Even the most ignorant cannot
know less than nothing. After all, negative knowledge
makes no sense. But, although this may be true
in the everyday world we are accustomed to, it
has been discovered that negative knowledge does
exist in the quantum world. Small objects such
as atoms, molecules and electrons behave radically
different than larger objects  they obey the
laws of quantum mechanics.
The discovery, that quantum knowledge can
be negative was made by three researchers,
Drs Michal Horodecki, Jonathan Oppenheim and
Andreas Winter, of the Universities of Gdansk,
Cambridge and Bristol. Their work was published
in the leading scientific journal Nature on
August 4.
What
could negative knowledge possibly mean? "If
I tell it to you, you will know less," explained
Dr Andreas Winter.
Such
strange situations can occur because what
it means to know something is very different
in the quantum world. "In the quantum world,
we can know too much," added Dr Oppenheim, "and
it is in these situations where one finds negative
knowledge." Negative knowledge (or more precisely – ‘negative
information') turns out to be precisely the
right amount to cancel the fact that we know
too much.
In
the quantum world, there are things we just
cannot know, no matter how clever we are.
For example, we cannot know both the position
and momentum of a small particle exactly. One
can also have situations where someone knows
more than everything. This is known as quantum ‘entanglement',
and when two people share entanglement, there
can be negative information.
While
all this might appear to be very mysterious,Dr
Michal Horodecki is quick to point out that
the idea of negative information can be put
on a rigorous scientific footing. "We can quantify
information in terms of how much stuff I need
to send you before you get to know something.
In the case of negative quantum information,
you can get to know something without me sending
you any quantum particles. In fact, you will
gain the potential to learn more quantum information
in the future."
Negative
information is due to exotic features of
quantum information theory, an exciting new
area of physics which includes such phenomena
as quantum teleportation and quantum computation.
Classical information theory deals with subjects
such as classical communication and computation.
Quantum information on the other hand, replaces
classical ‘bits' by quantum ‘qubits' which
are quantum particles like electrons or atoms.
While classical bits can only be in the state
0 or 1, qubits can be both in the 0 or 1 state
at the same time. By understanding that quantum
information can be negative, researchers hope
to gain deeper insights into phenomena such
as quantum teleportation and computation, as
well as the very structure of the quantum world.
