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We have developed a method for calculation of quantum fluctuation effects, in particular of the uncertainty zone developing at the potential curvature sign inversion, for a damped harmonic oscillator with arbitrary time dependence of frequency and for arbitrary temperature, within the Caldeira-Leggett model. The method has been applied to the calculation of the gray zone width ∆Ix of Josephson-junction balanced comparators driven by a specially designed low-impedance RSFQ circuit. The calculated temperature dependence of ∆Ix in the range 1.5 to 4.2K is in a virtually perfect agreement with experimental data for Nb-trilayer comparators with critical current densities of 1.0 and 5.5 kA/cm 2 , without any fitting parameters.The current attention to quantum information processing (see, e.g., the recent monograph [1]) has renewed interest in fast "single-shot" quantum measurements, especially in potentially scalable solid-state systems. Among such systems, superconductor "balanced comparator", based on two similar Josephson junctions (Fig. 1a), stands apart as a very simple, scalable system for which quantum-limited sensitivity has already been demonstrated experimentally [2].The device is essentially a SQUID (see, e.g., [3]) in which two similar junctions are biased in series by a source of Josephson phase difference φ e (t), and in parallel by the current I x to be measured. Let the system with |φ e | < π settle in an equilibrium state φ = φ i , and then apply a rapid phase change ∆φ e = 2π. (This can be readily done using the so-called RSFQ circuitry -see, e.g., the recent review [4].) As a result, the system becomes statically unstable and the Josephson phase φ has to switch to one of adjacent stable states, depending on the sign of I x . (For junctions with substantial damping, the choice is limited by two states closest to the initial value of φ: φ f = φ i ± π).This process may be readily understood using the "magnetic language": the driver circuit providing the pulse ∆φ e = 2π in fact injects a single flux quantum into a superconducting loop formed by its output stage and the comparator (Fig. 1a). Since the loop is lowinductive (non-quantizing), the flux quantum has to drop out across one of the comparator junctions, depending on the sign of I x . This transient process produces a large (discrete) output signal, the so-called SFQ pulse V (t) with V (t)dt = Φ 0 = h/2e across the corresponding junction. Such a pulse may be readily picked up and registered by relatively crude devices [4], so that the accuracy of the