Simulating single photons with realistic photon sources

Quantum information processing provides remarkable advantages over its classical counterpart. Quantum optical systems have been proved to be sufficient for realizing general quantum tasks, which, however, often rely on single-photon sources. In practice, imperfect single-photon sources, such as a weak-coherent-state source, are used instead, which will inevitably limit the power in demonstrating quantum effects. For instance, with imperfect photon sources, the key rate of the Bennett-Brassard 1984 (BB84) quantum key distribution protocol will be very low, which fortunately can be resolved by utilizing the decoy-state method. As a generalization, we investigate an efficient way to simulate single photons with imperfect ones to an arbitrary desired accuracy when the number of photonic inputs is small. Based on this simulator, we can thus replace the tasks that involve only a few single-photon inputs with the ones that make use of only imperfect photon sources. In addition, our method also provides a quantum simulator to quantum computation based on quantum optics. In the main context, we take a phase-randomized coherent state as an example for analysis. A general photon source applies similarly and may provide some further advantages for certain tasks.

Figure 1

Optical circuits with a single photon as input.

Figure 2

Error ${\mathrm{\Delta }}_L$ for specific usage of coherent intensities, ${\mu }_j=j/L$ for $j=0,1,\cdots ,L$. $L$ runs only from 1 to 10 for computational accuracy limit. Blue dots are the ${\mathrm{\Delta }}_L$ value, and the green line is the exponential fit.

Figure 3

Error factor $f$ for different $L$. Blue dots are the ${\mathrm{\Delta }}_L$ value, and the green line is the exponential fit.

Figure 4

Optimized total error for different numbers of samples. The blue dots are the total error for $L\left(M\right)$ coherent probe intensities. The green dots are the total error for a single-photon source, that is, $1/\sqrt{M}$.

Figure 5

Optimal number of nonzero probe intensities $L$ for different numbers of samples $M$.

Figure 6

Schematic for the a general quantum channel with $n$ optical input modes.

Figure 7

Optimized total error for different numbers of samples and different input modes.

Figure 8

Optimized number of nonzero probe intensities for different numbers of input modes. Top left, two modes; top right, three modes; bottom left, four modes; and bottom right, five modes.