In a conventional macro computer, copying and deleting of information are inevitable operations, a standard part of computing. But in nanoscale quantum computers it won't happen. A pair of physicists in Wales says you can't do it ("Nature" 404: 164-165).
Hit a key in a desktop computer and you perfectly delete whatever is under fire. But in a quantum computer cleaning up memory is out of the question. We've known for 20 years that you cannot copy unknown quantum states, the so-called no-cloning theorem. The new work says you also cannot delete an unknown quantum state.
In classical computing, deleting an extra copy of a bit is logically reversible with no thermodynamic cost. You can use the original that is still in the memory to reconstruct a new copy. You start with two arbitrary and unknown identical bits, an original and a copy. C-NOT (controlled not) is the conditional logical operation used to reset the copy bit to 0. It flips the state of the copy when the original is 1 and otherwise does nothing. Give C-NOT two identical 1s and it will leave the original bit untouched but reset the copy to 0. This is deletion. C-NOT is logically reversible. If you repeat it, the 0 on the blank copy becomes 1 if that's what the original is. Otherwise it stays 0. C-NOT deletes whether it or anybody else knows what either the original or the copy are.
Not so in a quantum computer. We have quantum C-NOTs and they are reversible. The problem is that not knowing what something is amounts to less clear-cut ignorance in quantum computing. In quantum physics a quantum two-state system, a qubit, can be in an arbitrary superposition of 0 and 1. But a perfectly legal quantum state can also involve complex numbers. The quantum C-NOT works like a classical C-NOT only when the copy and the original are in the preferred states, 0 or 1. An operation to clone or delete a state only works for a preferred set of mutually exclusive quantum states such as 0 or 1.
You would need a mechanism that takes two photons in the same initial polarization state and produces one photon in the same initial state and another in some standard polarization state. Then you could create a standard blank state onto which you could copy an unknown state. You could store new information in an already computed state by deleting the old information. The researchers at the University of Wales show this is impossible.
The fact that you can neither clone nor delete in quantum computing could have applications in information processing. It provides intrinsic security to quantum files in a quantum computer. No one can obliterate a copy of an unknown file from a collection of several copies. But more generally, you have to look at it as another limitation on the possibilities of building a quantum computer.
© John Wiley & Sons 2000