Relational superposition measurements with a material quantum ruler

Hui Wang1,2, Flaminia Giacomini3,4, Franco Nori2,5,6, and Miles P. Blencowe1

1Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755, USA
2Theoretical Quantum Physics Laboratory, Cluster for Pioneering Research, RIKEN, Wako-shi, Saitama 351-0198, Japan
3Perimeter Institute for Theoretical Physics, 31 Caroline St. N, Waterloo, Ontario, N2L 2Y5, Canada
4Institute for Theoretical Physics, ETH Zürich, Wolfgang-Pauli-Str. 27, Zürich, Switzerland
5Quantum Computing Center, RIKEN, Wako-shi, Saitama 351-0198, Japan
6Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA

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Abstract

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 $N$ 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.

In quantum physics, defining abstract concepts like time and space is not as straightforward as it might seem. A fruitful way to make progress in our understanding of these abstract concepts is to “operationally” construct concrete quantum models involving their measurement. While considerable progress has been made in operationally defining time using quantum clock models, operational definitions of spatial position measurements remain largely unexplored. Developing an operational procedure to obtain information about the evolving location of a quantum system is particularly important in order to further our understanding of the interface between quantum theory and gravity, where classical notions of space and time break down.

Here we propose and develop a concrete model of a “quantum ruler” that crucially meets the challenge of verifying that the ruler-measured particle system behaves according to quantum mechanics. Despite the many technical challenges in developing such a model, we have nevertheless made progress in overcoming some of them. By further refining the quantum ruler model and investigating new scenarios involving dynamical quantum systems, we can extend our findings in several directions, such as constructing more realistic models of the ruler and its interaction with various measured systems, including quantum field systems.

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Cited by

[1] Matthew J. Lake and Marek Miller, "Quantum reference frames, revisited", arXiv:2312.03811, (2023).

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