Measurement Result for GBS circuit

I have noticed that in every GBS circuit the maximum output probability state is the one that have all measurements 0 such as (0,0,0,0) for four input modes. I have three questions regarding this:

  1. How is this considered a measurements.
  2. If it is a measurement how we know that this measurement has occurred since no detector clicks.
  3. Why is the most probable state in any GBS circuit?

Hello there,

I can answer some of your questions.

  1. From a theoretical point of view, measuring vacuum is perfectly fine as long as you know that some system has arrived at your detector: in the ideal case it corresponds to a projector, just like when we measure a given number of photons.

  2. If the detector doesn’t click and a state was present then we say that vacuum has been measured (of course, with realistic losses and detector inefficiency, getting no clicks means having a rather mixed state in the unmeasured modes).

  3. I don’t think this should always be the case and it depends on your GBS setup. For sure if you have a Gaussian state the vacuum component is never zero (i.e. there’s always a finite probability of measuring the vacuum, even in the ideal case), but it doesn’t have to be the one with highest probability, e.g. if you produce a coherent state, which is Gaussian, you can make the vacuum amplitude as small as you want (but never zero).

I hope this helps.