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arXiv:1811.07322 · Physical Review A

Quantum-metrology estimation of spacetime parameters of the Earth outperforming classical precision

Jan Kohlrus, David Edward Bruschi, Ivette Fuentes

Published Mar 29, 2019• 20 citations
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Abstract

We consider quantum communication schemes where quantum optical signals are exchanged between a source on Earth and a satellite. The background curved spacetime affects the quantum state of the propagating photons. We employ quantum-metrology techniques to obtain optimal bounds for the precision of quantum measurements of relevant physical parameters encoded in the final state. We focus on satellites in low Earth orbits and we find that our scheme improves the precision of the measurement of the Schwarzschild radius obtained within previous studies. Therefore, our techniques can provide the theoretical tools for novel developments that can potentially outperform the state-of-the-art obtained through classical means. We also review the impact of the relativistic effects on a simple quantum key distribution protocol within satellite schemes and find that such effects can be greatly damaging if they are not properly accounted for.

DOI
10.1103/physreva.99.032350

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•Sep 27, 2019•1 citation
We consider quantum communication schemes where quantum optical signals are exchanged between a source on Earth and a satellite. The background curved spacetime affects the quantum state of the propagating photons. We employ quantum-metrology techniques to obtain optimal bounds for the precision of quantum measurements of relevant physical parameters encoded in the final state. We focus on satellites in low Earth orbits and we find that our scheme improves the precision of the measurement of the Schwarzschild radius obtained within previous studies. Therefore, our techniques can provide the theoretical tools for novel developments that can potentially outperform the state-of-the-art obtained through classical means. We also review the impact of the relativistic effects on a simple quantum key distribution protocol within satellite schemes and find that such effects can be greatly damaging if they are not properly accounted for.
We study how quantum systems that propagate in the spacetime of a rotating planet are affected by the curved background. Spacetime curvature affects wavepackets of photons propagating from Earth to a satellite, and the changes in the wavepacket encode the parameters of the spacetime. This allows us to evaluate quantitatively how quantum communications are affected by the curved spacetime background of the Earth and to achieve precise measurements of Earth's Schwarzschild radius and equatorial angular velocity. We then provide a comparison with the state of the art in parameter estimation obtained through classical means. Satellite to satellite communications and future directions are also discussed.
We propose a quantum experiment to measure with high precision the Schwarzschild spacetime parameters of the Earth. The scheme can also be applied to measure distances by taking into account the curvature of the Earth's spacetime. As a wave packet of (entangled) light is sent from the Earth to a satellite it is redshifted and deformed due to the curvature of spacetime. Measurements after the propagation enable the estimation of the spacetime parameters. We compare our results with the state of the art, which involves classical measurement methods, and discuss what developments are required in space-based quantum experiments to improve on the current measurement of the Schwarzschild radius of the Earth.
In this thesis we study relativistic effects on quantum systems. Quantum physics in curved spacetime is reviewed in a first place, with a focus on continuous variables formalism, quantum metrology techniques, and the relativistic treatment of polarised photons. Then, three topics of interest are studied. The first one is the phononic gravitational wave detector, where resonant mode-mixing and particle creation are triggered in a Bose-Einstein condensate by the passing of a gravitational wave, which can then be measured thanks to quantum metrology techniques. The theory for the phonons’ transformation is developed in details in different resonance scenarios and some sources of noise are considered, like shaking of the cavity where the condensate is trapped and thermal noise. The second topic adressed is quantum communication and metrology in space. In this part, we describe quantum experiments involving communications between Earth and satellites using frequency modes of photons. The propagated and measured photons encode parameters of the spacetime background that can be measured using quantum metrology. Several satellite schemes are discussed, such as satellite to satellite radial communications in Kerr spacetime or Earth to satellite communications in Schwarzschild spacetime. The last topic of this thesis is the evolution of helicity states of photons in a relativistic picture. Two experiments are considered: one where the photons propagate between Earth and satellites through the curved spacetime background surrounding the Earth. The other experiment looks at quantum states of polarised photons as seen by centrifuged observers. For each of these parts, we provide the theory for novel experimental proposals, within the frameworks of either (or both) quantum communications and quantum metrology, that, we believe, would lead to a better understanding in the overlap of quantum mechanics and the relativity theories.
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 generalize 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.
We present a framework for relativistic quantum metrology that is useful for both Earth-based and space-based technologies. Quantum metrology has been so far successfully applied to design precision instruments such as clocks and sensors which outperform classical devices by exploiting quantum properties. There are advanced plans to implement these and other quantum technologies in space, for instance Space-QUEST and Space Optical Clock projects intend to implement quantum communications and quantum clocks at regimes where relativity starts to kick in. However, typical setups do not take into account the effects of relativity on quantum properties. To include and exploit these effects, we introduce techniques for the application of metrology to quantum field theory. Quantum field theory properly incorporates quantum theory and relativity, in particular, at regimes where space-based experiments take place. This framework allows for high precision estimation of parameters that appear in quantum field theory including proper times and accelerations. Indeed, the techniques can be applied to develop a novel generation of relativistic quantum technologies for gravimeters, clocks and sensors. As an example, we present a high precision device which in principle improves the state-of-the-art in quantum accelerometers by exploiting relativistic effects.
n n n The precision of physical parameters is fundamentally limited by irreducible levelsof noise set by quantum mechanics. Quantum metrology is the study of reaching theselimits of noise by employing optimal schemes for parameter estimation. Techniquesin quantum metrology can assist in developing devices to measure the fundamentalinterplay between quantum mechanics and general relativity at state-of-the-artprecision. An example of this is the recent detection of gravitational waves bythe LIGO interferometer. In this thesis, we focus on using quantum metrologyfor estimating space-time parameters. We show the optimal quantum resourcesthat are needed for estimating the gravitational redshift of light propagating in theSchwarzschild space-time of Earth including the inevitable losses due to atmosphericdistortion. We also propose a quantum interferometer using higher order Kerrnon-linearities to improve the sensitivity of estimating gravitational time dilation.In principle, we would be able to downsize interferometers and probe gravity over asmall scale potentially making it practical for measuring gravitational gradients. Wethen study the interesting features of the metric around a rotating massive bodyknown as the Kerr metric and propose implementing a stationary interferometer tomeasure the effect of frame dragging. Finally, we consider loss in the visibility ofquantum interference of single photons in rotating reference frames, and analogouslyin the Kerr metric. In essence, the quantum interference of photons will be affectedby the relativistic effect of rotation. We find experimentally feasible parametersrequiring long optical fibre for long coherence lengths of photons. Our results willhopefully contribute to the efforts of building future quantum technologies that willenter a new regime where general relativistic effects can be measured.