# Can quantum probes satisfy the weak equivalence principle?

## Abstract

We address the question whether quantum probes in a gravitational field can be considered as test particles obeying the weak equivalence principle (WEP). A formulation of the WEP is proposed which applies also in the quantum regime, while maintaining the physical content of its classical counterpart. Such formulation requires the introduction of a gravitational field not to modify the Fisher information about the mass of a freely-falling probe, extractable through measurements of its position. We discover that, while in a uniform field quantum probes satisfy our formulation of the WEP exactly, gravity gradients can encode nontrivial information about the particle’s mass in its wavefunction, leading to violations of the WEP. - Highlights: • Can quantum probes under gravity be approximated as test-bodies? • A formulation of the weak equivalence principle for quantum probes is proposed. • Quantum probes are found to violate it as a matter of principle.

- Authors:

- Quantum Technology Lab, Dipartimento di Fisica, Università degli Studi di Milano, I-20133 Milano (Italy)
- (Italy)

- Publication Date:

- OSTI Identifier:
- 22617505

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics; Journal Volume: 380; Other Information: Copyright (c) 2017 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; EQUIVALENCE PRINCIPLE; GRAVITATIONAL FIELDS; QUANTUM MECHANICS; WAVE FUNCTIONS

### Citation Formats

```
Seveso, Luigi, E-mail: luigi.seveso@unimi.it, Paris, Matteo G.A., and INFN, Sezione di Milano, I-20133 Milano.
```*Can quantum probes satisfy the weak equivalence principle?*. United States: N. p., 2017.
Web. doi:10.1016/J.AOP.2017.03.021.

```
Seveso, Luigi, E-mail: luigi.seveso@unimi.it, Paris, Matteo G.A., & INFN, Sezione di Milano, I-20133 Milano.
```*Can quantum probes satisfy the weak equivalence principle?*. United States. doi:10.1016/J.AOP.2017.03.021.

```
Seveso, Luigi, E-mail: luigi.seveso@unimi.it, Paris, Matteo G.A., and INFN, Sezione di Milano, I-20133 Milano. Mon .
"Can quantum probes satisfy the weak equivalence principle?". United States.
doi:10.1016/J.AOP.2017.03.021.
```

```
@article{osti_22617505,
```

title = {Can quantum probes satisfy the weak equivalence principle?},

author = {Seveso, Luigi, E-mail: luigi.seveso@unimi.it and Paris, Matteo G.A. and INFN, Sezione di Milano, I-20133 Milano},

abstractNote = {We address the question whether quantum probes in a gravitational field can be considered as test particles obeying the weak equivalence principle (WEP). A formulation of the WEP is proposed which applies also in the quantum regime, while maintaining the physical content of its classical counterpart. Such formulation requires the introduction of a gravitational field not to modify the Fisher information about the mass of a freely-falling probe, extractable through measurements of its position. We discover that, while in a uniform field quantum probes satisfy our formulation of the WEP exactly, gravity gradients can encode nontrivial information about the particle’s mass in its wavefunction, leading to violations of the WEP. - Highlights: • Can quantum probes under gravity be approximated as test-bodies? • A formulation of the weak equivalence principle for quantum probes is proposed. • Quantum probes are found to violate it as a matter of principle.},

doi = {10.1016/J.AOP.2017.03.021},

journal = {Annals of Physics},

number = ,

volume = 380,

place = {United States},

year = {Mon May 15 00:00:00 EDT 2017},

month = {Mon May 15 00:00:00 EDT 2017}

}