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arXiv:0704.1468 · Journal of Modern Optics

Generation of entanglement outside of the light cone

J. D. Franson

Published Jul 18, 2008• 40 citations
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Abstract

The Feynman propagator has nonzero values outside of the forward light cone. That does not allow messages to be transmitted faster than the speed of light, but it is shown here that it does allow entanglement and mutual information to be generated at space-like separated points. These effects can be interpreted as being due to the propagation of virtual photons outside of the light cone or as a transfer of pre-existing entanglement from the quantum vacuum. The differences between these two interpretations are discussed.

DOI
10.1080/09500340801983129

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The Feynman propagator has nonzero values outside of the forward light cone. That does not allow messages to be transmitted faster than the speed of light, but it is shown here that it does allow entanglement and mutual information to be generated at space-like separated points. These effects can be interpreted as being due to the propagation of virtual photons outside of the light cone or as a transfer of pre-existing entanglement from the quantum vacuum. The differences between these two interpretations are discussed.
We analyze whether a pair of neutral two level atoms can become entangled in a finite time while they remain causally disconnected. The interaction with the electromagnetic field is treated perturbatively in the electric dipole approximation. We start from an initial vacuum state and obtain the final atomic correlations for the cases where n=0n=0n=0, 1, or 2 photons are produced in a time ttt, and also when the final field state is unknown. Our results show that correlations are sizable inside and outside the mutual light cone for n=1n=1n=1 and 2, and also that quantum correlations become classical by tracing over the field state. For n=0n=0n=0 we obtain entanglement generation by photon propagation between the atoms, the correlations come from the indistinguishability of the source for n=1n=1n=1, and may give rise to entanglement swapping for n=2n=2n=2.
It is possible to use two particles (A and B) with entangled properties to transmit information at faster than light speeds. This can be done, not by trying to modulate the results of how particle A is measured, but by modulating whether particle A is measured or not measured. The effect of this modulating method is to place particle B in either a single value (but arbitrary) state or leave it in a superposition of states. It is then possible for the reciever of particle B to distinguish between these two states by the use of an appropriately designed interferometer. Such a device can be designed to produce an interference pattern only when particle B is in a superposition of values and a straight simple image when particle B has a single (arbitrary) defined value. Under the Copenhagen interpretation and existing experimental results, this method will produce a way of signalling fater than light. It will require the use of multiple entangled pairs of particles to effectively transmit a single bit of information. Under the Multi-Worlds Interpretation, it will not be so easy to communicate faster than light by this mechanism, as detector B will be detecting photon B as a superposition of values in both cases.
We analyze the entanglement generated in a finite time between a pair of space-like separated atoms, one of which emits a photon. As we show to order e2, the origin of entanglement can be traced back to the uncertainty about which one of the atoms emitted the photon. We check this by comparing the time behaviors of the emission processes allowed by energy conservation versus those forbidden by the same reason. No physical signal propagates between the atoms in the processes considered, however an effective light cone separating non-entangled from entangled regions in space-time emerges from our calculations.
We consider the entanglement dynamics between two Unruh-DeWitt detectors at rest separated at a distance ddd. This simple model when analyzed properly in quantum field theory shows many interesting facets and helps to dispel some misunderstandings of entanglement dynamics. We find that there is spatial dependence of quantum entanglement in the stable regime due to the phase difference of vacuum fluctuations the two detectors experience, together with the interference of the mutual influences from the backreaction of one detector on the other. When two initially entangled detectors are still outside each other's light cone, the entanglement oscillates in time with an amplitude dependent on spatial separation ddd. When the two detectors begin to have causal contact, an interference pattern of the relative degree of entanglement (compared to those at spatial infinity) develops a parametric dependence on ddd. The detectors separated at those ddd with a stronger relative degree of entanglement enjoy longer disentanglement times. In the cases with weak coupling and large separation, the detectors always disentangle at late times. For sufficiently small ddd, the two detectors can have residual entanglement even if they initially were in a separable state, while for ddd a little larger, there could be transient entanglement created by mutual influences. However, we see no evidence of entanglement creation outside the light cone for initially separable states.