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10.1.3 Settling the Question Experimentally
J.F. Clauser, M.A. Horne, A. Shimony, and R.A. Holt later formulated one
example of an incompatibility between a hidden variable theory and quantum
mechanics into an experiment that could test whether quantum mechanics was
indeed incomplete [Clauser et al., 1969]. In the proposed experiment a source is
used that produces pairs of particles (e.g. photons or ions) in a perfectly anticorrelated
state (e.g. opposite polarization or spin). For the purposes of illustration,
the state of the entangled pair (particle A and B) can be taken to be the Bell
singlet state
| 01 〉−| 10 〉
√
2
. These particles are then physically separated by a large
enough distance to disallow any classical transfer of information between them
throughout the remainder of the experiment, i.e. d AB ≫ c t expt . At those remote
locations the particles are then measured along random axes (e.g. projected onto
the X, Y, or Z-axis of the Bloch sphere). If the singlet state is re-expressed in
the basis of the measurement axes, it will still show perfect anti-correlation if the
axes are equal, e.g.:
| X − X + 〉 − | X + X − 〉
√
2
=
=
=
| 0 〉−| 1 〉
√
2
⊗ | 0 〉+| 1 〉 √
2
− | 0 〉+| 1 〉 √
2
⊗ | 0 〉−| 1 〉 √
2
√
2
| 00 〉+| 01 〉−| 10 〉−| 11 〉
−
2
| 00 〉−| 01 〉+| 10 〉−| 11 〉
2
√
2
| 01 〉 − | 10 〉
√ (10.1)
2
Thus, every time both particles happen to be measured along the same axis
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