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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