  A central tenet of theoretical cryptography is the study of the minimal
assumptions required to implement a given cryptographic primitive. One such
primitive is the one-time memory (OTM), introduced by Goldwasser, Kalai, and
Rothblum [CRYPTO 2008], which is a classical functionality modeled after a
non-interactive 1-out-of-2 oblivious transfer, and which is complete for
one-time classical and quantum programs. It is known that secure OTMs do not
exist in the standard model in both the classical and quantum settings. Here,
we show how to use quantum information, together with the assumption of
stateless (i.e., reusable) hardware tokens, to build statistically secure OTMs.
This is in sharp contrast with the classical case, where stateless hardware
tokens alone cannot yield OTMs. In addition, our scheme is technologically
simple. We prove security in the quantum universal composability framework,
employing semi-definite programming results of Molina, Vidick and Watrous [TQC
2013] and combinatorial techniques of Pastawski et al. [Proc. Natl. Acad. Sci.
2012].
