  This paper, following [M. Ozawa, Phys. Rev. Lett. 60, 385 (1988)], reports a
refutation of the claim that for monitoring the position of a free mass such as
gravitational-wave interferometers the sensitivity is limited by the so called
standard quantum limit (SQL) due to the uncertainty principle. The latest proof
of the SQL is analyzed to revleal an unsupported assumption on quantum
measurements. Quantum measurement theory is introduced to give a general
criterion for physically realizable measurements in quantum mechanics. A theory
of approximate position measurements is developed to obtain a rigorous
condition for the SQL and also to show that a precise position measurement can
leave the object in an arbitrary family of states independent of the input
state. This concludes that Yuen's proposal of breaking the SQL by a contractive
state measurement, a measurement of the position leaving the free mass in a
state with the position uncertainty decreasing in time, is physically
realizable in principle. To enforce this conclusion, a model for error-free
position measurement that leaves the object in a contractive state is
constructed with a solvable Hamiltonian for measuring interaction. Finally,
this model is shown to break the SQL with arbitrary accuracy.
