Emergent quantum state designs from individual many-body wavefunctions

In this poster, we describe a universal phenomenon that occurs in strongly interacting many-body quantum dynamics, beyond the conventional notion of thermalization. Specifically, we point out that a single many-body wavefunction can encode a large ensemble of pure states defined on a subsystem. We analyze the statistical properties of the ensemble using a notion from quantum information theory called quantum state k-designs. We find that, across a wide range of examples, these ensembles are universal and highly random. First, we analytically prove that almost all many-body wavefunctions in Hilbert space encode ensembles sharing the same statistical properties, namely the formation of approximate k-designs. Second, we numerically establish that the same properties also arise from time-evolved states and from energy eigenstates of generic chaotic Hamiltonians at infinite temperature. The special case of our results at k=1 reproduces conventional thermalization. Our results offer a new approach for studying quantum chaos and provide a practical method for sampling approximately uniformly random states. The latter has wide-ranging applications in quantum information science from tomography to benchmarking, including a new benchmarking method that has been demonstrated in a Rydberg quantum simulator.