Quantum metrology for relativistic quantum fields

Abstract

In quantum metrology quantum properties such as squeezing and entanglement are exploited in the design of a new generation of clocks, sensors and other measurement devices that can outperform their classical counterparts. Applications of great technological relevance lie in the precise measurement of parameters which play a central role in relativity, such as proper accelerations, relative distances, time and gravitational field strengths. In this paper we generalise recently introduced techniques to estimate physical quantities within quantum field theory in flat and curved space-time. We consider a bosonic quantum field that undergoes a generic transformation, which encodes the parameter to be estimated. We present analytical formulas for optimal precision bounds on the estimation of small parameters in terms of Bogoliubov coefficients for single mode and two-mode Gaussian channels.Comment: Ivette Fuentes previously published as I. Fuentes-Guridi and I. Fuentes-Schulle

Quantum estimation of the Schwarzschild spacetime parameters of the Earth

“…It is therefore convenient to work in the covariance matrix formalism [30]. This formalism enables elegant and simplified calculations for the application of quantum information and metrology techniques in relativistic quantum field theory [6,7]. The formalism is applicable to bosonic fields as long as the analysis is restricted to Gaussian states.…”

“…This theory properly incorporates quantum and relativistic effects at regimes where space experiments take place. In this section we review general techniques and methods for the application of metrology to quantum field theory introduced in [6,7].…”

“…This theoretical framework enables one to incorporate relativistic effects at the low energy regimes that are being reached by cutting-edge quantum experiments. Recently, methods for the application of quantum metrology to quantum field theory have been introduced in [6,7]. Interestingly, relativistic effects such as particle creation, can be exploited to measure accelerations with an optimal measurement precision that is higher than the non-relativistic counterpart [7].…”

“…In this paper, we apply relativistic quantum metrology [6,7] to estimate the Schwarzschild space-time parameters of the Earth and we propose an implementation using realisable space-based experiments. An entangled light wave-packet is sent from Earth to a satellite (or equivalently in the opposite direction).…”

Quantum estimation of parameters of classical spacetimes

“…There has recently been some promising work in this direction [11][12][13], focusing on quantum probes consisting of scalar fields in Gaussian states. Here we present a general formalism for relativistic quantum metrology, using arbitrary fields and states.…”