Relativistic Quantum Information

Relativistic Quantum Information

Over the past decade the discipline of relativistic quantum information (RQI) has received much attention. Its aim is the study of the resources and tasks of quantum information science in the context of relativity, i.e. by combining elements of quantum information theory, quantum optics and quantum field theory with special and general relativity. In particular attention has been focused on the mechanisms that degrade or generate entanglement, the main resource of quantum information tasks, for a review see, e.g., [Alsing and Fuentes, Class. Quantum Grav. 29, 224001 (2012)].

Entanglement of quantum fields in non-uniformly moving cavities

Space-time diagram of cavity motion.

Amongst other things, my PhD thesis deals with the role of non-uniformly moving cavities in RQI, using the model first employed in [Bruschi, Fuentes and Louko, Phys. Rev. D 85, 061701(R) (2012)]. The cavities provide a framework that removes the idealisation of spatially delocalized field modes by confining quantum fields. This allows the consideration of entanglement between an inertial reference cavity (Alice, blue) and a non-uniformly moving cavity (Rob) on a worldline that consists of segments of inertial motion (red) and finite uniform acceleration (green). The entanglement between the cavities is degraded when only certain modes are observed. However, the degradation effects can be completely compensated by cleverly timing the travel scenario of the moving cavity for massless (1+1) dimensional, bosonic or fermionic fields.

The origin of the degradation effect [see, e.g., Friis, Lee, Bruschi and Louko, Phys. Rev. D 85, 025012 (2012)] between different cavities lies in the generation of entanglement within the single non-uniformly moving cavity, see [Friis, Bruschi, Louko and Fuentes, Phys. Rev. D 85, 081701(R) (2012)] or download a presentation [pdf].

Relativistic Quantum Teleportation

Teleportation in motion.

Quantum Teleportation – a concept that is more than an ingenious theoretical proposal, it is even more than a baffling quantum phenomenon that pushed researchers to the development of new technologies. “Teleportation” is a key word that is familiar to most people from popular television, so familiar, in fact, that researchers adopted the term for the puzzling quantum process, in which a property of a microscopic quantum system is transported to a second, distant quantum object without actually sending or even knowing the corresponding property. As in the fictitious stories that the term teleportation was borrowed from, the senders and receivers of information that is transmitted in this way are generally moving in space and time. In this context one may think of satellites orbiting our planet.

We have investigated the influence of the motion of the involved parties on the success of quantum teleportation. In particular, we have been interested in the effects of relativistic motion, that is, objects moving with varying, potentially high speeds, or in the presence of space-time curvature due to gravitation. We were able to give the first complete description of quantum teleportation between moving partners. Accounting for the motion in the teleportation protocol is not only conceptually satisfying, but the effects we describe may hopefully lead to the development of new relativistic quantum technologies that help to improve the precision and security of communication for the next generation of quantum technology, see [Friis, Lee, Truong, Sabín, Solano, Johansson and Fuentes, Phys. Rev. Lett. 110, 113602 (2013)] or download a presentation [pdf].

Spin - momentum entanglement of inertial observers

Relativistic observer Eve (drawing by R. A. Bertlmann)

One of the earliest approaches to RQI is based on the transformation properties of quantum states under the Poincaré group, the symmetry group of special relativity. In the unitary Wigner representation of a Lorentz transformation the particles' spins undergo momentum-dependent rotations. This leads to different descriptions of the amount of entanglement distributed amongst the various bi-partitions of spin- and momentum-degrees of freedom for different inertial observers, see [Friis, Bertlmann, Huber and Hiesmayr, Phys. Rev. A 81, 042114 (2010)].

While this still leaves the possibility to define Lorentz invariant classes of multipartite entanglement for the spin degrees of freedom, see [Huber, Friis, Gabriel, Spengler and Hiesmayr, Europhys. Lett. 95, 20002 (2011)], the physical requirements for spin measurements seem to suggest that only the Lorentz invariant partition into individual particles can be considered to be physical, see, e.g., [Saldanha and Vedral, New J. Phys. 14, 023041 (2012)].

A presentation can be downloaded here [pdf].

Entanglement of free quantum fields for uniformly accelerated observers

Alice falls into a black hole (by R. A. Bertlmann)

A key paradigm of RQI was formulated by I. Fuentes and R. B. Mann in the phrase "Alice Falls into a Black Hole" in [Phys. Rev. Lett. 95, 120404 (2005)]. An entangled state of two free field modes in Minkowski spacetime is viewed by a freely falling observer Alice and an eternally uniformly accelerating observer Rob. The entanglement between these two observes is degraded with respect to the initial entanglement due to the presence of the black hole horizon.

In the infinite acceleration limit the quantum correlations of single copies of the state are not non-local anymore, i.e., they can be modeled by local realistic theories, see [Friis, Köhler, Martín-Martínez and Bertlmann, Phys. Rev. A 84, 062111 (2011)].

Although such toy-models cannot be taken at face value (eternal accelerations, states with support in the whole spacetime, ideally localized observers), they do present some qualitatively interesting insights into effects expected in more realistic scenarios. A presentation can be found here [pdf].