Quantum states least affected by interactions with environment play a pivotal role in both foundations and applications of quantum mechanics. Known as pointer states, they surprisingly lacked a systematic description. Working within the Born-Markov approximation, we combine methods of group theory and open quantum systems and derive general conditions describing pointer states. Contrary to common expectations, they are in general different from coherent states. Thus the two notions of being "closest to the classical"-one defined by the uncertainty relations and the other by the interaction with the environment-are in general different. As an example, we study spin-spin and spin-boson models with an arbitrary central spin J.
Quantum states least affected by interactions with environment play a pivotal role in both foundations and applications of quantum mechanics. Known as pointer states, they surprisingly lacked a systematic description. Working within the Born-Markov approximation, we combine methods of group theory and open quantum systems and derive general conditions describing pointer states. Contrary to common expectations, they are in general different from coherent states. Thus the two notions of being "closest to the classical"-one defined by the uncertainty relations and the other by the interaction with the environment-are in general different. As an example, we study spin-spin and spin-boson models with an arbitrary central spin J.
The purpose of the present study is to derive the pointer states of a macroscopic system interacting with its environment, under the general assumptions, i.e., without assuming any form of the interaction Hamiltonian. The lowest order perturbation leads that the interaction energy shifts the phase factors of the state vectors. For a macroscopic system, these factors are the macroscopic quantities even for the very weak interaction. When we group the state vector of the total system by the view point of environmental side, the destructive interference occurs and the stationary phase approximation can be adopted. Only the pointer states then survive and the decoherence also occurs. The present approach is within the standard quantum mechanics as same as the standard decoherence theory, but the meaning of the classical state is much clear.
Three paradigms commonly used in classical, pre-quantum physics to describe particles (that is: the material point, the test-particle and the diluted particle (droplet model)) can be identified as limit-cases of a quantum regime in which pairs of particles interact without getting entangled with each other. This entanglement-free regime also provides a simplified model of what is called in the decoherence approach islands of classicality, that is, preferred bases that would be selected through evolution by a Darwinist mechanism that aims at optimising information. We show how, under very general conditions, coherent states are natural candidates for classical pointer states. This occurs essentially because, when a (supposedly bosonic) system coherently exchanges only one quantum at a time with the (supposedly bosonic) environment, coherent states of the system do not get entangled with the environment, due to the bosonic symmetry.
Quantum decoherence provides a framework to study the emergence of classicality from quantum systems by showing how interactions with the environment suppress interferences and select robust states known as pointer states. Earlier studies have linked Gaussian coherent states to pointer states. More recently, it was conjectured that more general quantum states called joint momenta-coordinates states may serve as more suitable candidates to be pointer states. These states are associated to the concept of quantum phase space and saturate, by definition, generalized uncertainty relations. In this work, we rigorously prove this conjecture. Building on the Lindblad framework for the damped harmonic oscillator, and applying Zurek's predictability-sieve criterion, we analyze both underdamped and overdamped regimes. We show that only in the underdamped case do joint momenta-coordinates states remain pure and robust for all times, establishing them as the true pointer states. This extends Isar's earlier underdamped treatment, generalizes the concept beyond Gaussian approximations, and embeds classical robustness in the quantum phase space formalism, with potential applications in error-resistant quantum information.
Abstract In quantum mechanics, pointer states are eigenstates of the observable of the measurement apparatus that represent the possible positions of the display pointer of the equipment. The origin of this concept lies in attempts to fill the blanks in Everett’s relative-state interpretation, and to make it a fully valid description of physical reality. To achieve this, it was necessary to consider not only the main system interacting with the measurement apparatus (like von Neumann and Everett did) but also the role of the environment in eliminating correlations between different possible measurements when interacting with the measurement apparatus. The interaction of the environment with the main system (and the measurement apparatus) is the core of the decoherence theory, which followed Everett’s thesis. In this article, we review the measurement process according to von Neumann, Everett’s relative state interpretation, the purpose of decoherence and some of its follow-up until Wojciech Zurek’s primordial paper that consolidated the concept of pointer states, previously presented by Heinz Dieter Zeh. Employing a simple physical model consisting of a pair of two-level systems—one representing the main system, the other the measurement apparatus—and a thermal bath—representing the environment—we show how pointer states emerge, explaining its contributions to the question of measurement in quantum mechanics, as well as its limitations. Finally, we briefly show some of its consequences. This paper is accessible to readers with elementary knowledge about quantum mechanics, on the level of graduate courses.
Abstract: In quantum mechanics, pointer states are eigenstates of the observable of the measurement apparatus that represent the possible positions of the display pointer of the equipment. The origin of this concept lies in attempts to fill the blanks in Everett's relative-state interpretation, and to make it a fully valid description of physical reality. To achieve this, it was necessary to consider not only the main system interacting with the measurement apparatus (like von Neumann and Everett did) but also the role of the environment in eliminating correlations between different possible measurements when interacting with the measurement apparatus. The interaction of the environment with the main system (and the measurement apparatus) is the core of the decoherence theory, which followed Everett's thesis. In this article, we review the measurement process according to von Neumann, Everett's relative state interpretation, the purpose of decoherence and some of its follow-up until Wojciech Zurek's primordial paper that consolidated the concept of pointer states, previously presented by Heinz Dieter Zeh. Employing a simple physical model consisting of a pair of two-level systems-one representing the main system, the other the measurement apparatus-and a thermal bath-representing the environment-we show how pointer states emerge, explaining its contributions to the question of measurement in quantum mechanics, as well as its limitations. Finally, we briefly show some of its consequences. This paper is accessible to readers with elementary knowledge about quantum mechanics, on the level of graduate courses
We consider the quasi-classical situation in which a quantum system interacts with another quantum system or with a quantum environment without getting entangled with it. We show how this regime is intimately linked to three paradigms commonly used in classical, pre-quantum physics to describe particles (that is, the material point, the test particle and the diluted particle (droplet model)). This entanglement-free regime also provides a simplified insight on what is called in the decoherence approach "islands of classicality", that is, preferred bases that would be selected through evolution by a Darwinist mechanism which aims at optimizing information. We show how, under very general conditions, coherent states are natural candidates for classical pointer states. This occurs essentially because, when a (supposedly bosonic) system coherently exchanges only one quantum at a time with its (supposedly bosonic) environment, coherent states of the system do not get entangled with the environment, due to the bosonic symmetry.