Quantum Purity

By Anil Ananthaswamy
New Scientist, April 2015

Edited by Andy Ross

Quantum weirdness is baffling. Giacomo Mauro D'Ariano and his colleagues Giulio Chiribella and Paolo Perinotti have come up with a non-weird foundation from which all quantum weirdness can arise.

Lucien Hardy: "When I look at quantum theory, I see something that's akin to the ad hoc nature of Kepler's laws of planetary motion and of Lorentz transformations. What we need is some deeper set of principles."

For both Hardy and D'Ariano's team, the fundamental concept is information. Five ideas are basic:

Causality: Stuff in the future cannot affect a measurement you're making right now.

Distinguishability: If a state is not too noisy, then there exists another state that can be distinguished from it.

Composition: If you know everything it is possible to know about all the stages of a process, then you know everything you can about the whole process.

Compression: There are ways to efficiently transmit all the information relevant to a measurement of a physical system without having to transmit the system itself.

Tomography: When you have a system with several parts, the statistics of measurements carried out on the parts is enough to identify the state of the whole system.

Quantum information theorists distinguish between different types of quantum state. Some states are pure: we know everything we can about such states. For mixed states our information is incomplete. One particle of an entangled pair is in a mixed state but both entangled particles together form a pure state.

Chiribella came up with a sixth principle:

Purification: It is always possible for someone with access to the pure state to make measurements consistent with those of less well positioned observers who are dealing with mixed states.

The purification principle makes quantum weirdness explicable. It allows one to derive much of the mathematics describing quantum oddities, such as superposition and the Born rule for calculating the probability of an outcome in a quantum measurement.

The purification principle might illuminate the irreversibility of thermodynamics. The second law of thermodynamics states that entropy will always increase over time. But that might be an artifact of perspective, because measurements are made on a subsystem in a mixed state. The deeper laws of physics are reversible.

AR This intrigues me.