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This work helps provide a better means for talking and thinking about quantum theory. For instance,
quantum equations rely on complex numbers – numbers that have a real component and an
imaginary component. While complex numbers may appear inconveniently complicated, their use
actually reflects a deep, beautiful, and very simple postulate of quantum theory: simply that the
state of a system having two parts can be determined by making separate measurements on each
of the parts. This postulate is common to all three Perimeter researchers’ sets of natural principles.
Creating a common, straightforward language does more than make quantum theory more
accessible. It also helps advance toward the field’s overarching goals, such as creating a theory
of quantum gravity.
Quantum theory is, at its heart, about calculating probabilities.
In the classical world, people deal with probabilities continually – games of chance, weather
forecasts, playing the stock market, and many other everyday experiences involve some
calculation of odds. In general, though, classical physics provides the opportunity to reach a
concrete outcome – we flip a coin, look out the window, check an investment statement – and
probabilities turn into certainties.
Such observational confirmations lead to the reasonable assumption that probabilities say
something about reality – even if there is a 60 percent chance of rain and the sun is shining, we
tend to believe that the forecast still speaks to a verifiable combination of humidity, regional cloud
cover, air currents, and temperature.
Alternative interpretations of statistics, though, can also be highly useful, particularly in the
realm of quantum theory. The Bayesian approach, for instance, interprets probabilities not as
assertions about reality, but as reflections of our incomplete knowledge and “degrees of belief.”
The percentage chance of precipitation will almost never tell you, for example, whether it is
actually raining or not. It will, however, affect your choice of whether to pack an umbrella.
Faculty member Robert Spekkens and collaborator Matthew Leifer have made important strides
in applying Bayesian approaches to quantum theory, where circumstances are often expressed
exclusively in terms of probability. Their analogue to a weather forecast is a “quantum conditional
state” whose specific properties can only be expressed in terms of likelihood, not actuality. By
treating the equations describing these states as a form of incomplete knowledge, they hope
to make it simpler to conceptualize and investigate the causal structures underlying quantum
L. Hardy, “Reformulating and reconstructing quantum theory,” arXiv:1104.206.
L. Masanes and M. P. Mueller, “A derivation of quantum theory from physical requirements,” New J. Phys. 13, 063001 (2011), arXiv:1004.1483.
Note: This paper was featured as a “Research Highlight” in Nature Physics on July 7, 2011.
G. Chiribella, G. M. D’Ariano, and P. Perinotti, “Informational derivation of Quantum Theory,” Phys. Rev. A 84, 012311 (2011), arXiv:1011.6451.
Note: This paper was highlighted by the American Physical Society with a “Viewpoint” article: C. Brukner, “Questioning the rules of the game,”
Physics 4, 55 (2011).
M. S. Leifer and R. W. Spekkens, “Formulating Quantum Theory as a Causally Neutral Theory of Bayesian Inference,” arXiv:1107.5849.