Effect of relativistic acceleration on localized two-mode Gaussian quantum states

Abstract

We study how an arbitrary Gaussian state of two localized wave packets, prepared in an inertial frame of reference, is described by a pair of uniformly accelerated observers. We explicitly compute the resulting state for arbitrarily chosen proper accelerations of the observers and independently tuned distance between them. To do so, we introduce a generalized Rindler frame of reference and analytically derive the corresponding state transformation as a Gaussian channel. Our approach provides several new insights into the phenomenon of vacuum entanglement such as the highly nontrivial effect of spatial separation between the observers including sudden death of entanglement. We also calculate the fidelity of the two-mode channel for non-vacuum Gaussian states and obtain bounds on classical and quantum capacities of a single-mode channel. Our framework can be directly applied to any continuous variable quantum information protocol in which the effects of acceleration or gravity cannot be neglected.

Two-mode Gaussian quantum states measured by collinearly and noncollinearly accelerating observers

“…Our aim is to describe two accelerating observers, moving along zaxis, that are separated by the distance D at their closest approach. By the introduction of the modified Rindler coordinates [54]:…”

“…The expressions for M and N will now be derived, for the cases and under the assumptions discussed in Ref. [54].…”

“…For a more realistic setup in which quantum states can be measured, transferred and exploited, some kind of localization in space and time is necessary. Different approaches have been employed to tackle this problemmoving cavities [39][40][41][42][43], point-like detectors [44][45][46][47][48] and localized wave-packets [49][50][51][52][53][54][55][56].…”

Entanglement enhanced thermometry in the detection of the Unruh effect

“…These include the approaches involving Bogolyubov transformation between the Minkowski and Rindler frames of reference [1,15,[18][19][20][21], the application of the Unruh-DeWitt detector model which offers an operational definition of a particle as a trigger for the transitions between the atomic energy levels [1,22], the manifestation of thermalization of open quantum systems involving decoherence and dissipation [23], understanding as a quantum noise channel [24], and the thermal correction to the energy shift and spontaneous excitation of atoms [25][26][27]. In recent years, the Unruh effect has been extensively considered in the field of quantum information.…”

“…In recent years, the Unruh effect has been extensively considered in the field of quantum information. It has been studied how the Unruh effect affects quantum entanglement between different observers [18][19][20][21][28][29][30][31][32][33][34][35][36], as well as other types of non-classical correlations [20,[37][38][39][40][41][42][43] and consequently quantum nonlocality [44][45][46][47], quantum teleportation [28,48], entropic uncertainty relations [49], and parameter estimation [50][51][52]. The Unruh effect has also been used to analyze how to improve information processing protocols [53,54] and quantum measurement techniques [55].…”