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 nonweird
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.
