Quantum connectivity of space-time and gravitationally induced decorrelation of entanglement

We discuss an alternative formulation of the problem of quantum optical fields in a curved space-time using localized operators. We contrast this formulation with the standard approach and find observable differences for entangled states. We propose an experiment in which an entangled pair of optical pulses are propagated through nonuniform gravitational fields and find that the alternative formulation predicts decorrelation of the optical entanglement under experimentally realistic conditions.

Figure 1

(Color online) Representation of the unitary interaction of a quantum system with its past via a wormhole. Consistent evolutions result if operators describing the past $\left(J_i^{\prime }\right)$ and future $\left(J_k\right)$ manifestations of the quantum system act on independent Hilbert subspaces. WF is the future mouth of the wormhole, and WP is the past mouth.

Figure 2

(Color online) Representation of local, mutually stationary reference frames for calculating $\tau$.

Figure 3

(Color online) Schematic of generic correlation experiment.

Figure 4

(Color online) Schematic of modified correlation experiment. Now the source, polarizing beam splitter, and second detector are approximately at height $x_p$, while the mirror, first detector, and the correlator are approximately at height $x_m$. A classical communication channel sends the information from the second detector to the correlOTator.