  We introduce a geometric path integral definition of wormhole partition
functions in a general class of 1D quantum systems obtained by quantizing a
phase space. We compute the wormhole partition function in a semi-classical
limit and in some simple examples. The partition function of the n-fold
wormhole is found to be identical to the n-th Renyi entropy of a thermal mixed
state of the doubled system. This mixed state incorporates three types of
quantum statistical behavior: classically correlated, quantum entangled, and
classically uncorrelated. We apply our prescription to 2D CFTs with Virasoro
symmetry and recover the holographic dual formulation in terms of AdS3 gravity.
