Toy model illustrating the effect of measurement dependence on a Bell
inequality
- URL: http://arxiv.org/abs/2307.07655v1
- Date: Fri, 14 Jul 2023 23:20:36 GMT
- Title: Toy model illustrating the effect of measurement dependence on a Bell
inequality
- Authors: Sophia M. Walls and Ian J. Ford
- Abstract summary: We show that the probabilities of adopting configurations of hidden variables describing a system prior to measurement are independent of the choice of physical property that will be measured.
We demonstrate how this can emerge and illustrate the relaxed upper limit using a simple toy model of dynamical quantum measurement.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Bell's inequalities rely on the assumption of measurement independence,
namely that the probabilities of adopting configurations of hidden variables
describing a system prior to measurement are independent of the choice of
physical property that will be measured. Weakening this assumption can change
the inequalities to accommodate experimental data. We illustrate this by
considering quantum measurement to be the dynamical evolution of hidden
variables to attractors in their phase space that correspond to eigenstates of
system observables. The probabilities of adopting configurations of these
variables prior to measurement then depend on the choice of physical property
measured by virtue of the boundary conditions acting on the dynamics. Allowing
for such measurement dependence raises the upper limit of the CHSH parameter in
Bell's analysis of an entangled pair of spin half particles subjected to
measurement of spin components along various axes, whilst maintaining local
interactions. We demonstrate how this can emerge and illustrate the relaxed
upper limit using a simple toy model of dynamical quantum measurement. The
conditioning of the hidden variable probability distribution on the chosen
measurement settings can persist far back in time in certain situations, a
memory that could explain the correlations exhibited in an entangled quantum
system.
Related papers
- A Family of Local Deterministic Models for Singlet Quantum State Correlations [0.0]
We introduce a new class of local deterministic models that account for both particle preparation and measurement settings.
Our model reproduces the quantum mechanical predictions under the assumption of relaxed measurement independence.
Our findings highlight the nuanced relationship between local determinism and quantum mechanics, offering new insights into the nature of quantum correlations and hidden variables.
arXiv Detail & Related papers (2024-08-18T19:38:15Z) - Enhanced Entanglement in the Measurement-Altered Quantum Ising Chain [46.99825956909532]
Local quantum measurements do not simply disentangle degrees of freedom, but may actually strengthen the entanglement in the system.
This paper explores how a finite density of local measurement modifies a given state's entanglement structure.
arXiv Detail & Related papers (2023-10-04T09:51:00Z) - Continuously Monitored Quantum Systems beyond Lindblad Dynamics [68.8204255655161]
We study the probability distribution of the expectation value of a given observable over the possible quantum trajectories.
The measurements are applied to the entire system, having the effect of projecting the system into a product state.
arXiv Detail & Related papers (2023-05-06T18:09:17Z) - Quantifying measurement-induced quantum-to-classical crossover using an
open-system entanglement measure [49.1574468325115]
We study the entanglement of a single particle under continuous measurements.
We find that the entanglement at intermediate time scales shows the same qualitative behavior as a function of the measurement strength.
arXiv Detail & Related papers (2023-04-06T09:45:11Z) - Evolution of many-body systems under ancilla quantum measurements [58.720142291102135]
We study the concept of implementing quantum measurements by coupling a many-body lattice system to an ancillary degree of freedom.
We find evidence of a disentangling-entangling measurement-induced transition as was previously observed in more abstract models.
arXiv Detail & Related papers (2023-03-13T13:06:40Z) - Localization properties in disordered quantum many-body dynamics under
continuous measurement [0.0]
We study localization properties of continuously monitored dynamics in quantum many-body systems.
By calculating the fidelity between random quantum trajectories, we demonstrate that the disorder and the measurement can lead to dynamical properties distinct from each other.
arXiv Detail & Related papers (2023-01-18T03:39:39Z) - Full counting statistics as probe of measurement-induced transitions in
the quantum Ising chain [62.997667081978825]
We show that local projective measurements induce a modification of the out-of-equilibrium probability distribution function of the local magnetization.
In particular we describe how the probability distribution of the former shows different behaviour in the area-law and volume-law regimes.
arXiv Detail & Related papers (2022-12-19T12:34:37Z) - Dependence of measurement outcomes on the dynamics of quantum coherent
interactions between the system and the meter [0.0]
We show that the values of physical properties obtained in quantum measurements originate from the quantum coherent system dynamics associated with the back-action on the system.
Measurement outcomes represent elements of the dynamics and cannot be explained by measurement independent elements of reality.
arXiv Detail & Related papers (2022-09-01T23:23:23Z) - Quantum Zeno effect appears in stages [64.41511459132334]
In the quantum Zeno effect, quantum measurements can block the coherent oscillation of a two level system by freezing its state to one of the measurement eigenstates.
We show that the onset of the Zeno regime is marked by a $textitcascade of transitions$ in the system dynamics as the measurement strength is increased.
arXiv Detail & Related papers (2020-03-23T18:17:36Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.