poly: quantum catalysis

Quantum entanglement is believed by many people to be the key resource
allowing quantum systems to do tasks like quantum computation
that are impossible with classical systems.

Entanglement is a resource of a distinctly non-classical nature;
iron in the classical world's bronze age. It is a crucial ingredient in
quantum teleportation, superdense coding, quantum algorithms, and most
other quantum information processing tasks.

An obvious question to ask is whether or not there are quantum resources
other than entanglement which take us beyond the classical
world.

In a very interesting preprint, Jonathan and Plenio show that there are
information processing tasks in which an essentially new type of
resource is being used:

http://xxx.lanl.gov/abs/quant-ph/990507

The idea is a bit technical. For those who are interested: two people,
Alice and Bob, share a quantum state which we'll call psi. Alice and Bob
can talk to each other classically, and they can both do whatever
operations they like on their own systems, but they have no quantum
communications channel between them by which to communicate quantum
states. (The lingo is that Alice and Bob can apply local operations and
classical communication to their state psi.)

A natural question to ask is what states phi can Alice and Bob generate
using these resources?

What Jonathan and Plenio noticed is the following: there are quantum
states psi and phi with the following two properties:

(a) Alice and Bob cannot transform psi into phi using only local
operations and classical communication.

(b) Suppose a third party, Scrooge, lends a _catalysing_ state, gamma,
to be shared by Alice and Bob. With the aid of this catalysing state it
becomes possible to transform psi into phi. Moreover, the catalysing
state is _left intact_ by this process.

These catalysing states are pretty interesting for two reasons. First,
they enable an information processing task of some interest. Second, and
more important, Jonathan and Plenio show that so-called "maximally
entangled" states are no good as catalysts. Thus, entanglement is not the
key property being used for catalysis; it is a new type of quantum
resource.

At this point in time it's pretty difficult to see what these "catalysing
states" are useful for other than the catalysing process described above.
However, the history of quantum computation and quantum information shows
that identifying new types of physical resources is of the utmost
importance; I hope that eventually we'll find all sorts of uses for these
funny new types of states.

Michael Nielsen
Ph: 626 395 8431 Fax: 626 793 9506
Email: mnielsen@theory.caltech.edu
Received on Wed Jun 2 15:32:21 1999