  We present a two-state practical quantum bit commitment protocol, the
security of which is based on the current technological limitations, namely the
nonexistence of either stable long-term quantum memories or nondemolition
measurements. For an optical realization of the protocol, we model the errors,
which occur due to the noise and equipment (source, fibers, and detectors)
imperfections, accumulated during emission, transmission, and measurement of
photons. The optical part is modeled as a combination of a depolarizing channel
(white noise), unitary evolution (e.g., systematic rotation of the polarization
axis of photons), and two other basis-dependent channels, namely the phase- and
bit-flip channels. We analyze quantitatively the effects of noise using two
common information-theoretic measures of probability distribution
distinguishability: the fidelity and the relative entropy. In particular, we
discuss the optimal cheating strategy and show that it is always advantageous
for a cheating agent to add some amount of white noise - the particular effect
not being present in standard quantum security protocols. We also analyze the
protocol's security when the use of (im)perfect nondemolition measurements and
noisy or bounded quantum memories is allowed. Finally, we discuss errors
occurring due to a finite detector efficiency, dark counts, and imperfect
single-photon sources, and we show that the effects are the same as those of
standard quantum cryptography.
