Entanglement in Curved Spacetime (13w5153)

Arriving in Banff, Alberta Sunday, September 22 and departing Friday September 27, 2013


(University of Waterloo)

Robert Mann (University of Waterloo)

(The University of Queensland)


Recent results have shown that new phenomena arise when quantum entanglement is combined with relativity. Since already entanglement that is merely non-relativistic is known to be a crucial resource for quantum communication and quantum computation, the study of entanglement when combined with relativity is highly significant.

For example, it has been shown that quantum teleportation fidelity is affected between observers in uniform relative acceleration. Entanglement was also found to be an observer-dependent property that is degraded from the perspective of accelerated observers moving in flat spacetime. Further, it was shown that entanglement can be obtained by swapping entanglement from the vacuum of relativistic quantum field theories. Entanglement can also be used to distinguish peculiar motion from cosmological expansion. While entanglement has long been known to play a key role in the Unruh and Hawking effects, the new quantum information-theoretic framework of quantum channels now provides powerful tools for studying matters of causality and information flow in quantum field theory in curved spacetimes.

To mention one issue in more detail: The relative alignment of reference frames around spacelike-separated events, e.g., in EPR-type setups is highly nontrivial in the presence of curvature. Indeed, it is expected that their proper alignment is not given by the geodesic transport between the two events. Rather, it is believed that the parallel transport that links the frames is to trace back the past paths that the EPR subsystems took. Even this is nontrivial in cases where the past paths are quantum delocalized on a scale that is affected by curvature. One of the ideas that is being discussed is, for example, whether this could be probed, in the medium term, e.g., involving EPR-type experiments with a satellite, and perhaps photons passing the sun when eclipsed. A proposal to the Canadian Space Agency, involving several workshop participants, has been submitted in 2011.

The workshop will aim to explore the theoretical and mathematical underpinnings of entanglement phenomena in curved space. This involves, for example, techniques of spectral geometry, a mathematical discipline which is in itself of high significance for the field of quantum gravity - because it naturally combines the languages of quantum theory, i.e., functional analysis, and the language of general relativity, i.e., differential geometry.