quantum theory is often ascribed to the interaction of a quantum system with its environment, which can be interpreted as environmental monitoring of the system. As a result, off-diagonal elements of the density matrix of the system are damped in the basis of a preferred observable, often taken to be the position, leading to the phenomenon of decoherence. This effect can be modeled dynamically in terms of a Lindblad equation driven by the position operator. Here the question of decoherence resulting from a monitoring of position and momentum, i.e., a phase-space measurement, by the environment is addressed. There is no standard quantum observable corresponding to the detection of phase-space points, which is forbidden by Heisenberg's uncertainty principle. This issue is addressed by use of a coherent-state-based positive operator-valued measure for modeling phase-space monitoring by the environment. In this scheme, decoherence in phase space implies the diagonalization of the density matrix in both position and momentum representations. This is shown to be linked to a Lindblad equation where position and momentum appear as two independent Lindblad operators.
Existence of physical reality in the classical world is a well-established fact from day-to-day observations. However within quantum theory, it is not straightforward to reach such a conclusion. A framework to analyse how observations can be described using some physical states of reality in a theory independent way was recently developed, known as ontological framework. Different principles when imposed on the ontological level give rise to different observations in physical experiments. Using the ontological framework, we formulate a novel notion of termed classicality which is based upon the physical principles that in classical theories pure states are physical states of reality and every projective measurement just observes the state of the system. We construct a communication task in which the success probability is bounded from above for ontological models satisfying the notion of universal classicality. Contrary to previous notions of which either required systems of dimension strictly greater than two or atleast three preparations, a violation of classicality can be observed using just a pair of qubits and a pair of incompatible measurements. We further show that violations of previously known notions of such as preparation non-contexuality and Bell's local causality is a violation of universal classicality.
At present there is a consensus about the fact that the emergence of the classical world from the underlying quantum reality involves the physical phenomenon of decoherence, which is usually studied in the version proposed by Zurek and his collaborators. According to this version, decoherence is a process resulting from the interaction between a quantum system and its environment (environment-induced decoherence, EID); this process singles out the observables that receive definite classical values. The aim of this paper is to propose a top-down approach to decoherence, which takes the perspective of the whole closed system, and considers whether each set of degrees of freedom decoheres or not. This approach is more general than the orthodox open-system perspective and dissolves some of its conceptual problems. Although decoherence becomes relative to the way in which the closed system is decomposed, the quantum-to-classical transition defines unequivocally the realm of classicality by identifying the observables with classical-like behavior.