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In physics, it is crucial to identify operational measurement procedures to give physical meaning to abstract quantities. There has been significant effort to define time operationally using quantum systems, but the same has not been achieved for space. Developing an operational procedure to obtain information about the location of a quantum system is particularly important for a theory combining general relativity and quantum theory, which cannot rest on the classical notion of spacetime. Here, we take a first step towards this goal, and introduce a model to describe an extended material quantum system working as a position measurement device. Such a quantum ruler is composed of harmonically interacting dipoles and serves as a (quantum) reference system for the position of another quantum system. We show that we can define a quantum measurement procedure corresponding to the superposition of positions, and that by performing this measurement we can distinguish when the quantum system is in a coherent or incoherent superposition in the position basis. The model is fully relational, because the only meaningful variables are the relative positions between the ruler and the system, and the measurement is expressed in terms of an interaction between the measurement device and the measured system.more » « lessFree, publicly-accessible full text available May 6, 2025
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Belenchia, Alessio; Wald, Robert M.; Giacomini, Flaminia; Castro-Ruiz, Esteban; Brukner, Časlav; Aspelmeyer, Markus (, International Journal of Modern Physics D)When a massive quantum body is put into a spatial superposition, it is of interest to consider the quantum aspects of the gravitational field sourced by the body. We argue that in order to understand how the body may become entangled with other massive bodies via gravitational interactions, it must be thought of as being entangled with its own Newtonian-like gravitational field. Thus, a Newtonian-like gravitational field must be capable of carrying quantum information. Our analysis supports the view that table-top experiments testing entanglement of systems interacting via gravity do probe the quantum nature of gravity, even if no “gravitons” are emitted during the experiment.more » « less
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Belenchia, Alessio; Wald, Robert M.; Giacomini, Flaminia; Castro-Ruiz, Esteban; Brukner, Časlav; Aspelmeyer, Markus (, Physical Review D)