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American Journal of Physics

Quantum Theory of Measurement: Comment on a Paper of Shimony

M. N. Hack

Published Nov 1, 1964• 1 citation
Publisher
DOI
10.1119/1.1969947

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The question raised by Shimony and Stein is examined and used to explain in more detail a key point of my proof that any theory that conforms to certain general ideas of orthodox relativistic quantum field theory must permit transfers of information over space-like intervals. It is also explained why this result is not a problem for relativistic quantum theory, but, on the contrary, opens the door to a satisfactory realistic relativistic quantum theory based on the ideas of Tomonaga, Schwinger, and von Neumann.
Abstract We define a family of ‘no signaling ’ bipartite boxes with arbitrary inputs and binary outputs, and with a range of marginal probabilities. The defining corre-lations are motivated by the Klyachko version of the Kochen-Specker theorem, so we call these boxes Kochen-Specker-Klyachko boxes or, briefly, KS-boxes. The mar-ginals cover a variety of cases, from those that can be simulated classically to the superquantum correlations that saturate the Clauser-Horne-Shimony-Holt inequality, when the KS-box is a generalized PR-box (hence a vertex of the ‘no signaling ’ poly-tope). We show that for certain marginal probabilities a KS-box is classical with respect to nonlocality as measured by the Clauser-Horne-Shimony-Holt correlation, i.e., no better than shared randomness as a resource in simulating a PR-box, even though such KS-boxes cannot be perfectly simulated by classical or quantum re-sources for all inputs. We comment on the significance of these results for contextu-ality and nonlocality in ‘no signaling ’ theories.