Quantum Amnesia Leaves Cryptographic Mementos: A Note On Quantum Skepticism

TL;DR

This paper explores how the inherent 'quantum amnesia' in quantum computers, which limits quantum memory retention, can be leveraged to achieve cryptographic primitives like secure commitment and oblivious transfer.

Contribution

It demonstrates that quantum amnesia, modeled by the quantum bounded storage model, can be used to construct cryptographic primitives using only transmission and measurement of BB84 states.

Findings

Quantum amnesia limits quantum memory retention.

Quantum bounded storage model enables cryptographic primitives.

Secure commitment and oblivious transfer are achievable with BB84 states.

Abstract

Leonard Shelby, the protagonist of Memento, uses mementos in the form of tattoos and pictures to handle his amnesia. Similar to Leonard, contemporary quantum computers suffer from "quantum amnesia": the inability to store quantum registers for a long duration. Quantum computers can only retain classical "mementos" of quantum registers by measuring them before those vanish. Some quantum skeptics argue that this quantum amnesia is inherent. We point out that this variant of a skeptic world is roughly described by the quantum bounded storage model, and although it is a computational obstacle that annuls potential quantum computational advantage, the seemingly undesired properties provide a cryptographic advantage. Namely, providing exotic primitives promised by the quantum bounded storage model, such as unconditionally secure commitment and oblivious transfer schemes, with constructions involving nothing but transmission and measurement of BB84 states.