Figure 4: Implementing two-qubit controlled-unitary operations by harnessing entanglement in a larger Hilbert space.
From: Adding control to arbitrary unknown quantum operations
(a–e) Experimentally measured 'truth tables' for several CU gates. For the inputs of the CH gate |M〉 and |N〉 (|J〉 and |K〉) are the eigenstates of 
with +1 and −1 eigenvalues respectively: that is |M〉=cos(π/8)|H〉+sin(π/8)|V〉; |N〉=sin(π/8)|H〉−cos(π/8)|V〉; |J〉=cos(5π/8)|H〉+sin(5π/8)|V〉; |K〉=sin(5π/8)|H〉−cos(5π/8)|V〉. Note that two different output measurement bases are applied for each truth table of CPhase(π/2) and CPhase(π/4). The red columns correspond to red output labels whereas the blue columns correspond to blue output labels, which include states such as |HL〉, |HR〉, |HS〉 and |HT〉 where 
and 
. Bounds on the process fidelities FP and average fidelities 
are calculated from the classical fidelities shown under the truth tables. Each truth table requires 16 measurements and each measurement takes 1 s. The count of each high column is around 2,000. Note that for probabilities near zero in the truth tables, we increased the integration time from 1 s to 10 s to improve the statistics.
