arXiv subjects

Sophia M. Walls

Publications and source records attributed to Sophia M. Walls.

4 recordsLinked to original sources

arXiv2025

Measurement dependence in a Bell inequality arising from the dynamics of hidden variables

Bell inequalities rely on an assumption that the probabilities of adopting configurations of hidden variables describing a system prior to measurement are independent of the choice of measured physical property, also known as measurement independence. Weakening this assumption could alter the inequalities to accommodate experimental data whilst maintaining local interactions. A natural avenue for achieving this would be to model measurement as a dynamical process involving an interaction between the system and its environment (the measurement apparatus), that drives the hidden variables towards attractors representing measurement outcomes of the observable. Implementing such hidden variable dynamics, we can infer from observed correlations the hidden variable probability distributions before measurement, which differ according to which measurement settings were chosen. We explore various models of the dynamics of the hidden variables under measurement, revealing features that can create measurement dependence and others that can not.

quant-ph↗

arXiv2025

Characterising quantum measurement through environmental stochastic entropy production in a two spin 1/2 system

Quantum state diffusion is a framework within which measurement may be described as the continuous and gradual collapse of a quantum system to an eigenstate as a result of interaction with its environment. The irreversible nature of the quantum trajectories that arise may be characterised by the environmental stochastic entropy production associated with the measurement. We consider a system of two spin 1/2 particles undergoing either single particle measurements or measurements of the total z-spin component S_{z}. The mean asymptotic rates of environmental stochastic entropy production associated with collapse can depend on the eigenstate of S_{z} selected, and on the initial state of the system, offering an additional avenue for characterising quantum measurement.

quant-ph↗

arXiv2024

Memory effects in a sequence of measurements of non-commuting observables

We use continuous, stochastic quantum trajectories within a framework of quantum state diffusion (QSD) to describe alternating measurements of two non-commuting observables. Projective measurement of an observable completely destroys memory of the outcome of a previous measurement of the conjugate observable. In contrast, measurement under QSD is not projective and it is possible to vary the rate at which information about previous measurement outcomes is lost by changing the strength of measurement. We apply our methods to a spin 1/2 system and a spin 1 system undergoing alternating measurements of the $S_{z}$ and $S_{x}$ spin observables. Performing strong $S_{z}$ measurements and weak $S_{x}$ measurements on the spin 1 system, we demonstrate return to the same eigenstate of $S_{z}$ to a degree beyond that expected from projective measurements and the Born rule. Such a memory effect appears to be greater for return to the $\pm1$ eigenstates than the $0$ eigenstate. Furthermore, the spin 1 system follows a measurement cascade process where an initial superposition of the three eigenstates of the observable evolves into a superposition of just two, before finally collapsing into a single eigenstate, giving rise to a distinctive pattern of evolution of the spin components.

quant-ph↗

arXiv2024

Stochastic quantum trajectories demonstrate the Quantum Zeno Effect in open spin 1/2, spin 1 and spin 3/2 systems

We investigate the Quantum Zeno Effect in spin 1/2, spin 1 and spin 3/2 open quantum systems undergoing Rabi oscillations, revealing unexplored features for the spin 1 and spin 3/2 systems. The systems interact with an environment designed to perform continuous measurements of an observable, driving the systems stochastically towards one of the eigenstates of the corresponding operator. The system-environment coupling constant represents the strength of the measurement. Stochastic quantum trajectories are generated by unravelling a Markovian Lindblad master equation using the quantum state diffusion formalism. These are regarded as a more appropriate representation of system behaviour than consideration of the averaged evolution since the latter can mask the effect of measurement. Complete positivity is maintained and thus the trajectories can be considered as physically meaningful. The Quantum Zeno Effect is investigated over a range of measurement strengths. Increasing the strength leads to greater system dwell in the vicinity of the eigenstates of the measured observable and lengthens the time taken by the system to return to that eigenstate,thus the Quantum Zeno Effect emerges. For very strong measurement, the Rabi oscillations resemble randomly occurring near-instantaneous jumps between eigenstates. The trajectories followed by the quantum system are heavily dependent on the measurement strength which other than slowing down and adding noise to the Rabi oscillations, changes the paths taken in spin phase space from a circular precession into elaborate figures-of-eight. For spin 1 and spin 3/2 systems, the measurement strength determines which eigenstates are explored and the Quantum Zeno Effect is stronger when the system dwells in the vicinity of certain eigenstates compared to others.

quant-ph↗