2 00 1 Reply to Comment on “ Proposal for the Measurement of Bell - Type Correlations from Continuous Variables ”

Recently K. Banaszek, I. A. Walmsley, K. Wodkiewicz (quant-ph/0012097) commented on our Proposal for the Measurement of Bell-Type Correlations from Continuous Variables [T. Their comment is based on a blatant misreading and misunderstanding of our letter and as such is simply wrong.1] on our letter [2] purports to present a hidden variable theory which describes our results. The hidden variable scheme described is based on the positive Wigner distribution which describes quadrature measurements on the parametric amplifier and vacuum background. It is well known, and was pointed out on three separate occasions in our paper, that such a description is possible if only quadrature measurements are performed. This is the reason why (as was also pointed out on three separate occasions) auxiliary intensity measurements must also be made. The comment incorrectly identifies these auxiliary measurements as being quadrature measurements of the vacuum. Instead, as is stated in the paper, they are quantum limited intensity measurements on the vacuum. As is also clearly stated in the paper, this auxiliary intensity measurement guarantees the positivity of the underlying (but inaccessible) individual measurements which make up our ensemble average. Without such a measurement the positivity of the individuals is not guaranteed and the Bell test cannot be applied. The authors say nothing that was not already stated in our letter when they make this point in their comment. It seems a cursory reading of our letter can lead to misconceptions. Given the brevity of the letter format this is perhaps understandable. A more detailed account is presently in preparation. Here we present a brief discussion aimed particularly at the point which the comment missed.