  Projective measurement is a commonly used assumption in quantum mechanics.
However, advances in quantum measurement techniques allow for partial
measurements, which accurately estimate state information while keeping the
wavefunction intact. In this dissertation, we employ partial measurements to
study two phenomena. First, we investigate an uncertainty relation -- in the
style of Heisenberg's 1929 thought experiment -- which includes partial
measurements in addition to projective measurements. We find that a weak
partial measurement can decrease the uncertainty between two incompatible
(non-commuting) observables. In the second study, we investigate the foundation
of irreversible dynamics resulting from partial measurements. We do so by
comparing the forward and time-reversed probabilities of measurement outcomes
resulting from post-selected feedback protocols with both causal and
reversed-causal order. We find that the statistics of partial measurements
produce entropy in accordance with generalized second laws of thermodynamics.
  We perform these experiments using superconducting qubits. This dissertation
also describes the fabrication process for these devices and details a novel
fabrication technique that allows fast, single-step lithography of
Josephson-junction superconducting circuits. The technique simplifies
processing by utilizing a direct-write photolithography system, in contrast to
traditional electron-beam lithography. Despite their large lithographic area,
Josephson junctions made with this method have low critical currents and high
coherence times.
