Violations of Bell’s Inequality for Macroscopic States
Einstein referred to the nonlocal collapse of the wave function as “spooky action at a
distance”. John Bell later showed that the hidden-variable theories advocated by Einstein were
inconsistent with the predictions of quantum mechanics. This distinction between quantum and
classical behavior is not limited to microscopic particles, and Bell’s inequality can be violated by
macroscopic systems as well. We recently showed that a photon number state incident on a
beam splitter will produce two output states whose phases are entangled . We also showed
that Bell’s inequality can be violated in this way regardless of how many photons are involved.
Macroscopic superposition states of this kind are very susceptible to decoherence due to loss. I
will describe how the decoherence of these states during transmission over large distances can be
made arbitrarily small by using noiseless attenuation  before transmission, followed by
noiseless amplification  after transmission. As time permits, I will also describe how the
effects of dispersion can be minimized using nonlocal dispersion cancellation  for three or
more photons, which may be useful for quantum networks.
1. S.U. Shringarpure and J.D. Franson, arXiv.1911.02468.
2. R.A. Brewster, T.C. Nodurft, T.B. Pittman, and J.D. Franson, Phys. Rev. A 96, 042309
3. T.C. Ralph and A.P. Lund, arXiv:0809.0326.
4. J.D. Franson, Phys. Rev. A 45, 3126 (1992).
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