Alice Falls Into A Black Hole: Acceleration And Quantum Entanglement

What would happen to their entanglement if Alice fell into a black holeand Bob stayed safely outside? We can model this situation byconsidering Alice to be stationary and Rob (formerly Bob) to beuniformly accelerated with respect to Alice. We found that although theentanglement between them is reduced due to Rob's acceleration, itremains nonzero as long as Rob's acceleration is not infinite.

It has long been known that an accelerated observer detects athermal bath of particles whereas an observer at rest sees only avacuum. Known as the Unruh effect, it is this that causes thedegradation in the entanglement measured by Alice and Rob. Our resultsare a first step in understanding how relativistic effects modifyquantum information, and they imply that different observers detectdifferent degrees of entanglement.

This has important consequences in quantum teleportation betweenrelatively accelerated parties, since entanglement is the main resource in this task.

This upcoming publication by I. Fuentes-Schuller and R. B. Mann will appear in Physical Review Letters.

The abstract: Two observers determine the entanglement between two freebosonic modes by each detecting one of the modes and observing thecorrelations between their measurements. We show that a state which ismaximally entangled in an inertial frame becomes less entangled if theobservers are relatively accelerated. This phenomenon, which is aconsequence of the Unruh effect, shows that entanglement is anobserver-dependent quantity in non-inertial frames. In the highacceleration limit, our results can be applied to a non-acceleratedobserver falling into a black hole while the accelerated one barelyescapes. If the observer escapes with infinite acceleration, thestate's distillable entanglement vanishes.