Adding or Subtracting a single Photon is the same for Pure Squeezed Vacuum States

The addition of a single photon to a light field can lead to exactly the same out-come as 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 = â cosh( z ) − â † sinh( z ).