The nonorthogonality of coherent states is a fundamental property which prevents them from being perfectly and deterministically discriminated. To circumvent this problem, we present an experimentally feasible protocol for the probabilistic orthogona
lisation of a pair of coherent states, independent of their amplitude and phase. In contrast to unambiguous state discrimination, successful operation of our protocol is heralded without measuring the states, such that they remain suitable for further manipulation. As such, the resulting orthogonalised state may be used for further processing. Indeed, these states are close approximations of the discrete-variable superposition state $frac{1}{sqrt{2}}left(|0rangle pm |1rangleright)$. This feature, coupled with the non-destructive nature of the operation, is especially useful when considering superpositions of coherent states: such states are mapped to the (weakly squeezed) vacuum or single photon Fock state, depending on the phase of the superposition. Thus this operation may find utility in hybrid continuous-discrete quantum information processing protocols.
The progress in building large quantum states and networks requires sophisticated detection techniques to verify the desired operation. To achieve this aim, a cost- and resource-efficient detection method is the time multiplexing of photonic states.
This design is assumed to be efficiently scalable; however, it is restricted by inevitable losses and limited detection efficiencies. Here, we investigate the scalability of time-multiplexed detectors under the effects of fiber dispersion and losses. We use the distinguishability of Fock states up to $n=20$ after passing the time-multiplexed detector as our figure of merit and find that, for realistic setup efficiencies of $eta=0.85$, the optimal size for time-multiplexed detectors is 256 bins.
Sampling the distribution of bosons that have undergone a random unitary evolution is strongly believed to be a computationally hard problem. Key to outperforming classical simulations of this task is to increase both the number of input photons and
the size of the network. We propose driven boson sampling, in which photons are input within the network itself, as a means to approach this goal. When using heralded single-photon sources based on parametric down-conversion, this approach offers an $sim e$-fold enhancement in the input state generation rate over scattershot boson sampling, reaching the scaling limit for such sources. More significantly, this approach offers a dramatic increase in the signal-to-noise ratio with respect to higher-order photon generation from such probabilistic sources, which removes the need for photon number resolution during the heralding process as the size of the system increases.
