Abstract
In this paper, we show how the GHZ paradox can be used to design a computing device that cannot be physically implemented within the context of classical physics, but nonetheless can be within quantum physics, i.e., in a quantum physics laboratory. This example gives an illustration of the many subtleties involved in the quantum control of distributed quantum systems. We also show how the second elementary symmetric Boolean function can be interpreted as a quantification of the nonlocality and indeterminism involved in the GHZ paradox.
Highlights
This paper began with an invitation to give the Annual George Washington University Mathematics Department April Fools Day Lecture in April of 2014
I chose to speak on the GHZ paradox, as embodied in Mermin’s machine [5]
We show how the Greenberger–Horne–Zeilinger (GHZ) paradox can be used to design a computing device that cannot be physically implemented within the context of classical physics, but can be within quantum physics, i.e., in a quantum physics laboratory
Summary
This paper began with an invitation to give the Annual George Washington University Mathematics Department April Fools Day Lecture in April of 2014. We show how the Greenberger–Horne–Zeilinger (GHZ) paradox can be used to design a computing device that cannot be physically implemented within the context of classical physics, but can be within quantum physics, i.e., in a quantum physics laboratory. This example gives an illustration of the many subtleties involved in the quantum control of distributed quantum systems [8]. Corollary 1 in Sect. 6 can be interpreted as showing that the second elementary symmetric Boolean function σ2 explicitly quantifies the nonlocality and indeterminism involved in the GHZ paradox
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