  Let $B$ be a star-algebra with a state $\phi$, and $t > 0$. Through a Fock
space construction, we define two states $\Phi_t$ and $\Psi_t$ on the tensor
algebra $T(B, \phi)$ such that under the natural map $(B, \phi) \rightarrow
(T(B, \phi), \Phi_t, \Psi_t)$, free independence of arguments leads to free
independence, while Boolean independence of centered arguments leads to
conditionally free independence. The construction gives a new operator
realization of the $(1+t)$'th free convolution power of any joint (star)
distribution. We also compute several von Neumann algebras which arise.
