Experimentally realizable quantum comparison of coherent states and its applications

When comparing quantum states to each other, it is possible to obtain an unambiguous answer, indicating that the states are definitely different, already after a single measurement. In this paper we investigate comparison of coherent states, which is the simplest example of quantum state comparison for continuous variables. The method we present has a high success probability, and is experimentally feasible to realize as the only required components are beam splitters and photon detectors. An easily realizable method for quantum state comparison could be important for real applications. As examples of such applications we present a “lock and key” scheme and a simple scheme for quantum public key distribution.

Figure 1

The beam splitter mixes the two input fields in a linear way into two output fields. The relations between input and output creation operators are expressed in Eq. (1).

Figure 2

The success probability of comparing two coherent states as a function of the absolute value of the difference between the coherent states' amplitudes $\mid \alpha -\beta \mid$. The knowledge that we deal with an a priori known class of states enables us to reach the ideal limit of $1$.

Figure 3

The balanced multiport is a passive device distributing an incoming photon with equal probability among all the outputs. The device can be constructed using beam splitters and phase shifters.

Figure 4

The von Neumann entropy as a function of the mean photon number $\mid \alpha {\mid }^2$ for $N=2,3,4,5,6$. The asymptotic value of the entropy increases with the number of states $N$.

Figure 5

The setup for public key distribution without a trusted center, when there are two recipients Bob and Charlie. Alice sends Bob and Charlie one copy each of her public key. In the picture, she uses a beam splitter to do this. Bob and Charlie then split their key copies in two using beam splitters, and exchange “key halves” with each other. They then perform comparison tests, indicated by the dashed circles, on their own half key copy and the one they received from the other recipient. If all parties are honest (and their detectors perfect), the output ports with the dashed arrows should only contain vacuum.