eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2024-01-24
82:1
82:23
10.4230/LIPIcs.ITCS.2024.82
article
A Computational Separation Between Quantum No-Cloning and No-Telegraphing
Nehoran, Barak
1
https://orcid.org/0000-0001-7371-0829
Zhandry, Mark
2
https://orcid.org/0000-0001-7071-6272
Princeton University, NJ, USA
NTT Research, Sunnyvale, CA, USA
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol287-itcs2024/LIPIcs.ITCS.2024.82/LIPIcs.ITCS.2024.82.pdf
Cloning
telegraphing
no-cloning theorem
oracle separations