  Standard quantum key distribution (QKD) protocols typically assume that the
distant parties share a common reference frame. In practice, however,
establishing and maintaining a good alignment between distant observers is
rarely a trivial issue, which may significantly restrain the implementation of
long-distance quantum communication protocols. Here we propose simple QKD
protocols that do not require the parties to share any reference frame, and
study their security and feasibility in both the usual device-dependent
case--in which the two parties use well characterized measurement devices--as
well as in the device-independent case--in which the measurement devices can be
untrusted, and the security relies on the violation of a Bell inequality. To
illustrate the practical relevance of these ideas, we present a
proof-of-principle demonstration of our protocols using polarization entangled
photons distributed over a coiled 10-km-long optical fiber. We consider two
situations, in which either the fiber spool freely drifts, or randomly chosen
polarization transformations are applied. The correlations obtained from
measurements allow, with high probability, to generate positive asymptotic
secret key rates in both the device-dependent and device-independent scenarios
(under the fair-sampling assumption for the latter case).
