Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0907.0150

Quantum Decoherence and Pointer Basis: Dynamics in State Vectors

Kentaro Urasaki

Published Jul 1, 2009• 0 citations
arXivHTMLPDF

Abstract

It is well-known that the pointer basis of a quantum system satisfies the condition to diagonalize the interaction Hamiltonian between the subsystems. We show that this condition can be translated into the form $δΛ=0,$ where $Λ$, so-called the action, is the time integrated interaction energy: it is found out naturally in the phase of state vectors due to diagonal interaction. The careful treatment of a two states system demonstrates that the states of the total system branch into the states with different values of the action. Mathematically the pointer states are selected out by the saddle point condition on the phase $Λ$. This study helps us to understand the precise mechanism and the general dynamics of decoherence.

DOI
10.48550/arxiv.0907.0150

Related papers

A General Derivation of Pointer States: Decoherence and Classicality

Kentaro Urasaki

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.

arXiv:1404.4457•Apr 17, 2014•0 citations

Pointer States and Decoherence in Quantum Unitarity: Energy Conservation for Weak Interaction Model

Kentaro Urasaki

The purpose of the present paper is to derive the pointer states of a macro-object using a simple perturbation method. We study the model Hamiltonian involving the weak interaction between the center of mass and its environment. The main conclusion is that the pointer states emerge as the small part of the total state vector when the interaction Hamiltonian is not dominant: the degrees of freedom being at the center of interaction can be localized. In the weak interaction case, if the disappearance of the energy contribution from the off-diagonal terms is caused by the decoherence, it threatens the conservation law. In this study, however, the energy conservation reasonably holds, since the non-classical (i.e., normal quantum) states give main contribution to it. The emergence of the pointer states also implies the special initial state in which the localized state makes the deep well of the potential. In the result, the unitary time evolution of a pointer state is very different from that of the majority of the original state vector of the total system.

arXiv:1610.06066•Oct 19, 2016•0 citations

Quantum Decoherence

Elise M. Crull

Quantum decoherence is a physical process resulting from a system’s entanglement with an environment. This chapter examines the explanatory wealth of decoherence when brought to bear on foundational issues such as the question of why certain measurement bases seem to be preferred by nature – including the pointer basis of measuring apparatuses – the old familiar measurement problem, and the emergence of classicality. Decoherence satisfactorily explains the behavior of the ammonia molecule. Decoherence introduces no additional nonlinearity but “simply takes real, inevitable, interaction with external degrees of freedom to bear in the Hamiltonian”. The basis-specific nature of decoherence will allow for a satisfying explanation to one of quantum mechanics’ oldest mysteries: that of the pointer basis. The basis-specific nature of decoherence will allow for a satisfying explanation to one of quantum mechanics’ oldest mysteries: that of the pointer basis.

Routledge eBooks•Aug 11, 2021•18 citations

The pointer basis and the feedback stabilization of quantum systems

L Li, A. Chia, Howard M. Wiseman

The dynamics for an open quantum system can be 'unravelled' in infinitely many ways, depending on how the environment is monitored, yielding different sorts of conditioned states, evolving stochastically. In the case of ideal monitoring these states are pure, and the set of states for a given monitoring forms a basis (which is overcomplete in general) for the system. It has been argued elsewhere (Atkins et al 2005 Europhys. Lett. 69 163 ) that the 'pointer basis' as introduced by Zurek et al (1993 Phys. Rev. Lett. 70 1187 ), should be identified with the unravelling -induced basis which decoheres most slowly. Here we show the applicability of this concept of pointer basis to the problem of state stabilization for quantum systems. In particular we prove that for linear Gaussian quantum systems, if the feedback control is assumed to be strong compared to the decoherence of the pointer basis, then the system can be stabilized in one of the pointer basis states with a fidelity close to one (the infidelity varies inversely with the control strength). Moreover, if the aim of the feedback is to maximize the fidelity of the unconditioned system state with a pure state that is one of its conditioned states, then the optimal unravelling for stabilizing the system in this way is that which induces the pointer basis for the conditioned states. We illustrate these results with a model system: quantum Brownian motion. We show that even if the feedback control strength is comparable to the decoherence, the optimal unravelling still induces a basis very close to the pointer basis. However if the feedback control is weak compared to the decoherence, this is not the case.

arXiv:1407.5007•New Journal of Physics•Nov 11, 2014•1 citation

Quantum decoherence: Mathematical foundations, physical mechanisms, and experimental tests

Sachin .

Quantum decoherence is widely regarded as the principal dynamical mechanism through which classical behaviour emerges from quantum dynamics. This review presents a technical account of decoherence as an open-system phenomenon, emphasizing its mathematical framework, microscopic models, experimental evidence, and foundational implications. Starting from system-environment interactions and reduced density operators, we introduce completely positive trace-preserving maps and Lindblad master equations. We then discuss pure dephasing, pointer-state selection, quantum Brownian motion, spin-boson dynamics, and collisional decoherence. Experimental evidence from atom and molecular interferometry, superconducting qubits, and mesoscopic platforms is examined. Finally, the review assesses the role of decoherence in the quantum measurement problem. Decoherence explains preferred-basis selection and practical suppression of interference, but it does not independently account for the occurrence of a unique measurement outcome.

International Journal of Physics and Applications•Jul 1, 2025•0 citations

The pointer basis and the feedback stabilization of quantum systems

L. Li, A. Chia, Howard M. Wiseman

Abstract. The dynamics for an open quantum system can be ‘unravelled ’ in infinitely many ways, depending on how the environment is monitored, yielding different sorts of conditioned states, evolving stochastically. In the case of ideal monitoring these states are pure, and the set of states for a given monitoring forms a basis (which is overcomplete in general) for the system. It has been argued elsewhere [D. Atkins et al., Europhys. Lett. 69, 163 (2005)] that the ‘pointer basis ’ as introduced by Zurek and Paz [Phys. Rev. Lett. 70, 1187 (1993)], should be identified with the unravelling-induced basis which decoheres most slowly. Here we show the applicability of this concept of pointer basis to the problem of state stabilization for quantum systems. In particular we prove that for linear Gaussian quantum systems, if the feedback control is assumed to be strong compared to the decoherence of the pointer basis, then the system can be stabilized in one of the pointer basis states with a fidelity close to one (the infidelity varies inversely with the control strength). Moreover, the optimal unravelling for stabilizing the system (in any state) is that which induces the pointer basis. We illustrate these results with a model system: quantum Brownian motion. We show that even if the feedback control strength is comparable to the decoherence, the optimal unravelling still induces a basis very close to the pointer basis. However if the feedback control is weak compared to the decoherence, this is not the case.

•Aug 17, 2016•1 citation
It is well-known that the pointer basis of a quantum system satisfies the condition to diagonalize the interaction Hamiltonian between the subsystems. We show that this condition can be translated into the form δΛ=0,δΛ=0,δΛ=0, where ΛΛΛ, so-called the action, is the time integrated interaction energy: it is found out naturally in the phase of state vectors due to diagonal interaction. The careful treatment of a two states system demonstrates that the states of the total system branch into the states with different values of the action. Mathematically the pointer states are selected out by the saddle point condition on the phase ΛΛΛ. This study helps us to understand the precise mechanism and the general dynamics of decoherence.
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.
The purpose of the present paper is to derive the pointer states of a macro-object using a simple perturbation method. We study the model Hamiltonian involving the weak interaction between the center of mass and its environment. The main conclusion is that the pointer states emerge as the small part of the total state vector when the interaction Hamiltonian is not dominant: the degrees of freedom being at the center of interaction can be localized. In the weak interaction case, if the disappearance of the energy contribution from the off-diagonal terms is caused by the decoherence, it threatens the conservation law. In this study, however, the energy conservation reasonably holds, since the non-classical (i.e., normal quantum) states give main contribution to it. The emergence of the pointer states also implies the special initial state in which the localized state makes the deep well of the potential. In the result, the unitary time evolution of a pointer state is very different from that of the majority of the original state vector of the total system.
Quantum decoherence is a physical process resulting from a system’s entanglement with an environment. This chapter examines the explanatory wealth of decoherence when brought to bear on foundational issues such as the question of why certain measurement bases seem to be preferred by nature – including the pointer basis of measuring apparatuses – the old familiar measurement problem, and the emergence of classicality. Decoherence satisfactorily explains the behavior of the ammonia molecule. Decoherence introduces no additional nonlinearity but “simply takes real, inevitable, interaction with external degrees of freedom to bear in the Hamiltonian”. The basis-specific nature of decoherence will allow for a satisfying explanation to one of quantum mechanics’ oldest mysteries: that of the pointer basis. The basis-specific nature of decoherence will allow for a satisfying explanation to one of quantum mechanics’ oldest mysteries: that of the pointer basis.
The dynamics for an open quantum system can be 'unravelled' in infinitely many ways, depending on how the environment is monitored, yielding different sorts of conditioned states, evolving stochastically. In the case of ideal monitoring these states are pure, and the set of states for a given monitoring forms a basis (which is overcomplete in general) for the system. It has been argued elsewhere (Atkins et al 2005 Europhys. Lett. 69 163 ) that the 'pointer basis' as introduced by Zurek et al (1993 Phys. Rev. Lett. 70 1187 ), should be identified with the unravelling -induced basis which decoheres most slowly. Here we show the applicability of this concept of pointer basis to the problem of state stabilization for quantum systems. In particular we prove that for linear Gaussian quantum systems, if the feedback control is assumed to be strong compared to the decoherence of the pointer basis, then the system can be stabilized in one of the pointer basis states with a fidelity close to one (the infidelity varies inversely with the control strength). Moreover, if the aim of the feedback is to maximize the fidelity of the unconditioned system state with a pure state that is one of its conditioned states, then the optimal unravelling for stabilizing the system in this way is that which induces the pointer basis for the conditioned states. We illustrate these results with a model system: quantum Brownian motion. We show that even if the feedback control strength is comparable to the decoherence, the optimal unravelling still induces a basis very close to the pointer basis. However if the feedback control is weak compared to the decoherence, this is not the case.
Quantum decoherence is widely regarded as the principal dynamical mechanism through which classical behaviour emerges from quantum dynamics. This review presents a technical account of decoherence as an open-system phenomenon, emphasizing its mathematical framework, microscopic models, experimental evidence, and foundational implications. Starting from system-environment interactions and reduced density operators, we introduce completely positive trace-preserving maps and Lindblad master equations. We then discuss pure dephasing, pointer-state selection, quantum Brownian motion, spin-boson dynamics, and collisional decoherence. Experimental evidence from atom and molecular interferometry, superconducting qubits, and mesoscopic platforms is examined. Finally, the review assesses the role of decoherence in the quantum measurement problem. Decoherence explains preferred-basis selection and practical suppression of interference, but it does not independently account for the occurrence of a unique measurement outcome.
Abstract. The dynamics for an open quantum system can be ‘unravelled ’ in infinitely many ways, depending on how the environment is monitored, yielding different sorts of conditioned states, evolving stochastically. In the case of ideal monitoring these states are pure, and the set of states for a given monitoring forms a basis (which is overcomplete in general) for the system. It has been argued elsewhere [D. Atkins et al., Europhys. Lett. 69, 163 (2005)] that the ‘pointer basis ’ as introduced by Zurek and Paz [Phys. Rev. Lett. 70, 1187 (1993)], should be identified with the unravelling-induced basis which decoheres most slowly. Here we show the applicability of this concept of pointer basis to the problem of state stabilization for quantum systems. In particular we prove that for linear Gaussian quantum systems, if the feedback control is assumed to be strong compared to the decoherence of the pointer basis, then the system can be stabilized in one of the pointer basis states with a fidelity close to one (the infidelity varies inversely with the control strength). Moreover, the optimal unravelling for stabilizing the system (in any state) is that which induces the pointer basis. We illustrate these results with a model system: quantum Brownian motion. We show that even if the feedback control strength is comparable to the decoherence, the optimal unravelling still induces a basis very close to the pointer basis. However if the feedback control is weak compared to the decoherence, this is not the case.