  A quantum key distribution protocol is proposed that is a variation of BB84
that provides raw key generation from correlations that violate a Bell-type
inequality for single qubit systems and not entangled pairs. Additionally, it
1) is state-independent, 2) involves two-way classical communication, and 3)
does not require basis matching between the two parties. The
Brukner-Taylor-Cheung-Vedral (BTCV) time-like form of the Bell-CHSH inequality
[C. Brukner, S. Taylor, S. Cheung, V. Vedral arXiv:quant-ph/0402127] is
employed as an eavesdropping check; sequential measurements lead to an
inequality identical in form to the Bell-CHSH inequality, which relies only on
the measurements performed with no regard for the qubit states. We show that
this form manifests naturally from the non-commutativity of observables.
