Experimental Realization of Maximum Confidence Quantum State Discrimination for the Extraction of Quantum Information

We present the first experimental demonstration of the maximum confidence measurement strategy for quantum state discrimination. Applying this strategy to an arbitrary set of states assigns to each input state a measurement outcome which, when realized, gives the highest possible confidence that the state was indeed present. The theoretically optimal measurement for discriminating between three equiprobable symmetric qubit states is implemented in a polarization-based free-space interferometer. The maximum confidence in the measurement result is $2/3$. This is the first explicit demonstration that an improvement in the confidence over the optimal minimum error measurement is possible for linearly dependent states.

Figure 1

Experimental apparatus. $\mathrm{LD}=\mathrm{\text{Laser diode}}$, $\mathrm{SMF}=\mathrm{\text{single mode fiber}}$, $\mathrm{PBS}1–5=\mathrm{\text{polarizing beam splitters}}$, $\mathrm{HWP}1–7=\mathrm{\text{zero-order half wave plates}}$, $\mathrm{QWP}1–3=\mathrm{\text{zero}}\mathrm{\text{−}}\mathrm{\text{order quarter wave plates}}$, PD0–2, $\mathrm{PD}?=$amplified photodiodes.

Figure 2

Experimental results alongside the theoretical predictions without error (dashed lines) and with nonideal beamsplitters PBS2 and PBS3 (solid lines), as a function of $\theta$, for each of the input states $|{\Psi }_0⟩$, $|{\Psi }_1⟩$, $|{\Psi }_2⟩$ ($l\mathrm{\text{−}}r$). Points show the normalized voltage at each detector, with triangles, squares, circles, diamonds corresponding to PD0, PD?, PD1, PD2, respectively. Experimental errors in the measured voltages are smaller than the size of the data points.

Figure 3

Experimental and theoretical values for the confidence figure of merit, and the confidence achieved by the optimal minimum error measurement (dashed line). Diamonds, squares, triangles show the proportion of the voltage at detector $\mathrm{PD}i$, $i=0$, 1, 2, respectively, due to input state $|{\Psi }_i⟩$, i.e., the confidence that a voltage in $\mathrm{PD}i$ indicates that the input state was $|{\Psi }_i⟩$. Shaded regions show the range of values consistent with the nonideal model, while the ideal theoretical value of $2/3$ is also shown (dotted line).