Universal Programmable Quantum State Discriminator that is Optimal for Unambiguously Distinguishing between Unknown States

We construct a device that can unambiguously discriminate between two unknown quantum states. The unknown states are provided as inputs, or programs, for the program registers, and a third system, which is guaranteed to be prepared in one of the states stored in the program registers, is fed into the data register of the device. The device will then, with some probability of success, tell us whether the unknown state in the data register matches the state stored in the first or the second program register. We show that the optimal device, i.e., the one that maximizes the probability of success, is universal. It does not depend on the actual unknown states that we wish to discriminate.

Figure 1

Optimal average success probability, $P$, vs the a priori probability, ${\eta }_1$. Dashed line, $P_1$ from Eq. (20); dotted line, $P_2$ from Eq. (21); solid line, $P_{\mathrm{POVM}}$ from Eq. (17). For the figure we replaced $1-|⟨{\psi }_1|{\psi }_2⟩{|}^2$ by its average, $\frac{1}{2}$. The optimal $P$ is given by $P_2$ for ${\eta }_1<0.2$, by $P_{\mathrm{POVM}}$ for $0.2\le {\eta }_1\le 0.8$, and by $P_1$ for $0.8<{\eta }_1$.