Quantum mechanics has found some rather unusual applications in the last 25 years. Since its discovery over 100 years ago, it has mainly been used to describe the behavior of atomic and subatomic systems. In the 1980s, however, a few visionaries began to think about using quantum mechanical systems to process and store information. The results have been spectacular.
Employing the principle that photos transmitted in an optical state cannot be intercepted without altering that state, quantum mechanical methods can now be used to distribute secure cryptographic keys. They can also be used as the basis for algorithms that can perform tasks much faster than is possible on conventional computers. Research whose ultimate aim is to build a quantum computer is now proceeding on several continents.
Privacy protection is another task for which quantum-based methods may prove suited. Consider a group of people who want to determine whether one of them has ever sent e-mails falsely claiming to be a former Nigerian government official. Presumably, if one of them has done so, he or she would want to remain anonymous. Is it possible to determine whether one individual is the guilty spammer without revealing his or her identity? Indeed, it is. An anonymous broadcast channel enables each party to send a message to all of the other parties, but only the sender knows who sent it.
A quantum variant on this scenario was recently proposed by Christandl and Wehner.1 A particle is distributed to each party. These particles are in an entangled quantum state. Such a state implies that measurement correlations of the particles are stronger than allowed in classical physics. Thus, when a person wants to send a message, consisting in this case of one bit, the operation performed on his or her particle changes the quantum state describing all the particles. The new state, however, does not contain any information about the sender. The same state results whether I sent it or you sent it. Hence, the message is encoded and privacy protected. The parties then measure their particles and announce the results. Each one can deduce the value of the transmitted bit.
Secret ballot voting can represent another application of anonymous broadcasting. Asked on a referendum to vote yes or no on a specific measure, each voter wants information about how he or she voted to remain secret. Last year, two papers on quantum voting schemes using quantum entanglement to protect privacy appeared within a week of each other.2 I shall concentrate on the schemes described in the second of these publications, authored by myself, Mario Ziman, Vladimir Bužek, and Martina Bielikova.3 We presented two quantum voting procedures.
The first procedure, the traveling ballot scheme, uses two entangled particles. An authority, who is to count the votes, holds one of the particles. The second is sent to a voter, whose operation on the particle corresponds to his or her vote (yes or no). The voter then sends the ballot particle to the next voter, and the process is repeated until the final voter registers her vote, after which she returns the particle to the authority. The authority can measure the two-particle state and determine the number of yes votes. However, during the voting procedure, no particle carries any information about the votes being cast. This information resides in the correlations between the particles, so that one has to be in possession of both particles to gain information about the voting. This protects the privacy of the votes from both inquisitive voters and an inquisitive authority.
The second procedure, a distributed ballot scheme, makes use of an entangled state of N particles. Each one of the N voters receives one particle and performs an operation on the particle corresponding to his or her vote. Then, all of the particles are sent to the authority, who measures the multiparticle state and is thereby able to determine the number of yes votes. Again, with all the information about the votes contained in the correlations between the particles, the quantum state contains no information about how individuals voted.
An interesting variant on this scheme was recently proposed by Dolev, Pitowski, and Tamir.4 It uses the same entangled state as the distributed ballot scheme but different voting operators. This involves adding a random number to each vote, but the effect of these numbers disappears when the ballots are counted. (They add to 0 modulo N.) The vote-counting authority thus becomes superfluous. Each voter measures his particle after applying his voting operator, and the result is his vote plus a random number. All voters can add the announced results. And because the effect of the random numbers disappears, the outcome is represented by the number of yes votes.
Quantum voting schemes are still at a very early stage of design and development. Detailed studies of methods to avoid fraud on the part of either voters or authorities will be required. In addition, serious thought needs to be applied to practical implementation.
Figure 1. Two ballot schemes for quantum voting make use of particles in an entangled state. In the traveling ballot scheme, the authority keeps one of two entangled particles, while the other is sent successively from one voter to the next, and eventually returned to the authority. In the distributed ballot scheme, each voter receives their own particle.