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What is the quantum state of the universe? Although there have been severalinteresting suggestions, the question remains open. In this paper, I consider anatural choice for the universal quantum state arising from the PastHypothesis, a boundary condition that accounts for the time-asymmetry of theuniverse. The natural choice is given not by a wave function (representing apure state) but by a density matrix (representing a mixed state).  I begin by classifying quantum theories into two types: theories with afundamental wave function and theories with a fundamental density matrix. ThePast Hypothesis is compatible with infinitely many initial wave functions, noneof which seems to be particularly natural. However, once we turn to densitymatrices, the Past Hypothesis provides a natural choice---the normalizedprojection onto the Past Hypothesis subspace in the Hilbert space.Nevertheless, the two types of theories can be empirically equivalent. Toprovide a concrete understanding of the empirical equivalence, I provide anovel subsystem analysis in the context of Bohmian theories. Given theempirical equivalence, it seems empirically underdetermined whether theuniverse is in a pure state or a mixed state. Finally, I discuss sometheoretical payoffs of the density-matrix theories and present some openproblems for future research.

Quantum States of a Time-Asymmetric Universe: Wave Function, Density Matrix, and Empirical Equivalence