Quantum one-time programs

TL;DR

This paper proves the impossibility of purely quantum one-time programs for classical and quantum functions, but also presents a construction for secure quantum one-time programs using quantum authentication and one-time memories.

Contribution

It establishes a strong impossibility result for quantum one-time programs and provides a new construction for secure quantum programs with one-time memories.

Findings

Quantum one-time programs for classical and quantum maps do not exist without additional assumptions.

A new quantum authentication scheme enables secure quantum one-time programs.

The construction achieves security in the universal composability framework.

Abstract

One-time programs are modelled after a black box that allows a single evaluation of a function, and then self-destructs. Because software can, in principle, be copied, general one-time programs exists only in the hardware token model: it has been shown that any function admits a one-time program as long as we assume access to physical devices called one-time memories. Quantum information, with its well-known property of no-cloning, would, at first glance, prevent the basic copying attack for classical programs. We show that this intuition is false: one-time programs for both classical and quantum maps, based solely on quantum information, do not exist, even with computational assumptions. We complement this strong impossibility proof by an equally strong possibility result: assuming the same basic one-time memories as used for classical one-time programs, we show that every quantum map has a quantum one-time program that is secure in the universal composability framework. Our construction relies on a new, simpler quantum authentication scheme and corresponding mechanism for computing on authenticated data.