  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 propose a scheme for using quantum information, together with the assumption
of stateless (i.e., reusable) hardware tokens, to build statistically secure
OTMs. Via the semidefinite programming-based quantum games framework of Gutoski
and Watrous [STOC 2007], we prove security for a malicious receiver making at
most 0.114n adaptive queries to the token (for n the key size), in the quantum
universal composability framework, but leave open the question of security
against a polynomial amount of queries. Compared to alternative schemes derived
from the literature on quantum money, our scheme is technologically simple
since it is of the "prepare-and-measure" type. We also give two impossibility
results showing certain assumptions in our scheme cannot be relaxed.
