  We suggest a new type of the magnetic flux detector which can be optimized
with respect to the measurement back-action, e.g. for the situation of quantum
measurements. The detector is based on manipulation of ballistic motion of
individual fluxons in a Josephson transmission line (JTL), with the output
information contained in either probabilities of fluxon
transmission/reflection, or time delay associated with the fluxon propagation
through the JTL. We calculate the detector characteristics of the JTL and
derive equations for conditional evolution of the measured system both in the
transmission/reflection and the time-delay regimes. Combination of the
quantum-limited detection with control over individual fluxons should make the
JTL detector suitable for implementation of non-trivial quantum measurement
strategies, including conditional measurements and feedback control schemes.
