they were still bouncing off of the molecules and producing a sim-
ilar decrease in the coherence length. This decoherence effect was
the reason that the experiment was limited to molecules of the size
they used. Even though the molecules took only about 400 nanosec-
onds to fly through the apparatus, there was a significant amount
of decoherence. A larger molecule would have been a bigger target
for photons and would have undergone decoherence more quickly,
making interference unobservable.
As in the example of spying on one slit of a double-slit experi-
ment, the question arises of what has happened to the phase infor-
mation that appears to have been erased by decoherence, violating
unitarity. The resolution is the same (p. 999): the information has
flowed out into the environment, but is no longer in a form in which
it is practical to recover it.14.10 Quantum computing and the no-cloning
theorem
Computers and information transmission systems such as the inter-
net are currently implemented as classical devices. For example, the
wavelengths of the electrons that carry signals in a computer chip
are currently orders of magnitude shorter than the size of the logic
gates, so that wave effects such as diffraction and interference are
not important (problem 22, p. 944). Even if the current devices
such as silicon chips and fiber-optic cables could simply be scaled
down to sizes comparable to the electrons’ wavelengths, quantum
effects would at some point simply make them start breaking down
or behaving unreliably.
It is possible, however, to design qualitatively different devices
in which information and signals are intentionally manipulated in an
explicitly quantum-mechanical fashion. This is the frontier known
as quantum computing. In a quantum computer, the basic unit of
information is not the classical bit but the quantum bit orqubit. A
qubit can exist in a superposition of the 0 and 1 states, with a well
defined phase, e.g., Ψ 0 + Ψ 1 is a different state than Ψ 0 −Ψ 1 or
Ψ 0 +iΨ 1. Furthermore, one qubit can have its state entangled with
another’s. For example, Ψ 01 +Ψ 10 describes a state in which we have
two bits, neither in a definite 0 or 1 state, but which are guaranteed
to add up to 1. That is, if one is true, then the other is guaranteed
to be false. It has been shown that some problems that are hard
for classical computers are more tractable for a quantum computer.
For example, there is a known quantum computing algorithm that
is capable of efficiently factoring large integers, and when this is
eventually implemented in a practical device, it will have the effect
of breaking the cryptographic algorithms that you currently use for
online privacy and security, since the security of those algorithms is
predicated on the assumption that factorization is hard. This would
Section 14.10 Quantum computing and the no-cloning theorem 1001