Abstract
We present a simple quantum interactive proof (QIP) protocol using the quantum state teleportation and quantum energy teleportation (QET) protocols. QET is a technique that allows a receiver at a distance to extract the local energy by local operations and classical communication (LOCC), using the energy injected by the supplier as collateral. QET works for any local Hamiltonian with entanglement and, for our study, it is important that getting the ground state of a generic local Hamiltonian is quantum Merlin–Arthur-hard. The key motivations behind employing QET for these purposes are clarified. Firstly, in cases where a prover possesses the correct state and executes the appropriate operations, the verifier can effectively validate the presence of negative energy with a high probability (completeness). Failure to select the appropriate operators or an incorrect state renders the verifier incapable of observing negative energy (soundness). Importantly, the verifier solely observes a single qubit from the prover’s transmitted state, while remaining oblivious to the prover’s Hamiltonian and state (zero-knowledge). Furthermore, the analysis is extended to distributed quantum interactive proofs, where we propose multiple solutions for the verification of each player’s measurement. The results in the N-party scenario could have particular relevance for the implementation of future quantum networks, where verification of quantum information is a necessity. The complexity class of our protocol in the most general case belongs to QIP(3)=PSPACE; hence, it provides a secure quantum authentication scheme that can be implemented in small quantum communication devices. It is straightforward to extend our protocol to Quantum Multi-Prover Interactive Proof (QMIP) systems, where the complexity is expected to be more powerful (PSPACE⊂QMIP=NEXPTIME). In our case, all provers share the ground state entanglement; hence, it should belong to a more powerful complexity class QMIP∗.
Original language | English |
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Article number | 236 |
Number of pages | 23 |
Journal | Quantum Information Processing |
Volume | 23 |
Issue number | 6 |
Early online date | 12 Jun 2024 |
DOIs | |
Publication status | Published - 12 Jun 2024 |
Bibliographical note
Copyright © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024. This version of the article has been accepted for publication, after peer review and is subject to Springer Nature’s AM terms of use [https://www.springernature.com/gp/open-research/policies/accepted-manuscript-terms], but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s11128-024-04448-0Data Access Statement
Data sharing is not performed for this study.Keywords
- Computational complexity theory
- Entanglement
- Quantum energy teleportation
- Quantum interactive proofs
- Quantum Multi-Prover Interactive Proofs
- Quantum teleportation
- Quantum zero-knowledge proofs