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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.

IN

QUANTUM

PHYSICS

,

DOES

REALITY

MATTER

AS

MUCH

AS

BELIEF

?

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

systems.

References:

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.