Quantum generalisation of Einstein’s equivalence principle can be verified with entangled clocks as quantum reference frames

Abstract

The Einstein equivalence principle (EEP) is of crucial importance to test the foundations of general relativity. When the particles involved in the test exhibit quantum properties, it is unknown whether this principle still holds. A violation of the EEP would have drastic consequences for physics. A more conservative possibility is that the EEP holds in a generalised form for delocalised quantum particles. Here we formulate such a generalised EEP by extending one of its paradigmatic tests with clocks to quantum clocks that are in a quantum superposition of positions and velocities. We show that the validity of such a generalised version of the EEP is equivalent to the possibility of transforming to the perspective of an arbitrary Quantum Reference Frame (QRF), namely a reference frame associated to the quantum state of the clock. We further show that this generalised EEP can be verified by measuring the proper time of entangled clocks in a quantum superposition of positions in the Earth gravitational field. The violation of the generalised EEP corresponds to the impossibility of defining dynamical evolution in the frame of each clock, and results in a modification to the probabilities of measurements calculated in the laboratory frame. Hence, it can be verified experimentally, for instance in an atom interferometer.