Indefinite temporal order on a superposition of spherical shells

Zoom link: https://us06web.zoom.us/j/84071837246?pwd=lfDx39Z6xYOzBxHrxQuR2VutPC241g.1

Meeting ID: 840 7183 724

Access code: 433817

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]. 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 new protocol for performing a gravitational quantum switch [4]. 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.

[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, Quantum 8, 1248 (2024).

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