Web edition: July 19, 2011
Print edition: August 13, 2011; Vol.180 #4 (p. 12)
Physicists in Canada and Italy have derived quantum mechanics from physical principles related to the storage, manipulation and retrieval of information.
The new work is a step in a long, ongoing effort to find fundamental physical motivation for the math of quantum physics, which describes processes in the atomic and subatomic realms with unerring accuracy but defies commonsense understanding.
“We’d like to have a set of axioms that give us a little better physical understanding of quantum mechanics,” says Michael Westmoreland, a mathematician at Denison University in Granville, Ohio.
Quantum theory’s foundations currently rest on abstract mathematical formulations known as Hilbert spaces and C* algebras. These abstractions work well for calculating the probability of a particular outcome in an experiment. But they lack the intuitive physical meaning that physicists crave — the elegance of Einstein’s theory of special relativity, for instance, which says that the speed of light is constant and that laws of physics don’t change from one reference frame to the next.
Giulio Chiribella, a theoretical physicist at the Perimeter Institute for Theoretical Physics in Ontario, Canada, and colleagues based their approach on a postulate called “purification.” A system with uncertain properties (a “mixed state”) is always part of a larger “pure state” that can, in principle, be completely known, the team proposes in the July Physical Review A.
Consider the pion. This particle, which has a spin of zero, can decay into two spinning photons. Each single photon is in a mixed state – it has an equal chance of spinning up or down. The pair of photons together, though, comprise a pure state in which they must always spin in opposite directions.
“We can be ignorant of the part, but we can have maximal knowledge of the whole,” says Chiribella.
This purification principle requires the quantum phenomenon known as entanglement, which connects the parts to the whole. It also explains why quantum information can’t be copied without destroying it but can be “teleported” — replicated at a distant location after being destroyed at its point of origin.
Building on this principle, Chiribella and colleagues reproduced the mathematical structure of quantum mechanics with the aid of five additional axioms related to information processing. Their axioms include causality, the idea that a measurement now can’t be influenced by future measurements, and “ideal compression,” meaning that information can be encoded in a physical system and then decoded without error. Other axioms involve the ability to distinguish states from each other and the ability of measurements to create pure states.
“They nail it,” says Christopher Fuchs, a theoretical physicist at the Perimeter Institute. “This now approaches something that I think is along the lines of trying to find a crisp physical principle.”
Whether this new derivation of quantum theory will prove to the simplest and most physically meaningful remains to be seen.
“What is simple or physically plausible is a matter of taste,” says Časlav Brukner, a physicist at the University of Vienna in Austria who has developed an alternative set of axioms.
Some speculate that recasting quantum theory in terms of information could help to solve outstanding problems in physics, such as how to unify quantum mechanics and gravity.
“If you have lots of formulations of the same theory, you’re more likely to have one that leads to whatever the next physics is,” says Ben Schumacher, a theoretical physicist at Kenyon College in Gambier, Ohio.
G. Chiribella, G.M. D’Ariano and P. Perinotti. Informational derivation of quantum theory. Physical Review A. Vol. 84, July 2011, p. 012311-1. doi:10.1103/PhysrevA.84.012311. [Go to]
C. Brukner. Questioning the rules of the game. Physics. Published online July 11, 2011. doi:10.1103/Physics.4.55. [Go to]
L. Hardy. Quantum theory from five reasonable axioms. arXiv:quant-ph/0101012v4. Posted Sep. 25, 2001. [Go to]
B. Dakić and C. Brukner. Quantum theory and beyond: Is entanglement special? arXiv:0911.0695v1. Posted Nov. 3, 2009. [Go to]