be a disaster for online economic activity and could have effects such
as unmasking political dissidents.
A different application, and one that is easier to explain, is that
quantum computing makes it possible in theory to make copy-proof
information. This would not be useful to Hollywood studios trying
to prevent copying of their movies, since the images have to pass
through classical devices anyway in order to be displayed, but it
means that one might be able to send private information through
a quantum internet in such a way that it could not be copied by
snoops, even in theory. In contrast, current classical methods of
encryption are designed to allow eavesdropping on an information
packet as it hops across the internet, but to make the copy useless
to prying eyes because it cannot be decoded.
The theoretical key to this application of quantum computing is
the counterintuitiveno-cloning theorem, which states that it is not
possible to make a copy of an unknown quantum state.^11 To see why
this works, suppose that we implement a qubit using the spin 1/2
of a silver atom, with the convention that the 0 state is represented
bysx= − 1 /2 and 1 bysx= +1/2. If you provide me with an
atom that you have prepared, then it might seem straightforward,
at least in principle, for me to copy its state. I can shoot it through
a magnetic spectrometer, as in the Stern-Gerlach experiment, and
measure its sx. Then I prepare another silver atom in the same
state. What’s the problem?
The problem is that if the state of the atom is truly unknown to
me, then I have no way of knowing that it is actually in one of the
two statessx=− 1 /2 andsx= +1/2. It could instead be in some
superposition of these, such as Ψsx=− 1 / 2 /√
2 +iΨsx=+1/ 2 /√
2, with
a 90-degree phase angle between the two components. Then when
I send your atom through the spectrometer, the world becomes one
in which both the spectrometer and my brain are in a superposition
of the two states. In one of these worlds, I then go ahead and pre-
pare my copy-atom in thesx=− 1 /2 state, and in the other one I
set it up as a +1/2. You could say that my copy-atom is, like the
original, in a superposition of the twosxstates, but there is no rea-
son to think that it will be thesamesuperposition, with the same
90-degree phase angle. In fact, by the argument on p. 997 we know
that it is not possible byany measurement to extract this phase
information and convert it into classical information. Furthermore,
our final result is not really as simple as a copy-atom in some un-
known superposition of the twosxstates. It is a silver atom whose
spin is correlated with the state of the original, but also correlated
with the state of the spectrometer and the state of my brain.
The impossibility of copying an unknown quantum state is en-(^11) The prohibition actually only applies to making a copy that can be separated
from the original. For the complete statement of this, see p. 1006.
1002 Chapter 14 Additional Topics in Quantum Physics