A Computational Separation Between Quantum No-cloning and No-telegraphing

TL;DR

This paper demonstrates a quantum oracle separation showing states that are efficiently clonable but not efficiently telegraphable, challenging the assumed equivalence of these properties under computational constraints, with implications for quantum cryptography.

Contribution

It introduces a quantum oracle separation between efficient clonability and telegraphability, and explores the complexity class clonableQMA versus QCMA, with cryptographic applications.

Findings

States efficiently clonable but not telegraphable under certain oracles.

Quantum oracle separation between clonableQMA and QCMA.

Application of such states in cryptography to prevent key exfiltration.

Abstract

Two of the fundamental no-go theorems of quantum information are the no-cloning theorem (that it is impossible to make copies of general quantum states) and the no-teleportation theorem (the prohibition on telegraphing, or sending quantum states over classical channels without pre-shared entanglement). They are known to be equivalent, in the sense that a collection of quantum states is telegraphable if and only if it is clonable. Our main result suggests that this is not the case when computational efficiency is considered. We give a collection of quantum states and quantum oracles relative to which these states are efficiently clonable but not efficiently telegraphable. Given that the opposite scenario is impossible (states that can be telegraphed can always trivially be cloned), this gives the most complete quantum oracle separation possible between these two important no-go properties. We additionally study the complexity class clonableQMA, a subset of QMA whose witnesses are efficiently clonable. As a consequence of our main result, we give a quantum oracle separation between clonableQMA and the class QCMA, whose witnesses are restricted to classical strings. We also propose a candidate oracle-free promise problem separating these classes. We finally demonstrate an application of clonable-but-not-telegraphable states to cryptography, by showing how such states can be used to protect against key exfiltration.