Phase-space approaches to decoherence and classicality in quantum theory
File(s)
Author(s)
Melanathuru, Rishindra
Type
Thesis
Abstract
This thesis presents a comprehensive study of phase-space measurements, decoherence, and the emergence of classicality in quantum systems.
Motivated by limitations of position-based localisation in standard decoherence models, we develop a phase-space decoherence formalism using coherent-state positive operator-valued measures (POVMs).
These generalised measurements, constructed from overcomplete sets of coherent states, provide a natural and physically motivated framework for modelling coarse-grained quantum observations.
We develop an iterative measurement scheme for phase-space decoherence in systems with Heisenberg-Weyl, $\mathrm{SU}(2)$, $\mathrm{SU}(1,1)$, and $\mathrm{SU}(N)$ symmetries.
In each case, repeated weak measurements gradually suppress quantum interference, driving the system toward a maximally mixed state.
A universal structure is shown to emerge: a single iteration maps the Wigner function to the Husimi $Q$-function, removing negativity, while full decoherence maps the singular Glauber-Sudarshan $P$-function to the $Q$-function, eliminating all singularities.
This establishes a group-independent mechanism by which phase-space measurements induce classicality.
We compare this model to Lindblad-type dynamics, which describe open quantum systems via completely positive, trace-preserving semigroups.
For Heisenberg-Weyl and tomographic $\mathrm{SU}(N)$ systems, the measurement channel coincides exactly with isotropic Lindblad evolution.
In $\mathrm{SU}(2)$ and $\mathrm{SU}(1,1)$ cases, the correspondence is only partial, with exact agreement in asymptotic regimes.
A universal decoherence timescale, $t_*$, emerges beyond which quasi-probability distributions become strictly positive.
We then construct a stochastic unravelling based on Brownian motion on phase space, offering a geometric alternative to standard stochastic Schr\"odinger equations.
This reveals that decoherence occurs without GKSL-type dynamics in noncompact systems.
Such unravellings preserve the intrinsic phase-space symmetry and provide a natural setting for studying semiclassical limits and quantum-to-classical transitions.
Finally, we extend the framework to relativistic quantum systems by defining a covariant coherent-state POVM on the future tube and constructing a Bargmann transform to the forward light cone.
Preliminary results on relativistic phase-space decoherence are presented, along with possible directions for future research.
Motivated by limitations of position-based localisation in standard decoherence models, we develop a phase-space decoherence formalism using coherent-state positive operator-valued measures (POVMs).
These generalised measurements, constructed from overcomplete sets of coherent states, provide a natural and physically motivated framework for modelling coarse-grained quantum observations.
We develop an iterative measurement scheme for phase-space decoherence in systems with Heisenberg-Weyl, $\mathrm{SU}(2)$, $\mathrm{SU}(1,1)$, and $\mathrm{SU}(N)$ symmetries.
In each case, repeated weak measurements gradually suppress quantum interference, driving the system toward a maximally mixed state.
A universal structure is shown to emerge: a single iteration maps the Wigner function to the Husimi $Q$-function, removing negativity, while full decoherence maps the singular Glauber-Sudarshan $P$-function to the $Q$-function, eliminating all singularities.
This establishes a group-independent mechanism by which phase-space measurements induce classicality.
We compare this model to Lindblad-type dynamics, which describe open quantum systems via completely positive, trace-preserving semigroups.
For Heisenberg-Weyl and tomographic $\mathrm{SU}(N)$ systems, the measurement channel coincides exactly with isotropic Lindblad evolution.
In $\mathrm{SU}(2)$ and $\mathrm{SU}(1,1)$ cases, the correspondence is only partial, with exact agreement in asymptotic regimes.
A universal decoherence timescale, $t_*$, emerges beyond which quasi-probability distributions become strictly positive.
We then construct a stochastic unravelling based on Brownian motion on phase space, offering a geometric alternative to standard stochastic Schr\"odinger equations.
This reveals that decoherence occurs without GKSL-type dynamics in noncompact systems.
Such unravellings preserve the intrinsic phase-space symmetry and provide a natural setting for studying semiclassical limits and quantum-to-classical transitions.
Finally, we extend the framework to relativistic quantum systems by defining a covariant coherent-state POVM on the future tube and constructing a Bargmann transform to the forward light cone.
Preliminary results on relativistic phase-space decoherence are presented, along with possible directions for future research.
Version
Open Access
Date Issued
2025-10-02
Date Awarded
01/02/2026
License URL
Advisor
Brody, Dorje
Graefe, Eva-Maria
Sponsor
President's PhD Scholarship
Publisher Department
Department of Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)