Characterization of quantum and classical correlations in the Earth’s curved space-time

Abstract

The preparation of quantum systems and the execution of quantum information tasks between distant users are always affected by gravitational and relativistic effects. In this work, we quantitatively analyze how the curved space-time background of the Earth affects the classical and quantum correlations between photon pairs that are initially prepared in a two-mode squeezed state. More specifically, considering the rotation of the Earth, the space-time around the Earth is described by the Kerr metric. Our results show that these state correlations, which initially increase for a specific range of satellite’s orbital altitude, will gradually approach a finite value with increasing height of satellite’s orbit (when the special relativistic effects become relevant). More importantly, our analysis demonstrates that the changes of correlations generated by the total gravitational frequency shift could reach the level of $$<0.5\%$$ < 0.5 % within the satellite’s height at geostationary Earth orbits.

Gravity enhanced quantum spatial target detection

“…In fact, the propagation of photon between two different locations in curved spacetime can be described in a quantum optics way. To be specific, the mode ā received by the observer at (τ B , r B ) is always possible to be decomposed in terms of the mode â prepared at (τ A , r A ) and an orthogonal mode â⊥ [11,13,17,24]…”

“…Comparing with our final state with the flat space case [2], it is easy to find that the difference in Eqs. (17) and (18) are that the original B is replaced with 1 − Θ 2 + Θ 2 B in our model.…”

“…In realistic situation, the preparation of quantum state and implement of quantum information tasks are inevitably influenced by relativistic effects because gravitational interaction is nonmaskable. Therefore, it is significant to study how gravitational effect of the Earth influences quantum systems in laboratories [10] or long-distance quantum information processing tasks [11][12][13][14][15][16][17][18]. The studies of quantum information in relativistic settings are believed to provide new insights into some key questions in quantum mechanics and relativity, such as nonlocality, causality, and the information paradox of black holes.…”

“…To this end, the framework for the quantum information description of the Earth's gravity on quantum state of photons was introduced in [11]. Such method has been employed to study quantum communication [11,12], quantum metrology [13][14][15], quantum correlations [16,17], and quantum clock synchronization [18] under the influence of spacetime curvature of the Earth. In the scenario of spatial target detection, the transmission of signal beam inevitably involves long distances in curved spacetime, therefore the spacetime effect of the Earth should be seriously considered [19,20].…”

Relativistic motion on Gaussian quantum steering for two-mode localized Gaussian states

“…In general, a photon can be modeled by a wave packet of excitations of a bosonic field. [52] In order to achieve the real scalar quantum field with the relativistic effect, we first focus on the photon wave packet in rest frames, and then extend it to in accelerated coordinates. Here we adopt the following form of the wave packets which are approximately localized and consist of only positive frequency in respective rest frames.…”