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:2509.18206

Joint momenta-coordinates states as pointer states in quantum decoherence

Nomenjanahary Tanjonirina Manampisoa, Ravo Tokiniaina Ranaivoson, R. Raboanary, Raoelina Andriambololona, Rivo Herivola Manjakamanana Ravelonjato, Rabesiranana, Naivo

Published Sep 20, 2025• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2509.18206

Related papers

Predictability sieve and quantum trajectories: For pointer states quantum unravellings are classically robust

Diego A. R. Dalvit, Jacek Dziarmaga, Wojciech Hubert Zurek

We study various measures of classicality of the states of open quantum systems subject to decoherence and continuous quantum measurement. Classical states are expected to be stable in spite of decoherence, and are thought to leave conspicuous imprints on the environment. Here these expected features of environment-induced superselection (einselection) are quantified using four different criteria: predictability sieve (which selects states that produce least entropy), purification time (which looks for states that are the easiest to find out from the imprint they leave on the environment), efficiency threshold (which finds states that can be deduced from measurements on a smallest fraction of the environment), and purity loss time (that looks for states for which it takes the longest to lose a set fraction of their initial purity). We show that when pointer states, the most predictable states of an open quantum system selected by the predictability sieve, are well defined, all four criteria agree that they are indeed the most classical states. We illustrate this with two examples: an underdamped harmonic oscillator, for which coherent states are unanimously chosen by all criteria, and a free particle undergoing quantum Brownian motion, for which most criteria select almost identical Gaussian states (although, in this case, predictability sieve does not select well defined pointer states.)

•Sep 23, 2005•0 citations

Predictability sieve, pointer states, and the classicality of quantum trajectories

Diego A. R. Dalvit, Jacek Dziarmaga, Wojciech Hubert Zurek

We study various measures of classicality of the states of open quantum systems subject to decoherence. Classical states are expected to be stable in spite of decoherence, and are thought to leave conspicuous imprints on the environment. Here these expected features of environment-induced superselection are quantified using four different criteria: predictability sieve (which selects states that produce least entropy), purification time (which looks for states that are the easiest to find out from the imprint they leave on the environment), efficiency threshold (which finds states that can be deduced from measurements on a smallest fraction of the environment), and purity loss time (that looks for states for which it takes the longest to lose a set fraction of their initial purity). We show that when pointer states---the most predictable states of an open quantum system selected by the predictability sieve---are well defined, all four criteria agree that they are indeed the most classical states. We illustrate this with two examples: an underdamped harmonic oscillator, for which coherent states are unanimously chosen by all criteria, and a free particle undergoing quantum Brownian motion, for which most criteria select almost identical Gaussian states (although, in this case, the predictability sieve does not select well defined pointer states).

arXiv:quant-ph/0509174•Physical Review A•Dec 1, 2005•33 citations

Pointer states via decoherence in a quantum measurement

Anu Venugopalan

We consider the interaction of a quantum system (spin-$\frac{1}{2})$ with a macroscopic quantum apparatus (harmonic oscillator) which in turn is coupled to a bath of harmonic oscillators. Exact solutions of the Markovian master equation show that the reduced density matrix of the system-apparatus combination decoheres to a statistical mixture where up and down spins eventually correlate with pointer states of the apparatus (harmonic oscillator), with associated probabilities in accordance with quantum principles. For the zero-temperature bath these pointer states turn out to be coherent states of the harmonic oscillator (apparatus) for arbitrary initial states of the apparatus. Further, we see that the decoherence time is inversely proportional to the square of the separation between the two coherent states with which the spins correlate. For a high-temperature bath, pointer states no longer remain coherent states but are Gaussian distributions (generalized coherent states). Spin up and down states of the system now correlate with nearly diagonal distributions in position of these generalized coherent states. The diagonalization in position increases with the temperature of the bath. The off-diagonal elements in spin space decohere over a time scale which goes inversely as the square of the separation between the peaks of the two position distributions that correlate with the spin states. Zurek's earlier approximate result for the decoherence time is consistent with our exact results. Our analysis brings out the importance of looking at a measurementlike scenario where definite correlations are established between the system and apparatus to determine the nature of the pointer basis of the apparatus. Further, our exact results demonstrate in an unambiguous way that the pointer states in this measurement model emerge independent of the initial state of the apparatus.

arXiv:quant-ph/9909005•Physical Review A•Dec 8, 1999•34 citations

Quantum Phase Space framework for Relativistic Decoherence

Ravo Tokiniaina Ranaivoson, Raoelina Andriambololona, Diary Lova Ratsimbazafy +4 more

This work addresses how classical-like behavior emerges in a relativistic quantum setting. Decoherence is described as the evolution of general quantum states belonging to a total state bundle toward a classical-like mixture of pointer states. The pointer states are geometrically supported by the relativistic quantum phase space (RQPS), defined as the subspace of the expectation-value space equipped with a ground variance field that saturates the uncertainty relations and satisfies an LCT-compatible de Sitter constraint.

•Nov 1, 2026•0 citations

Quantum Phase Space framework for Relativistic Decoherence

Ravo Tokiniaina Ranaivoson, Raoelina Andriambololona, Diary Lova Ratsimbazafy +4 more

This work addresses how classical-like behavior emerges in a relativistic quantum setting. Decoherence is described as the evolution of general quantum states belonging to a total state bundle toward a classical-like mixture of pointer states. The pointer states are geometrically supported by the relativistic quantum phase space (RQPS), defined as the subspace of the expectation-value space equipped with a ground variance field that saturates the uncertainty relations and satisfies an LCT-compatible de Sitter constraint.

•Oct 30, 2026•0 citations

Decoherence challenges in Nanoscience: A Quantum Phase Space perspective

Ravo Tokiniaina Ranaivoson, Angelo Mamitiana Ralaikoto, Diary Lova Ratsimbazafy +5 more

Quantum decoherence is both the fundamental mechanism underlying the quantum-to-classical transition and a major challenge for the development of scalable nanoscale quantum technologies. This work introduces a Quantum Phase Space (QPS) framework that provides a unified geometric description of decoherence. The framework is based on a dual structure consisting of an overcomplete continuous frame of minimum-uncertainty states that defines the QPS geometry, and an orthonormal basis that satisfies the strict mathematical requirements for decoherence within the Spectrum Broadcast Structure (SBS) objectivity criterion for pointer states. Within this framework, the variance-covariance matrix of the QPS ground states serves as a universal indicator of decoherence regimes:it is time-independent for Markovian (memoryless) dynamics, and time-dependent for non-Markovian dynamics with memory and information backflow. To illustrate the formalism, the Hu-Paz-Zhang (HPZ) model is generalized to include simultaneous position and momentum couplings to the environment, leading to a generalized non-Markovian master equation characterized by a spectral-density matrix. The corresponding evolution equations for the first moments$\ (\left\langle p(t) \right\rangle,\left\langle x(t) \right\rangle)$ and for the ground covariance matrix establish a direct connection between microscopic environmental properties, classical-like trajectories and the QPS geometry. The proposed framework provides a unified theoretical foundation for modeling decoherence in nanoscale systems involving simultaneous position and momentum interactions with the environment. The QPS framework may thus bridge fundamental theory and practical quantum engineering, offering a promising coherent pathway to understand, control, and exploit decoherence at the nanoscience frontier.

quant-pharXiv:2512.22297•Nano-Horizons Journal of Nanosciences and Nanotechnologies•Dec 29, 2025•0 citations
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.
We study various measures of classicality of the states of open quantum systems subject to decoherence and continuous quantum measurement. Classical states are expected to be stable in spite of decoherence, and are thought to leave conspicuous imprints on the environment. Here these expected features of environment-induced superselection (einselection) are quantified using four different criteria: predictability sieve (which selects states that produce least entropy), purification time (which looks for states that are the easiest to find out from the imprint they leave on the environment), efficiency threshold (which finds states that can be deduced from measurements on a smallest fraction of the environment), and purity loss time (that looks for states for which it takes the longest to lose a set fraction of their initial purity). We show that when pointer states, the most predictable states of an open quantum system selected by the predictability sieve, are well defined, all four criteria agree that they are indeed the most classical states. We illustrate this with two examples: an underdamped harmonic oscillator, for which coherent states are unanimously chosen by all criteria, and a free particle undergoing quantum Brownian motion, for which most criteria select almost identical Gaussian states (although, in this case, predictability sieve does not select well defined pointer states.)
We study various measures of classicality of the states of open quantum systems subject to decoherence. Classical states are expected to be stable in spite of decoherence, and are thought to leave conspicuous imprints on the environment. Here these expected features of environment-induced superselection are quantified using four different criteria: predictability sieve (which selects states that produce least entropy), purification time (which looks for states that are the easiest to find out from the imprint they leave on the environment), efficiency threshold (which finds states that can be deduced from measurements on a smallest fraction of the environment), and purity loss time (that looks for states for which it takes the longest to lose a set fraction of their initial purity). We show that when pointer states---the most predictable states of an open quantum system selected by the predictability sieve---are well defined, all four criteria agree that they are indeed the most classical states. We illustrate this with two examples: an underdamped harmonic oscillator, for which coherent states are unanimously chosen by all criteria, and a free particle undergoing quantum Brownian motion, for which most criteria select almost identical Gaussian states (although, in this case, the predictability sieve does not select well defined pointer states).
We consider the interaction of a quantum system (spin-12)\frac{1}{2})21​) with a macroscopic quantum apparatus (harmonic oscillator) which in turn is coupled to a bath of harmonic oscillators. Exact solutions of the Markovian master equation show that the reduced density matrix of the system-apparatus combination decoheres to a statistical mixture where up and down spins eventually correlate with pointer states of the apparatus (harmonic oscillator), with associated probabilities in accordance with quantum principles. For the zero-temperature bath these pointer states turn out to be coherent states of the harmonic oscillator (apparatus) for arbitrary initial states of the apparatus. Further, we see that the decoherence time is inversely proportional to the square of the separation between the two coherent states with which the spins correlate. For a high-temperature bath, pointer states no longer remain coherent states but are Gaussian distributions (generalized coherent states). Spin up and down states of the system now correlate with nearly diagonal distributions in position of these generalized coherent states. The diagonalization in position increases with the temperature of the bath. The off-diagonal elements in spin space decohere over a time scale which goes inversely as the square of the separation between the peaks of the two position distributions that correlate with the spin states. Zurek's earlier approximate result for the decoherence time is consistent with our exact results. Our analysis brings out the importance of looking at a measurementlike scenario where definite correlations are established between the system and apparatus to determine the nature of the pointer basis of the apparatus. Further, our exact results demonstrate in an unambiguous way that the pointer states in this measurement model emerge independent of the initial state of the apparatus.
This work addresses how classical-like behavior emerges in a relativistic quantum setting. Decoherence is described as the evolution of general quantum states belonging to a total state bundle toward a classical-like mixture of pointer states. The pointer states are geometrically supported by the relativistic quantum phase space (RQPS), defined as the subspace of the expectation-value space equipped with a ground variance field that saturates the uncertainty relations and satisfies an LCT-compatible de Sitter constraint.
This work addresses how classical-like behavior emerges in a relativistic quantum setting. Decoherence is described as the evolution of general quantum states belonging to a total state bundle toward a classical-like mixture of pointer states. The pointer states are geometrically supported by the relativistic quantum phase space (RQPS), defined as the subspace of the expectation-value space equipped with a ground variance field that saturates the uncertainty relations and satisfies an LCT-compatible de Sitter constraint.
Quantum decoherence is both the fundamental mechanism underlying the quantum-to-classical transition and a major challenge for the development of scalable nanoscale quantum technologies. This work introduces a Quantum Phase Space (QPS) framework that provides a unified geometric description of decoherence. The framework is based on a dual structure consisting of an overcomplete continuous frame of minimum-uncertainty states that defines the QPS geometry, and an orthonormal basis that satisfies the strict mathematical requirements for decoherence within the Spectrum Broadcast Structure (SBS) objectivity criterion for pointer states. Within this framework, the variance-covariance matrix of the QPS ground states serves as a universal indicator of decoherence regimes:it is time-independent for Markovian (memoryless) dynamics, and time-dependent for non-Markovian dynamics with memory and information backflow. To illustrate the formalism, the Hu-Paz-Zhang (HPZ) model is generalized to include simultaneous position and momentum couplings to the environment, leading to a generalized non-Markovian master equation characterized by a spectral-density matrix. The corresponding evolution equations for the first moments (⟨p(t)⟩,⟨x(t)⟩)\ (\left\langle p(t) \right\rangle,\left\langle x(t) \right\rangle) (⟨p(t)⟩,⟨x(t)⟩) and for the ground covariance matrix establish a direct connection between microscopic environmental properties, classical-like trajectories and the QPS geometry. The proposed framework provides a unified theoretical foundation for modeling decoherence in nanoscale systems involving simultaneous position and momentum interactions with the environment. The QPS framework may thus bridge fundamental theory and practical quantum engineering, offering a promising coherent pathway to understand, control, and exploit decoherence at the nanoscience frontier.