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Modal quantum theory · Around

2010

Modal quantum theory

Schumacher, Benjamin, Westmoreland, Michael D.

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We present a discrete model theory similar in structure to ordinary quantum mechanics, but based on a finite field instead of complex amplitudes.

The interpretation of this theory involves only the "modal" concepts of possibility and necessity rather than quantitative probability measures.
Despite its simplicity, our model theory includes entangled states and has versions of both Bell's theorem and the no cloning theorem.

Built on

D. Finkelstein, J. M. Jauch, S. Schiminovich and D. Speiser, “Foundations of quaternion quantum mechanics”, Journal of Mathematical Physics
1962
Earlier work this paper cites.
J. S. Bell, “On the Einstein-Podolsky-Rosen paradox”, Physics
1964
Earlier work this paper cites.
W. K. Wootters and W. H. Zurek, “A single quantum cannot be cloned”, Nature
1982
Earlier work this paper cites.

Similar

C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states”, Physical Review Letters
1992
Cited alongside, same era.
L. Hardy, “Non-locality for two particles without inequalities for almost all entangled states”, Physical Review Letters
1993
Cited alongside, same era.
C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres and W. Wootters, “Teleporting an unknown quantum state via dual classical and EPR channels”, Physical Review Letters
Original
1993
Cited alongside, same era.

Then

G. Hughes and M. Cresswell, A New Introduction to Modal Logic
1996
Later among the works it cites.
S. Aaronson, “Is Quantum Mechanics an Island In Theoryspace?”, Proceedings of the Växjö Conference “Quantum Theory: Reconsideration of Foundations”
2004
Later among the works it cites.

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