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Previous Programs

2018 Agency in the Physical World
Awardees; RFP download

2016 Physics of the Observer
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2015 The Physics of What Happens
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2013 Physics of Information
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2010 The Nature of Time
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2008 Foundational Questions in Physics and Cosmology
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2006 Foundational Questions in Physics and Cosmology
Awardees; RFP download

Alexander Wilce
Susquehanna University

Project Title

Conjugates, Correlation and Quantum Mechanics

Project Summary

Quantum mechanics makes probabilistic predictions about outcomes of experiments. To this extent, it's about information. In fact, finite-dimensional quantum mechanics (QM) has been derived (in several ways) from purely information-theoretic principles. One of these is that the state of a pair of systems is determined by an assignment of joint probabilities to outcomes of measurements made on the two systems separately. However, this fails in two well-known, and arguably reasonable, variants of standard QM, called real and quaternionic QM. What happens if we drop this assumption? In some ways, things become simpler. Using much weaker information-theoretic assumptions, we obtain a theory that unifies standard QM with real and quaternionic QM, while leaving just a bit of additional room beyond these. The basic idea is that each system can be paired with a 'conjugate' copy of itself, in a joint state in which every measurement on either system looks completely random, but is nevertheless exactly correlated with its counterpart on the other. In standard QM, this conjugate system is a time-reversed version of the original. This project aims to clarify the meaning of conjugate systems in general, and to study the information processing power of the theory based on them.

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