  We describe new unconditionally secure bit commitment schemes whose security
is based on Minkowski causality and the monogamy of quantum entanglement. We
first describe an ideal scheme that is purely deterministic, in the sense that
neither party needs to generate any secret randomness at any stage. We also
describe a variant that allows the committer to proceed deterministically,
requires only local randomness generation from the receiver, and allows the
commitment to be verified in the neighbourhood of the unveiling point. We show
that these schemes still offer near-perfect security in the presence of losses
and errors, which can be made perfect if the committer uses an extra single
random secret bit. We discuss scenarios where these advantages are significant.
