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We consider non-local properties of quanternionic quantum mechanics, in which the complex numbers are replaced by the quaternions as the underlying algebra.
Simulating quantum systems using real hilbert spaces
Matthew McKague, Michele Mosca, and Nicolas Gisin · 1923
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Proposed experiment to test local hidden-variable theories
John F. Clauser, Michael A. Horne, Abner Shimony, and Richard A. Holt · 1969
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Quantum generalizations of bell’s inequality
B. S. Cirel’son · 1980
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Quantum nonlocality as an axiom
Sandu Popescu and Daniel Rohrlich · 1994
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Quaternionic Quantum Mechanics and Quantum Fields
Stephen Adler · 1995
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Quaternionic computing, July 2003
Jose M. Fernandez and William A. Schneeberger · 2003
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Implausible consequences of superstrong nonlocality, January 2005
Wim van Dam · 2005
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Limit on nonlocality in any world in which communication complexity is not trivial
Gilles Brassard, Harry Buhrman, Noah Linden, Andre Allan Methot, Alain Tapp, and Falk Unger · 2006
Cited alongside, same era.
Phys771 lecture 9: Quantum
Scott Aaronson
Cited in the paper.
On quaternions, or on a new system of imaginaries in algebra
William Rowan Hamilton
Cited in the paper.
Quantum nonlocality and beyond: Limits from nonlocal computation
Noah Linden, Sandu Popescu, Anthony J. Short, and Andreas Winter · 2007
Later among the works it cites.
Simulating quantum circuits using real valued unitaries
Matthew McKague and Michele Mosca · 2007
Later among the works it cites.
A new physical principle: Information causality
M. Pawlowski, T. Paterek, D. Kaszlikowski, V. Scarani, A. Winter, and M. Zukowski · 2009
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