Communication between general-relativistic observers without a shared reference frame

Abstract

We show how to reliably encode quantum information and send it between two arbitrary generalrelativistic observers without a shared reference frame. Information stored in a quantum field will inevitably be destroyed by an unknown Bogolyubov transformation relating the observers. However certain quantum correlations between different, independent fields will be preserved, no matter what transformation is applied. We show how to efficiently use these correlations in communication between arbitrary observers.-Introduction. The central question of the quantum information theory: how to reliably encode, send and decode information [1,2] becomes much more difficult to answer when relativistic effects are taken into account. In the non-relativistic case it is usually implicitly assumed that the sender and receiver share a common reference frame, i.e. they are not moving relative to each other, and their common frame is inertial. As soon as one departs from this assumption one encounters serious conceptual difficulties. It is known that changing an observer's reference frame results in a certain Bogolyubov transformation of the observed state. The most well known consequence of that is the Unruh effect [3]: a vacuum state of a quantum field, as observed by an inertial observer, ceases to be vacuum from the perspective of a uniformly accelerated observer. The latter will detect a thermal state with the temperature proportional to his proper acceleration. Such relativity of the vacuum state is just one example, in general any state will undergo a certain unitary transformation due to motion of the observer. The number of particles, entanglement and other characteristic quantities are affected in general. Furthermore, entering the regime of curved space-times adds more sophistication to the picture, as even the concept of a particle is not well defined and, as a consequence, the notion of a quantum state has no clear interpretation [4].In this work we propose a general method of overcoming the problems of mutual communication with quantum states between two observers without a shared reference frame. When one party wishes to send a quantum state to the other, the state becomes distorted due to relative motion. However, following the idea of Ref.[5] we note that any type of motion affects states of all quantum fields in an analogous way. Consider a number of independent, non-interacting quantum fields, such as two polarization components of the free electromagnetic field. Although the states of both polarization components will be affected by the relative motion in a certain way, some correlations between the two will remain unaffected. Therefore if the sender and the receiver have access to two or more independent quantum fields, they can securely encode information into correlations between the fields and such information will not be affected by their relative motion. We show how the ability to create and measure these correlations allows the observers to reliably communicate even without sharing a common reference frame....

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

“…Our framework can readily be applied to quantum information protocols in which the effect of acceleration or gravity cannot be ignored. As a future line of research, we are interested in employing our framework to study the effect of acceleration on communication between two relativistic observers without a shared reference frame [28,29] as well as continuous variable teleportation [30,31]. We are also interested in investigating analogous effects in other types of quantum fields such as massless (that cannot be obtained by taking m → 0 limit of the results of this paper; see footnote 1 in Sec.…”

Monogamy of Einstein‐Podolsky‐Rosen Steering in the Background of an Asymptotically Flat Black Hole

“…And for this reason, quantum correlations in fact intrinsically relevant to the foundational core of thermodynamics and information loss problem of black holes. On the other hand, the influence of gravity on quantum systems cannot be ignored with the advance in theory and technology of quantum information processing. For example, it has been experimentally demonstrated that the gravitational effects of the Earth notably influence the precision of atomic clocks for a variation of 0.33 m in height .…”

Gaussian quantum steering and its asymmetry in curved spacetime

“…On the other hand, relativistic quantum information [20][21][22][23][24][25][26][27][28][29][30][31][32][33], the study of quantum information processes and concepts in a relativistic setting, has been a blooming area of research for both conceptual and experimental reasons. Understanding quantum phenomena in a relativistic framework is necessary because the realistic quantum systems are essentially nonin-ertial.…”