# Entanglement and the process of measuring the position of a quantum particle

## Abstract

We explore the entanglement-related features exhibited by the dynamics of a composite quantum system consisting of a particle and an apparatus (here referred to as the “pointer”) that measures the position of the particle. We consider measurements of finite duration, and also the limit case of instantaneous measurements. We investigate the time evolution of the quantum entanglement between the particle and the pointer, with special emphasis on the final entanglement associated with the limit case of an impulsive interaction. We consider entanglement indicators based on the expectation values of an appropriate family of observables, and also an entanglement measure computed on particular exact analytical solutions of the particle–pointer Schrödinger equation. The general behavior exhibited by the entanglement indicators is consistent with that shown by the entanglement measure evaluated on particular analytical solutions of the Schrödinger equation. In the limit of instantaneous measurements the system’s entanglement dynamics corresponds to that of an ideal quantum measurement process. On the contrary, we show that the entanglement evolution corresponding to measurements of finite duration departs in important ways from the behavior associated with ideal measurements. In particular, highly localized initial states of the particle lead to highly entangled final states of the particle–pointer system. Thismore »

- Authors:

- Departamento de Física, Universidad Católica del Norte, Av. Angamos 0610, Antofagasta (Chile)
- Universidad Nacional Noroeste-Buenos Aires, UNNOBA and Conicet, Roque Saenz Peña 456, Junin (Argentina)

- Publication Date:

- OSTI Identifier:
- 22447619

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics; Journal Volume: 354; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANALYTICAL SOLUTION; QUANTUM ENTANGLEMENT; QUANTUM SYSTEMS; SCHROEDINGER EQUATION; TIME DEPENDENCE

### Citation Formats

```
Apel, V.M., Curilef, S., and Plastino, A.R., E-mail: arplastino@unnoba.edu.ar.
```*Entanglement and the process of measuring the position of a quantum particle*. United States: N. p., 2015.
Web. doi:10.1016/J.AOP.2015.01.019.

```
Apel, V.M., Curilef, S., & Plastino, A.R., E-mail: arplastino@unnoba.edu.ar.
```*Entanglement and the process of measuring the position of a quantum particle*. United States. doi:10.1016/J.AOP.2015.01.019.

```
Apel, V.M., Curilef, S., and Plastino, A.R., E-mail: arplastino@unnoba.edu.ar. Sun .
"Entanglement and the process of measuring the position of a quantum particle". United States.
doi:10.1016/J.AOP.2015.01.019.
```

```
@article{osti_22447619,
```

title = {Entanglement and the process of measuring the position of a quantum particle},

author = {Apel, V.M. and Curilef, S. and Plastino, A.R., E-mail: arplastino@unnoba.edu.ar},

abstractNote = {We explore the entanglement-related features exhibited by the dynamics of a composite quantum system consisting of a particle and an apparatus (here referred to as the “pointer”) that measures the position of the particle. We consider measurements of finite duration, and also the limit case of instantaneous measurements. We investigate the time evolution of the quantum entanglement between the particle and the pointer, with special emphasis on the final entanglement associated with the limit case of an impulsive interaction. We consider entanglement indicators based on the expectation values of an appropriate family of observables, and also an entanglement measure computed on particular exact analytical solutions of the particle–pointer Schrödinger equation. The general behavior exhibited by the entanglement indicators is consistent with that shown by the entanglement measure evaluated on particular analytical solutions of the Schrödinger equation. In the limit of instantaneous measurements the system’s entanglement dynamics corresponds to that of an ideal quantum measurement process. On the contrary, we show that the entanglement evolution corresponding to measurements of finite duration departs in important ways from the behavior associated with ideal measurements. In particular, highly localized initial states of the particle lead to highly entangled final states of the particle–pointer system. This indicates that the above mentioned initial states, in spite of having an arbitrarily small position uncertainty, are not left unchanged by a finite-duration position measurement process. - Highlights: • We explore entanglement features of a quantum position measurement. • We consider instantaneous and finite-duration measurements. • We evaluate the entanglement of exact time-dependent particle–pointer states.},

doi = {10.1016/J.AOP.2015.01.019},

journal = {Annals of Physics},

number = ,

volume = 354,

place = {United States},

year = {Sun Mar 15 00:00:00 EDT 2015},

month = {Sun Mar 15 00:00:00 EDT 2015}

}