# Indefinite temporal order on a superposition of spherical shells - VIRTUAL

### APA

Salomé Móller, N. (2024). Indefinite temporal order on a superposition of spherical shells - VIRTUAL. Perimeter Institute. https://pirsa.org/24010078

### MLA

Salomé Móller, Natália. Indefinite temporal order on a superposition of spherical shells - VIRTUAL. Perimeter Institute, Jan. 11, 2024, https://pirsa.org/24010078

### BibTex

@misc{ pirsa_PIRSA:24010078, doi = {10.48660/24010078}, url = {https://pirsa.org/24010078}, author = {Salom{\'e} M{\'o}ller, Nat{\'a}lia}, keywords = {Quantum Foundations}, language = {en}, title = {Indefinite temporal order on a superposition of spherical shells - VIRTUAL}, publisher = {Perimeter Institute}, year = {2024}, month = {jan}, note = {PIRSA:24010078 see, \url{https://pirsa.org}} }

Natália Salomé Móller Slovak Academy of Sciences

## Abstract

The field of indefinite order in quantum theory was born from an attempt to construct a theory of quantum gravity, where the first step is to construct a generalized quantum theory in which events could have an indefinite order [1]. It is expected that such a theory would lead us more naturally to the construction of a quantum gravity theory. One way to explore this topic operationally is to consider that two agents Alice and Bob apply operations A and B on a given target system and that quantum mechanics holds locally for each agent [2]. The quantum switch is the simplest example of a task with indefinite order, where the order of operations applied by two agents on a target system is entangled with the state of a quantum control system. In particular, in the gravitational quantum switch, the order of these operations is entangled with the state of a quantum spacetime [3].

In this talk, I will present a recent result, where we propose a distinct protocol for performing a gravitational quantum switch [4]. One of the agents crosses the interior region of massive spherical shells in a superposition of different radii and becomes entangled with their geometry. This entanglement is used as a resource to control the order of operation in the implementation of the quantum switch. Novel features of the protocol include: i) the superposition of nonisometric geometries; ii) the existence of a region with a definite geometry; iii) the fact that the agent that experiences the superposition of geometries is in free fall, preventing information on the global geometry to be obtained by this agent.

[1] Hardy, J. Phys. A: Math. Theor. **40**, 3081 (2007);

[2] Chiribella, D’Ariano, Perinotti, Valiron, PRA **88**, 022318 (2013); Oreshkov, Costa, Brukner, Nat. Commun. **3**, 1092 (2012).

[3] Zych, Costa, Pikovski, Brukner, Nat. Commun.** 10**, 3772 (2019).

[4] Móller, Sahdo, Yokomizo, arXiv:2306.10984 (2023).

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