  In optical quantum information processing with continuous variables, optical
non-Gaussian quantum states are essential for universal and fault-tolerant
quantum computation. Experimentally, their most typical generation method is
photon subtraction (PS) where single-photon detection by an on/off detector
probabilistically heralds the generation of squeezed single-photon states. In
PS, however, trying to avoid unwanted multi-photon detection inevitably limits
the generation rate, hindering the application of squeezed single-photon
states. Here, we theoretically show that generalized photon subtraction (GPS),
a simple extension of PS, can improve the generation rate while maintaining the
quality of the generated states. Furthermore, we experimentally demonstrate the
generation rate improvement for 2 dB- and 4 dB-squeezed single-photon states
compared to PS, by more than one order of magnitude particularly for the case
of 2 dB. Our results will accelerate the application of squeezed single-photon
states to more advanced quantum information protocols.
