Multicopy quantum state teleportation with application to storage and retrieval of quantum programs
1Sorbonne Université, CNRS, LIP6, F-75005 Paris, France
2International Centre for Theory of Quantum Technologies, University of Gdańsk, Jana Bażyńskiego 1A, 80-309 Gdańsk, Poland
3Department of Physics, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
4Trans-scale Quantum Science Institute, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan
5Institute of Theoretical Physics and Astrophysics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, Wita Stwosza 57, 80-308 Gdańsk, Poland
| Published: | 2026-05-13, volume 10, page 2105 |
| Editor: | Jiangwei Shang |
| Eprint: | arXiv:2409.10393v2 |
| Doi: | https://doi.org/10.22331/q-2026-05-13-2105 |
| Citation: | Quantum 10, 2105 (2026). |
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Abstract
This work considers a teleportation task for Alice and Bob in a scenario where Bob cannot perform corrections. In particular, we analyse the task of $\textit{multicopy state teleportation}$, where Alice has $k$ identical copies of an arbitrary unknown $d$-dimensional qudit state $\vert\psi\rangle$ to teleport a single copy of $\vert\psi\rangle$ to Bob using a maximally entangled two-qudit state shared between Alice and Bob without Bob's correction. Alice may perform a joint measurement on her half of the entangled state and the $k$ copies of $\vert\psi\rangle$. We prove that the maximal probability of success for teleporting the exact state $\vert\psi\rangle$ to Bob is $p(d,k)=\frac{k}{d(k-1+d)}$ and present an explicit protocol to attain this performance. Then, by utilising $k$ copies of an arbitrary target state $\vert\psi\rangle$, we show how the multicopy state teleportation protocol can be employed to enhance the success probability of storage and retrieval of quantum programs, which aims to universally retrieve the action of an arbitrary quantum channel that is stored in a state. Our proofs make use of group representation theory methods, which may find applications beyond the problems addressed in this work.
Featured image: Pictorial illustration of the teleportation scenario considered in this work. Alice and Bob share one pair of a maximally entangled qudit state $|\phi_d^+\rangle$ and Alice has $k$ copies of an arbitrary qudit $|{\psi}\rangle$. In order to teleport the state $|{\psi}\rangle$ to Bob, Alice performs a joint measurement $M$ on all quantum states on her side. We consider the case where Bob probabilistically receives a single copy of $|{\psi}\rangle$ without any corrections, hence Alice's measurement outcome may be assumed to be dichotomic, where one measurement outcome corresponds to success, where Bob receives the exact state $|\psi\rangle$ with probability $p(d,k)$, and a failure case where Bob receives a quantum state which is not $|\psi\rangle$.
Popular summary
Quantum teleportation allows two parties, referred to as Alice and Bob, to transmit a quantum state without having access to a quantum channel, but by consuming quantum entanglement. In standard quantum teleportation, Bob must perform a "correction step" based on classical information sent by Alice to recover the exact quantum state. For some applications, this correction step does not pose any issue, Bob may just perform a local correction that will depend on Alice’s classical message. However, this correction step causes problems for certain advanced tasks. In particular, it prevents us from using standard teleportation to store a "quantum program" (a quantum operation) and later retrieve it to apply to a new state. While alternative methods like "Port-Based Teleportation" can work without corrections, they require access to a large entangled resource.
In our paper, we explore a new scenario: what happens if Alice and Bob still only share a single pair of entangled particles, but Alice has access to multiple identical copies (let's call the number of copies k) of the unknown quantum state she wants to send? We discovered that Alice can process all k copies together by performing a joint measurement. By doing this, she can improve the success probability of successfully teleport a single, perfect copy of the state to Bob without him needing to perform any correction at all.
In a nutshell, Alice performs a joint measurement on her side and sends a single bit of information to Bob—essentially a simple "success" or "failure" message. When the protocol succeeds, Bob holds the exact intended quantum state. We mathematically proved that the highest possible probability of success is exactly $p(d,k)=k/(d(k−1+d))$, where d is the dimension of the quantum system to be teleported. This formula shows a clear advantage: the more copies Alice starts with, the higher the chance of a perfect, correction-free teleportation.
This multicopy teleportation protocol can be directly applied to improve the storage and retrieval of quantum programs. When a user wants to retrieve a stored quantum operation and apply it to a target state, having multiple copies of that target state enhances the probability of successfully retrieving the program. From a broader perspective, the methods and approach of this work may find applications in other tasks where one may have access to multiple copies of a target state.
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[2] Vanessa Brzić, Satoshi Yoshida, Mio Murao, and Marco Túlio Quintino, "Higher-order quantum computing with known input states", arXiv:2510.20530, (2025).
[3] Oscar Scholin and Theresa W. Lynn, "Exchange-symmetrized qudit Bell bases and Bell-state distinguishability", Physical Review Research 7 3, 033124 (2025).
[4] Juntai Zhou, Stefano Chessa, Eric Chitambar, and Felix Leditzky, "On the distinguishability of geometrically uniform quantum states", Journal of Physics A Mathematical General 58 41, 415303 (2025).
[5] Piotr Kopszak, Dmitry Grinko, Adam Burchardt, Maris Ozols, Michał Studziński, and Marek Mozrzymas, "Entanglement recycling in two-step port-based teleportation", arXiv:2504.00710, (2025).
[6] Chloe Kim, Eric Chitambar, and Felix Leditzky, "A resource theory of asynchronous quantum information processing", arXiv:2504.12945, (2025).
[7] Piotr Kopszak, Dmitry Grinko, Adam Burchardt, Maris Ozols, Michał Studziński, and Marek Mozrzymas, "Entanglement Recycling in Two-Step Port-Based Teleportation", IEEE Transactions on Information Theory 72 4, 2343 (2026).
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