Discrimination of metric theories

Abstract

We study the possibility of discriminating between metric theories within the Parametrized Post-Newtonian formalism. In this approach, the two-dimensional quantum state of a massive quantum clock becomes, after propagating at low speed and in a weak gravitational field, a function of the post-Newtonian parameters and thus a signature of a metric theory. To discriminate among metric theories, we resort to quantum-state discrimination strategies such as minimum-error and unambiguous discrimination. In particular, we show that it is possible to refute the hypothesis that a particular metric theory describes spacetime with a single detection event and that it is possible to discriminate with certainty between two different metrics, also with a single detection event. In general, the success probability of the discrimination strategy is a harmonic function of the product of the difference of the proper time corresponding to each quantum clock state, the energy difference between the energy eigenstates of the quantum clock, the propagation length, and speed. It is thus possible to find suitable length and speed scales such that the success probability is close to one by selecting a quantum system with the highest energy difference and the longest natural lifetime. According to this, atomic nuclei such as thorium are considered the most suitable quantum clocks. We also show that the use of a ensemble of quantum clocks leads to a significant increase in the probability of success in discriminating between post-Newtonian parameters that differ by $10^{-5}$. This facilitates achieving a probability of success approaching unity with distances on the scale of several kilometers and velocities approximating one-thousandth of the speed of light for a ensemble of only 10 quantum clocks.

16 pages, 15 figures and 1 appendix

References in corpus (21)

• Advanced Virgo: a 2nd generation interferometric gravitational wave detector
• The Confrontation between General Relativity and Experiment
• Quantum state discrimination and its applications
• Modified theories of Gravity: Why, How and What?
• Maximum Confidence Quantum Measurements
• Observation of the radiative decay of the ${}^{229}\mathrm{Th}$ nuclear clock isomer
• Demonstration of near-Optimal Discrimination of Optical Coherent States
• A new PPN parameter to test Chern-Simons gravity
• Experimental minimum-error quantum-state discrimination in high dimensions
• Parametrized tests of post-Newtonian theory using principal component analysis
• Discriminating single-photon states unambiguously in high dimensions
• Effects of electrons on nuclear clock transition frequency in ${}^{229}$Th ions
• Direct Estimate of the Post-Newtonian Parameter and Cosmic Curvature from Galaxy-scale Strong Gravitational Lensing
• Post-Newtonian parameters $\gamma$ and $\beta$ of scalar-tensor gravity for a homogeneous gravitating sphere
• Experimental quantum state discrimination using the optimal fixed rate of inconclusive outcomes strategy
• Enhanced discrimination of high-dimensional quantum states by concatenated optimal measurement strategies
• Parametrized post-Newtonian limit of generalized scalar-nonmetricity theories of gravity
• Quantum time dilation in a gravitational field
• Testing quantum theory on curved space-time with quantum networks
• An invitation to the sample complexity of quantum hypothesis testing
• Training quantum measurement devices to discriminate unknown non-orthogonal quantum states