AAWSAP DIRD, The Space Communication Implications of Quantum Entanglement and Nonlocality, March 2010

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I. Quantum Entanglement, Nonlocality, and EPR
Experiments
In the quantum mechanical description of elementary entities like photons, there is a
duality between the description as a particle and as a wave. Photons can be thought of
as traveling through space as waves but delivering energy (and other conserved
quantities) at detection as particles. By choosing the kinds of measurements made on
such objects, one can force wave-like or particle-like behavior to be exhibited in the
measurements results. Between the entangled parts of a quantum system (for
example, the emission of a pair of entangled photons), this wave-like or particle-like
behavior in a measurement on one part of the system may force similar behavior in the
other part. This is considered further in Section IV below.
The quantum entanglement condition is usually a consequence of some conservation
law acting within the system, so that the subsystems are connected by the conserved
quantities. For example, if two photons are emitted back to back in a joint state that
has zero angular momentum and positive parity, then whatever linear or circular
polarization state one photon is measured to have, the other photon must have an
identical polarization if measured in the same basis (linear or circular). This condition
must exist to ensure that the net angular momentum of the two photon states is zero.
In this situation, if the photons are measured for circular polarization, they must both
be in states of right circular polarization or in states of left circular polarization. Because
linear polarization is a coherent superposition of circular polarization states, if measured
in the vertical/horizontal linear polarization basis, they must be in the same vertical or
horizontal polarization state, and in the 45° left or right linear polarization basis, they
must be in the same 45° left/right polarization state.
Classically, such a polarization correlation condition could in principle exist in some
particular polarization basis but not in all of the many possible polarization bases
simultaneously. This is the underlying physics of the Bell Inequalities (Reference 8),
which deal with the falloff rate of the correlations as the polarization basis of one of the
measurements is rotated in angle. The Bell Inequalities demonstrate mathematically
that the predictions of semi-classical local hidden-variable theories are inconsistent with
those of standard quantum mechanics. Tests of such polarization correlations have
been the basis for a number of Bell-Inequality tests (or so-called EPR experiments), in
which the validity of the predictions of quantum mechanics and the inadequacies of
semi-classical local hidden-variable theories have been demonstrated to high statistical
precision (Reference 1, 2) .
It was later demonstrated (Reference 5, 6) that the issues surrounding a violation of
the Bell Inequalities could be separated into violations of either parameter
independence (the outcome probability of a measurement on one of a pair of entangled
particles is independent of the choice of parameters of a measurement performed on
the other member of the entangled pair) and violations of outcome independence (the
outcome probability of a measurement on one of a pair of entangled particles is
independent of the outcome of a measurement performed on the other member of the
entangled pair). The observation of a violation of the Bell Inequalities indicates a
violation of either parameter independence or outcome independence (or both).
Outcome independence is fairly evident in the quantum formalism, while parameter
independence is more elusive and depends on specific assumptions. Below, the
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