One-time memories (OTM's) are simple tamper-resistant cryptographic devices,
which can be used to implement one-time programs, a very general form of
software protection and program obfuscation. Here we investigate the
possibility of building OTM's using quantum mechanical devices. It is known
that OTM's cannot exist in a fully-quantum world or in a fully-classical world.
Instead, we propose a new model based on "isolated qubits" -- qubits that can
only be accessed using local operations and classical communication (LOCC).
This model combines a quantum resource (single-qubit measurements) with a
classical restriction (on communication between qubits), and can be implemented
using current technologies, such as nitrogen vacancy centers in diamond. In
this model, we construct OTM's that are information-theoretically secure
against one-pass LOCC adversaries that use 2-outcome measurements.
Our construction resembles Wiesner's old idea of quantum conjugate coding,
implemented using random error-correcting codes; our proof of security uses
entropy chaining to bound the supremum of a suitable empirical process. In
addition, we conjecture that our random codes can be replaced by some class of
efficiently-decodable codes, to get computationally-efficient OTM's that are
secure against computationally-bounded LOCC adversaries.
In addition, we construct data-hiding states, which allow an LOCC sender to
encode an (n-O(1))-bit messsage into n qubits, such that at most half of the
message can be extracted by a one-pass LOCC receiver, but the whole message can
be extracted by a general quantum receiver.