Relativity of quantum superpositions

Abstract

In modern physics only relative quantities are considered to have physical significance. For example, position assigned to a system depends on the choice of coordinates, and only relative distances between different systems have physical relevance. On the other hand, in quantum theory the scenario where one system, A, is localised around certain position while another system B is in a spatial superposition is considered to be physically different from the scenario where A is in a superposition, while B is localised. Different physical effects are anticipated in the two scenarios especially when the two systems have widely different masses. Here we show that for any superposed amplitudes that are related by a symmetry transformation, the above scenarios are physically equivalent: probabilities for any measurement are the same whether we assign the superposition state to system A or to system B. More generally, linearity of quantum theory guarantees that if a theory is invariant under some symmetry transformations it is necessarily also invariant under their arbitrary `superpositions'. Thus the notion of a superposition turns out to be relative to the choice of coordinates, once it is realised that relations between coordinates do not need to be classical.

4+3 pages, 2 figures

References in corpus (6)

• Precision Measurement of the Newtonian Gravitational Constant Using Cold Atoms
• Quantum mechanics and the covariance of physical laws in quantum reference frames
• Measurement of the Gravity-Field Curvature by Atom Interferometry
• General relativistic effects in quantum interference of photons
• Bounds on quantum communication via Newtonian gravity
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Cited by in corpus (9)

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• Quantum reference frames for an indefinite metric
• A relational perspective on the Wigner-Araki-Yanase theorem
• Simulating indefinite causal order with Rindler observers
• Quantum switch in the gravity of Earth
• Universal Transformation of Displacement Operators and its Application to Homodyne Tomography In Differing Relativistic Reference Frames
• Consistency of quantum computation and the equivalence principle
• Quantum Non-Gaussianity From An Indefinite Causal Order of Gaussian Operations