This paper investigates asymptotically optimal scalar quantizers to address QIM watermark detection with i.i.d. host data and additive noise. False-alarm probability of detection is chosen as the cost to be minimized, keeping the embedding distortion and the miss probability upper-bounded. To avoid the intractability of false-alarm probability, Kullback distance between watermarked and non-watermarked data is adopted instead. The problem is then to seek the quantizer which maximizes the false-alarm error exponent under distortion constraint. Using Lagrange multiplier minimization, a quantizer updating Lloyd-Max-like procedure is used to solve the optimization. For experimental aspects, host data and noise have been set gaussian. In comparison with uniform or Lloyd-Max quantizers, it turns out that detection performances can be notably enhanced by using proposed application-optimized quantizers. The gain is effective even for small number N of sample at the detector input. However, this gain becomes more substantial as N grows. This also emphasises that good quantizers in terms of distortion are not suitable for detection task.