We firstly present an all-optical scheme to implement the non-deterministic quantum logic operation of Knill, Laflamme and Milburn (Nature, 409, 46-52(2001)). In our scheme, squeezed vacuum state is acted as auxiliary state instead of single photon resources. Then we demonstrate that same setup can be used to teleport a superposition of vacuum and single photon state of the form
α∣0>+β∣1> and a superposition of vacuum and single polarized photon state of the form
α∣0>+β∣H>+γ∣V>.
The addition of a single photon to a light field can lead to exactly the same out-comeas the subtraction of a single photon. We prove that this identity-of-outcome is true for pure squeezed vacuum states of light, and in some sense only for those. We show that mixed states can show this identity-of-outcome for addition or subtraction of a photon if they are generated from incoherent sums of pure squeezed vacuum states with the same squeezing. Our results gives a reinterpretation to the fact that pure squeezed vacuum states are formally annihilated by Bogoliubov-transformed annihilation operators: â z = âcosh(z) − ↠sinh(z).
Triggered single-photon sources produce the vacuum state with nonzero probability, but produce a much smaller multiphoton component. It is therefore reasonable to approximate the output of these photon sources as a mixture of the vacuum and single-photon states with probabilities $1\ensuremath{-}p$ and
p, respectively. Here we are concerned with increasing the efficiency
p by directing multiple copies of the single-photon-vacuum mixture into a linear optical device and applying photodetection on some outputs. We prove that it is impossible, under certain conditions, to increase
p via linear optics and conditional preparation based on photodetection. We also establish a class of photodetection events for which
p can be improved, although with an added multiphoton component. In addition we prove that it is not possible to obtain perfect single-photon states via this method from imperfect
(p<1) inputs.