Gravitational quantum switch on a superposition of spherical shells

Natália S. Móller1, Bruna Sahdo2, and Nelson Yokomizo2

1RCQI, Institute of Physics, Slovak Academy of Sciences, Dúbravská Cesta 9, 84511 Bratislava, Slovakia
2Departamento de Física–ICEx, Universidade Federal de Minas Gerais, CP702, 30161-970, Belo Horizonte, MG, Brazil

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In the absence of a complete theory of quantum gravity, phenomenological models built upon minimal assumptions have been explored for the analysis of possible quantum effects in gravitational systems. Implications of a superposition of geometries have been considered in such models, including the occurrence of processes with indefinite order. In a gravitational quantum switch, in particular, the order of operations applied by two agents on a target system is entangled with the state of the geometry. We consider a model describing the superposition of geometries produced by distinct arrangements of spherical mass shells, and show that a protocol for the implementation of a gravitational quantum switch can be formulated in such a system. The geometries in superposition are identical in an exterior region outside a given radius, and differ within such a radius. The exterior region provides a classical frame from which the superposition of geometries in the interior region can be probed. One of the agents crosses the interior region and becomes entangled with the geometry, which is explored as a resource for the implementation of the quantum switch. Novel features of the protocol include the superposition of nonisometric geometries, the existence of a region with a definite geometry, and the fact that the agent that experiences the superposition of geometries is in free fall, preventing information on the global geometry to be obtained from within its laboratory.

Presentation at Perimeter Institute “Indefinite temporal order on a superposition of spherical shells” by  Natália Salomé Móller Slovak Academy of Sciences – Institute of Physics

The field of indefinite order in quantum theory was born from an attempt to construct a theory of quantum gravity, in which the first step is to construct a generalized quantum theory that allows events to have an indefinite order. 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. The quantum switch is the simplest example of a task with indefinite order, where the order of operations applied by these 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.

We propose a new protocol for performing a gravitational quantum switch. A freely falling agent crosses the interior region of massive spherical shells in a superposition of different radii and becomes entangled with the spacetime geometry. Just as in Einstein's elevator thought experiment, the agent would not be able to acquire any information on the external geometry. Such an entanglement is used as a resource to control the order of the operations in the implementation of the quantum switch. Our protocol implements the quantum switch in a universal sense, independently of the nature of the operations performed by the agents inside their laboratories.

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Cited by

[1] V. Vilasini and Renato Renner, "Embedding cyclic causal structures in acyclic space-times: no-go results for indefinite causality", arXiv:2203.11245, (2022).

[2] Thiago H. Moreira and Lucas C. Céleri, "Decoherence of a composite particle induced by a weak quantized gravitational field", Classical and Quantum Gravity 41 1, 015006 (2024).

[3] Ravi Kunjwal and Ognyan Oreshkov, "Nonclassicality in correlations without causal order", arXiv:2307.02565, (2023).

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