Quantum money

Quantum Money is a proposed design of bank notes making them impossible to forge, by using quantum physics. The idea influenced the development of quantum key distribution protocols used in quantum cryptography.

The idea was put forward in about 1970 by Stephen Wiesner, a graduate student at Columbia University, though it was rejected by a number of scientific journals, meaning that it remained unpublished until 1983.^[1]

How it works

In addition to a unique serial number on each bank note (these notes are actually more like cheques, since a verification step with the bank is required for each transaction), there is a series of isolated two-state quantum systems.^[2] For example, photons in one of four polarizations could be used: at 0°, 45°, 90° and 135° to some axis, which is referred to as the vertical. Each of these is a two-state system in one of two bases: the horizontal basis has states with polarizations at 0° and 90° to the vertical, and the diagonal basis has states at 45° and 135° to the vertical.

At the bank, there is a record of all the polarizations and the corresponding serial numbers. On the bank note, the serial number is printed, but the polarizations are kept secret. Thus, whilst the bank can always verify the polarizations by measuring the polarization of each photon in the correct basis without introducing any disturbance, a would-be counterfeiter ignorant of the bases cannot create a copy of the photon polarization states, since even if he knows the two bases, if he chooses the wrong one to measure a photon, it will change the polarization of the photon in the trap, and the forged banknote created will be with this wrong polarization.

For each photon, the would-be counterfeiter has a probability $3/4$ of success in duplicating it correctly. If the total number of photons on the bank note is $N$, a duplicate will have probability $(3/4)^{N}$ of passing the bank's verification test. If $N$ is large, this probability becomes exponentially small. The fact that a quantum state cannot be copied is ultimately guaranteed by its proof by the no-cloning theorem, which underlies the security of this system.

Practical limitations

At the moment, the technology that would be needed to implement quantum money does not exist at all, let alone in a form cost-efficient enough to allow for practical use, so discussion of its limitations is purely a theoretical exercise.

Rather than physical bills, one might try to make quantum money into a digital currency. However, unlike common digital currencies such as Bitcoin, quantum money would not be able to be backed up, due to the no-cloning theorem. A partial solution is to use quantum error-correcting codes, and keep the money in, say, 4 places, such that if 1 part is destroyed, the error can be recovered.

If a note does not pass the bank's verification test, it does not necessarily mean that it has been forged: it could be a real note whose photon polarizations have been tampered with or measured in the incorrect basis (perhaps by a would-be counterfeiter or malfunctioning teller machine).

References

1. S. Wiesner, Sigact News, 15, 78 (1983)
2. Lo, Spiller & Popescu, Introduction to Quantum computation and information (1998) pp. 81–83