Multicopy quantum state teleportation with application to storage and retrieval of quantum programs
Summarize this article with:
AbstractThis 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 summaryTeleporting Quantum States Without Corrections: The Power of Multiple Copies 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.► BibTeX data@article{Grosshans2026multicopyquantum, doi = {10.22331/q-2026-05-13-2105}, url = {https://doi.org/10.22331/q-2026-05-13-2105}, title = {Multicopy quantum state teleportation with application to storage and retrieval of quantum programs}, author = {Grosshans, Fr{\'{e}}d{\'{e}}ric and Horodecki, Micha{\l{}} and Murao, Mio and M{\l{}}ynik, Tomasz and Quintino, Marco T{\'{u}}lio and Studzi{\'{n}}ski, Micha{\l{}} and Yoshida, Satoshi}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2105}, month = may, year = {2026} }► References [1] C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Teleporting an unknown quantum state via dual classical and einstein-podolsky-rosen channels, Phys. Rev. Lett. 70, 1895–1899 (1993). https://doi.org/10.1103/PhysRevLett.70.1895 [2] H.-J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, Quantum repeaters: The role of imperfect local operations in quantum communication, Phys. Rev. Lett. 81, 5932–5935 (1998), arXiv:quant-ph/9803056 [quant-ph]. https://doi.org/10.1103/PhysRevLett.81.5932 arXiv:quant-ph/9803056 [3] D. Gottesman and I. L. Chuang, Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations, Nature 402, 390–393 (1999a), arXiv:quant-ph/9908010 [quant-ph]. https://doi.org/10.1038/46503 arXiv:quant-ph/9908010 [4] C. H. Bennett, D. P. Divincenzo, J. A. Smolin, and W. K. Wootters, Mixed-state entanglement and quantum error correction, Phys. Rev. A 54, 3824–3851 (1996), arXiv:quant-ph/9604024 [quant-ph]. https://doi.org/10.1103/PhysRevA.54.3824 arXiv:quant-ph/9604024 [5] M. A. Nielsen and I. L. Chuang, Programmable Quantum Gate Arrays, Phys. Rev. Lett. 79, 321–324 (1997), arXiv:quant-ph/9703032 [quant-ph]. https://doi.org/10.1103/PhysRevLett.79.321 arXiv:quant-ph/9703032 [6] E. Chitambar and F. Leditzky, On the duality of teleportation and dense coding, IEEE Transactions on Information Theory 70, 3529–3537 (2024), arXiv:2302.14798 [quant-ph]. https://doi.org/10.1109/TIT.2023.3331821 arXiv:2302.14798 [7] M. Murao, D. Jonathan, M. B. Plenio, and V. Vedral, Quantum telecloning and multiparticle entanglement, Phys. Rev. A 59, 156–161 (1999), arXiv:quant-ph/9806082 [quant-ph]. https://doi.org/10.1103/PhysRevA.59.156 arXiv:quant-ph/9806082 [8] R. Jozsa, An introduction to measurement based quantum computation, arXiv e-prints (2005), quant-ph/0508124 [quant-ph]. arXiv:quant-ph/0508124 [9] D. Gottesman and I. L. Chuang, Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations, Nature 402, 390–393 (1999b), quant-ph/9908010. https://doi.org/10.1038/46503 arXiv:quant-ph/9908010 [10] M. Nielsen and I. Chuang, Quantum Computation and Quantum Information, Cambridge Series on Information and the Natural Sciences (Cambridge University Press, 2000). [11] M. M. Wilde, From Classical to Quantum Shannon Theory, arXiv e-prints (2011), arXiv:1106.1445 [quant-ph]. https://doi.org/10.1017/9781316809976 arXiv:1106.1445 [12] S. Ishizaka and T. Hiroshima, Asymptotic Teleportation Scheme as a Universal Programmable Quantum Processor, Phys. Rev. Lett. 101, 240501 (2008), arXiv:0807.4568 [quant-ph]. https://doi.org/10.1103/PhysRevLett.101.240501 arXiv:0807.4568 [13] S. Ishizaka and T. Hiroshima, Quantum teleportation scheme by selecting one of multiple output ports, Phys. Rev. A 79, 042306 (2009), arXiv:0901.2975 [quant-ph]. https://doi.org/10.1103/PhysRevA.79.042306 arXiv:0901.2975 [14] M. Studziński, S. Strelchuk, M. Mozrzymas, and M. Horodecki, Port-based teleportation in arbitrary dimension, Scientific Reports 7, 10871 (2017), arXiv:1612.09260 [quant-ph]. https://doi.org/10.1038/s41598-017-10051-4 arXiv:1612.09260 [15] M. Mozrzymas, M. Studziński, S. Strelchuk, and M. Horodecki, Optimal port-based teleportation, New Journal of Physics 20, 053006 (2018), arXiv:1707.08456 [quant-ph]. https://doi.org/10.1088/1367-2630/aab8e7 arXiv:1707.08456 [16] S. Strelchuk, M. Horodecki, and J. Oppenheim, Generalized Teleportation and Entanglement Recycling, Phys. Rev. Lett. 110, 010505 (2013), arXiv:1209.2683 [quant-ph]. https://doi.org/10.1103/PhysRevLett.110.010505 arXiv:1209.2683 [17] M. Studziński, M. Mozrzymas, P. Kopszak, and M. Horodecki, Efficient multi port-based teleportation schemes, IEEE Transactions on Information Theory 68, 7892–7912 (2022). https://doi.org/10.1109/TIT.2022.3187852 [18] A. Bisio, G. Chiribella, G. M. D'Ariano, S. Facchini, and P. Perinotti, Optimal quantum learning of a unitary transformation, Phys. Rev. A 81, 032324 (2010), arXiv:0903.0543 [quant-ph]. https://doi.org/10.1103/PhysRevA.81.032324 arXiv:0903.0543 [19] M. Sedlák, A. Bisio, and M. Ziman, Optimal Probabilistic Storage and Retrieval of Unitary Channels, Phys. Rev. Lett. 122, 170502 (2019), arXiv:1809.04552 [quant-ph]. https://doi.org/10.1103/PhysRevLett.122.170502 arXiv:1809.04552 [20] S. Yoshida, Y. Koizumi, M. Studziński, M. T. Quintino, and M. Murao, One-to-one Correspondence between Deterministic Port-Based Teleportation and Unitary Estimation, IEEE Transactions on Information Theory 72, 2358–2377 (2026), arXiv:2408.11902 [quant-ph]. https://doi.org/10.1109/tit.2026.3658543 arXiv:2408.11902 [21] M. T. Quintino, Q. Dong, A. Shimbo, A. Soeda, and M. Murao, Reversing Unknown Quantum Transformations: Universal Quantum Circuit for Inverting General Unitary Operations, Phys. Rev. Lett., 123, 210502 (2019a), arXiv:1810.06944 [quant-ph]. https://doi.org/10.1103/PhysRevLett.123.210502 arXiv:1810.06944 [22] M. T. Quintino and D. Ebler, Deterministic transformations between unitary operations: Exponential advantage with adaptive quantum circuits and the power of indefinite causality, Quantum 6, 679 (2022), arXiv:2109.08202 [quant-ph]. https://doi.org/10.22331/q-2022-03-31-679 arXiv:2109.08202 [23] M. T. Quintino, Q. Dong, A. Shimbo, A. Soeda, and M. Murao, Probabilistic exact universal quantum circuits for transforming unitary operations, Phys. Rev. A 100, 062339 (2019b), arXiv:1909.01366 [quant-ph]. https://doi.org/10.1103/PhysRevA.100.062339 arXiv:1909.01366 [24] H. Buhrman, L. Czekaj, A. Grudka, M. Horodecki, P. Horodecki, M. Markiewicz, F. Speelman, and S. Strelchuk, Quantum communication complexity advantage implies violation of a Bell inequality, Proceedings of the National Academy of Science 113, 3191–3196 (2016), arXiv:1502.01058 [quant-ph]. https://doi.org/10.1073/pnas.1507647113 arXiv:1502.01058 [25] S. Beigi and R. König, Simplified instantaneous non-local quantum computation with applications to position-based cryptography, New Journal of Physics 13, 093036 (2011), arXiv:1101.1065 [quant-ph]. https://doi.org/10.1088/1367-2630/13/9/093036 arXiv:1101.1065 [26] S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, J. L. Pereira, M. Razavi, J. Shamsul Shaari, M. Tomamichel, V. C. Usenko, G. Vallone, P. Villoresi, and P. Wallden, Advances in quantum cryptography, Advances in Optics and Photonics 12, 1012 (2020), arXiv:1906.01645 [quant-ph]. https://doi.org/10.1364/AOP.361502 arXiv:1906.01645 [27] B. Schumacher, Quantum coding, Phys. Rev. A 51, 2738–2747 (1995). https://doi.org/10.1103/PhysRevA.51.2738 [28] Y. Yang, G. Chiribella, and D. Ebler, Efficient Quantum Compression for Ensembles of Identically Prepared Mixed States, Phys. Rev. Lett. 116, 080501 (2016), arXiv:1506.03542 [quant-ph]. https://doi.org/10.1103/PhysRevLett.116.080501 arXiv:1506.03542 [29] R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Reviews of Modern Physics 81, 865–942 (2009), quant-ph/0702225. https://doi.org/10.1103/RevModPhys.81.865 arXiv:quant-ph/0702225 [30] D. Boschi, S. Branca, F. de Martini, L. Hardy, and S. Popescu, Experimental Realization of Teleporting an Unknown Pure Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels, Phys. Rev. Lett. 80, 1121–1125 (1998), arXiv:quant-ph/9710013 [quant-ph]. https://doi.org/10.1103/PhysRevLett.80.1121 arXiv:quant-ph/9710013 [31] J. Watrous, The Theory of Quantum Information (Cambridge University Press, 2018). [32] A. W. Harrow, The Church of the Symmetric Subspace, arXiv e-prints (2013), arXiv:1308.6595 [quant-ph]. arXiv:1308.6595 [33] C. H. Bennett, D. P. Divincenzo, P. W. Shor, J. A. Smolin, B. M. Terhal, and W. K. Wootters, Remote State Preparation, Phys. Rev. Lett. 87, 077902 (2001), arXiv:quant-ph/0006044 [quant-ph]. https://doi.org/10.1103/PhysRevLett.87.077902 arXiv:quant-ph/0006044 [34] D. Genkina, G. Chiribella, and L. Hardy, Optimal probabilistic simulation of quantum channels from the future to the past, Phys. Rev. A 85, 022330 (2012), arXiv:1112.1469. https://doi.org/10.1103/PhysRevA.85.022330 arXiv:1112.1469 [35] G. Muguruza and F. Speelman, Port-Based State Preparation and Applications, arXiv e-prints (2024), arXiv:2402.18356 [quant-ph]. https://doi.org/10.22331/q-2024-12-18-1573 arXiv:2402.18356 [36] V. Brzić, S. Yoshida, M. Murao, and M. T. Quintino, Higher-order quantum computing with known input states, arXiv e-prints (2025), arXiv:2510.20530 [quant-ph]. arXiv:2510.20530 [37] A. M. Vershik, Hooks formula and related identities, J. Soviet Math., 59 (1992), 1029–1040 59:5, 1029–1040 (1992). https://doi.org/10.1007/BF01480684 [38] T. Ceccherini-Silberstein, F. Scarabotti, and F. Tolli, Representation Theory of the Symmetric Groups: The Okounkov-Vershik Approach, Character Formulas, and Partition Algebras, Vol. 121 (Cambridge University Press, 2010). https://doi.org/10.1017/CBO9781139192361 [39] W. Fulton, Young Tableaux: With Applications to Representation Theory and Geometry, 35 (Cambridge University Press, 1997). https://doi.org/10.1017/CBO9780511626241 [40] M. Mozrzymas, M. Studziński, and M. Horodecki, A simplified formalism of the algebra of partially transposed permutation operators with applications, Journal of Physics A: Mathematical and Theoretical 51, 125202 (2018). https://doi.org/10.1088/1751-8121/aaad15 [41] J. Fei, S. Timmerman, and P. Hayden, Efficient quantum algorithm for port-based teleportation (2023), arXiv:2310.01637 [quant-ph]. arXiv:2310.01637 [42] D. Grinko, A. Burchardt, and M. Ozols, Gelfand-Tsetlin basis for partially transposed permutations, with applications to quantum information, arXiv e-prints (2023a), arXiv:2310.02252 [quant-ph]. arXiv:2310.02252 [43] D. Grinko, A. Burchardt, and M. Ozols, Efficient quantum circuits for port-based teleportation, arXiv e-prints (2023b), arXiv:2312.03188 [quant-ph]. arXiv:2312.03188 [44] D. Grinko and M. Ozols, Linear programming with unitary-equivariant constraints, arXiv e-prints (2022), arXiv:2207.05713 [quant-ph]. https://doi.org/10.1007/s00220-024-05108-1 arXiv:2207.05713 [45] M. Mozrzymas, M. Horodecki, and M. Studziński, Structure and properties of the algebra of partially transposed permutation operators, Journal of Mathematical Physics 55, 032202 (2014). https://doi.org/10.1063/1.4869027 [46] Y. Yang and M. Hayashi, Representation matching for remote quantum computing, PRX Quantum 2, 020327 (2021). https://doi.org/10.1103/PRXQuantum.2.020327Cited byCould not fetch Crossref cited-by data during last attempt 2026-05-13 07:02:48: Could not fetch cited-by data for 10.22331/q-2026-05-13-2105 from Crossref. This is normal if the DOI was registered recently. Could not fetch ADS cited-by data during last attempt 2026-05-13 07:02:48: No response from ADS or unable to decode the received json data when getting the list of citing works.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. AbstractThis 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 summaryTeleporting Quantum States Without Corrections: The Power of Multiple Copies 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.► BibTeX data@article{Grosshans2026multicopyquantum, doi = {10.22331/q-2026-05-13-2105}, url = {https://doi.org/10.22331/q-2026-05-13-2105}, title = {Multicopy quantum state teleportation with application to storage and retrieval of quantum programs}, author = {Grosshans, Fr{\'{e}}d{\'{e}}ric and Horodecki, Micha{\l{}} and Murao, Mio and M{\l{}}ynik, Tomasz and Quintino, Marco T{\'{u}}lio and Studzi{\'{n}}ski, Micha{\l{}} and Yoshida, Satoshi}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2105}, month = may, year = {2026} }► References [1] C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Teleporting an unknown quantum state via dual classical and einstein-podolsky-rosen channels, Phys. Rev. Lett. 70, 1895–1899 (1993). https://doi.org/10.1103/PhysRevLett.70.1895 [2] H.-J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, Quantum repeaters: The role of imperfect local operations in quantum communication, Phys. Rev. Lett. 81, 5932–5935 (1998), arXiv:quant-ph/9803056 [quant-ph]. https://doi.org/10.1103/PhysRevLett.81.5932 arXiv:quant-ph/9803056 [3] D. Gottesman and I. L. Chuang, Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations, Nature 402, 390–393 (1999a), arXiv:quant-ph/9908010 [quant-ph]. https://doi.org/10.1038/46503 arXiv:quant-ph/9908010 [4] C. H. Bennett, D. P. Divincenzo, J. A. Smolin, and W. K. Wootters, Mixed-state entanglement and quantum error correction, Phys. Rev. A 54, 3824–3851 (1996), arXiv:quant-ph/9604024 [quant-ph]. https://doi.org/10.1103/PhysRevA.54.3824 arXiv:quant-ph/9604024 [5] M. A. Nielsen and I. L. Chuang, Programmable Quantum Gate Arrays, Phys. Rev. Lett. 79, 321–324 (1997), arXiv:quant-ph/9703032 [quant-ph]. https://doi.org/10.1103/PhysRevLett.79.321 arXiv:quant-ph/9703032 [6] E. Chitambar and F. Leditzky, On the duality of teleportation and dense coding, IEEE Transactions on Information Theory 70, 3529–3537 (2024), arXiv:2302.14798 [quant-ph]. https://doi.org/10.1109/TIT.2023.3331821 arXiv:2302.14798 [7] M. Murao, D. Jonathan, M. B. Plenio, and V. Vedral, Quantum telecloning and multiparticle entanglement, Phys. Rev. A 59, 156–161 (1999), arXiv:quant-ph/9806082 [quant-ph]. https://doi.org/10.1103/PhysRevA.59.156 arXiv:quant-ph/9806082 [8] R. Jozsa, An introduction to measurement based quantum computation, arXiv e-prints (2005), quant-ph/0508124 [quant-ph]. arXiv:quant-ph/0508124 [9] D. Gottesman and I. L. Chuang, Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations, Nature 402, 390–393 (1999b), quant-ph/9908010. https://doi.org/10.1038/46503 arXiv:quant-ph/9908010 [10] M. Nielsen and I. Chuang, Quantum Computation and Quantum Information, Cambridge Series on Information and the Natural Sciences (Cambridge University Press, 2000). [11] M. M. Wilde, From Classical to Quantum Shannon Theory, arXiv e-prints (2011), arXiv:1106.1445 [quant-ph]. https://doi.org/10.1017/9781316809976 arXiv:1106.1445 [12] S. Ishizaka and T. Hiroshima, Asymptotic Teleportation Scheme as a Universal Programmable Quantum Processor, Phys. Rev. Lett. 101, 240501 (2008), arXiv:0807.4568 [quant-ph]. https://doi.org/10.1103/PhysRevLett.101.240501 arXiv:0807.4568 [13] S. Ishizaka and T. Hiroshima, Quantum teleportation scheme by selecting one of multiple output ports, Phys. Rev. A 79, 042306 (2009), arXiv:0901.2975 [quant-ph]. https://doi.org/10.1103/PhysRevA.79.042306 arXiv:0901.2975 [14] M. Studziński, S. Strelchuk, M. Mozrzymas, and M. Horodecki, Port-based teleportation in arbitrary dimension, Scientific Reports 7, 10871 (2017), arXiv:1612.09260 [quant-ph]. https://doi.org/10.1038/s41598-017-10051-4 arXiv:1612.09260 [15] M. Mozrzymas, M. Studziński, S. Strelchuk, and M. Horodecki, Optimal port-based teleportation, New Journal of Physics 20, 053006 (2018), arXiv:1707.08456 [quant-ph]. https://doi.org/10.1088/1367-2630/aab8e7 arXiv:1707.08456 [16] S. Strelchuk, M. Horodecki, and J. Oppenheim, Generalized Teleportation and Entanglement Recycling, Phys. Rev. Lett. 110, 010505 (2013), arXiv:1209.2683 [quant-ph]. https://doi.org/10.1103/PhysRevLett.110.010505 arXiv:1209.2683 [17] M. Studziński, M. Mozrzymas, P. Kopszak, and M. Horodecki, Efficient multi port-based teleportation schemes, IEEE Transactions on Information Theory 68, 7892–7912 (2022). https://doi.org/10.1109/TIT.2022.3187852 [18] A. Bisio, G. Chiribella, G. M. D'Ariano, S. Facchini, and P. Perinotti, Optimal quantum learning of a unitary transformation, Phys. Rev. A 81, 032324 (2010), arXiv:0903.0543 [quant-ph]. https://doi.org/10.1103/PhysRevA.81.032324 arXiv:0903.0543 [19] M. Sedlák, A. Bisio, and M. Ziman, Optimal Probabilistic Storage and Retrieval of Unitary Channels, Phys. Rev. Lett. 122, 170502 (2019), arXiv:1809.04552 [quant-ph]. https://doi.org/10.1103/PhysRevLett.122.170502 arXiv:1809.04552 [20] S. Yoshida, Y. Koizumi, M. Studziński, M. T. Quintino, and M. Murao, One-to-one Correspondence between Deterministic Port-Based Teleportation and Unitary Estimation, IEEE Transactions on Information Theory 72, 2358–2377 (2026), arXiv:2408.11902 [quant-ph]. https://doi.org/10.1109/tit.2026.3658543 arXiv:2408.11902 [21] M. T. Quintino, Q. Dong, A. Shimbo, A. Soeda, and M. Murao, Reversing Unknown Quantum Transformations: Universal Quantum Circuit for Inverting General Unitary Operations, Phys. Rev. Lett., 123, 210502 (2019a), arXiv:1810.06944 [quant-ph]. https://doi.org/10.1103/PhysRevLett.123.210502 arXiv:1810.06944 [22] M. T. Quintino and D. Ebler, Deterministic transformations between unitary operations: Exponential advantage with adaptive quantum circuits and the power of indefinite causality, Quantum 6, 679 (2022), arXiv:2109.08202 [quant-ph]. https://doi.org/10.22331/q-2022-03-31-679 arXiv:2109.08202 [23] M. T. Quintino, Q. Dong, A. Shimbo, A. Soeda, and M. Murao, Probabilistic exact universal quantum circuits for transforming unitary operations, Phys. Rev. A 100, 062339 (2019b), arXiv:1909.01366 [quant-ph]. https://doi.org/10.1103/PhysRevA.100.062339 arXiv:1909.01366 [24] H. Buhrman, L. Czekaj, A. Grudka, M. Horodecki, P. Horodecki, M. Markiewicz, F. Speelman, and S. Strelchuk, Quantum communication complexity advantage implies violation of a Bell inequality, Proceedings of the National Academy of Science 113, 3191–3196 (2016), arXiv:1502.01058 [quant-ph]. https://doi.org/10.1073/pnas.1507647113 arXiv:1502.01058 [25] S. Beigi and R. König, Simplified instantaneous non-local quantum computation with applications to position-based cryptography, New Journal of Physics 13, 093036 (2011), arXiv:1101.1065 [quant-ph]. https://doi.org/10.1088/1367-2630/13/9/093036 arXiv:1101.1065 [26] S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, J. L. Pereira, M. Razavi, J. Shamsul Shaari, M. Tomamichel, V. C. Usenko, G. Vallone, P. Villoresi, and P. Wallden, Advances in quantum cryptography, Advances in Optics and Photonics 12, 1012 (2020), arXiv:1906.01645 [quant-ph]. https://doi.org/10.1364/AOP.361502 arXiv:1906.01645 [27] B. Schumacher, Quantum coding, Phys. Rev. A 51, 2738–2747 (1995). https://doi.org/10.1103/PhysRevA.51.2738 [28] Y. Yang, G. Chiribella, and D. Ebler, Efficient Quantum Compression for Ensembles of Identically Prepared Mixed States, Phys. Rev. Lett. 116, 080501 (2016), arXiv:1506.03542 [quant-ph]. https://doi.org/10.1103/PhysRevLett.116.080501 arXiv:1506.03542 [29] R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Reviews of Modern Physics 81, 865–942 (2009), quant-ph/0702225. https://doi.org/10.1103/RevModPhys.81.865 arXiv:quant-ph/0702225 [30] D. Boschi, S. Branca, F. de Martini, L. Hardy, and S. Popescu, Experimental Realization of Teleporting an Unknown Pure Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels, Phys. Rev. Lett. 80, 1121–1125 (1998), arXiv:quant-ph/9710013 [quant-ph]. https://doi.org/10.1103/PhysRevLett.80.1121 arXiv:quant-ph/9710013 [31] J. Watrous, The Theory of Quantum Information (Cambridge University Press, 2018). [32] A. W. Harrow, The Church of the Symmetric Subspace, arXiv e-prints (2013), arXiv:1308.6595 [quant-ph]. arXiv:1308.6595 [33] C. H. Bennett, D. P. Divincenzo, P. W. Shor, J. A. Smolin, B. M. Terhal, and W. K. Wootters, Remote State Preparation, Phys. Rev. Lett. 87, 077902 (2001), arXiv:quant-ph/0006044 [quant-ph]. https://doi.org/10.1103/PhysRevLett.87.077902 arXiv:quant-ph/0006044 [34] D. Genkina, G. Chiribella, and L. Hardy, Optimal probabilistic simulation of quantum channels from the future to the past, Phys. Rev. A 85, 022330 (2012), arXiv:1112.1469. https://doi.org/10.1103/PhysRevA.85.022330 arXiv:1112.1469 [35] G. Muguruza and F. Speelman, Port-Based State Preparation and Applications, arXiv e-prints (2024), arXiv:2402.18356 [quant-ph]. https://doi.org/10.22331/q-2024-12-18-1573 arXiv:2402.18356 [36] V. Brzić, S. Yoshida, M. Murao, and M. T. Quintino, Higher-order quantum computing with known input states, arXiv e-prints (2025), arXiv:2510.20530 [quant-ph]. arXiv:2510.20530 [37] A. M. Vershik, Hooks formula and related identities, J. Soviet Math., 59 (1992), 1029–1040 59:5, 1029–1040 (1992). https://doi.org/10.1007/BF01480684 [38] T. Ceccherini-Silberstein, F. Scarabotti, and F. Tolli, Representation Theory of the Symmetric Groups: The Okounkov-Vershik Approach, Character Formulas, and Partition Algebras, Vol. 121 (Cambridge University Press, 2010). https://doi.org/10.1017/CBO9781139192361 [39] W. Fulton, Young Tableaux: With Applications to Representation Theory and Geometry, 35 (Cambridge University Press, 1997). https://doi.org/10.1017/CBO9780511626241 [40] M. Mozrzymas, M. Studziński, and M. Horodecki, A simplified formalism of the algebra of partially transposed permutation operators with applications, Journal of Physics A: Mathematical and Theoretical 51, 125202 (2018). https://doi.org/10.1088/1751-8121/aaad15 [41] J. Fei, S. Timmerman, and P. Hayden, Efficient quantum algorithm for port-based teleportation (2023), arXiv:2310.01637 [quant-ph]. arXiv:2310.01637 [42] D. Grinko, A. Burchardt, and M. Ozols, Gelfand-Tsetlin basis for partially transposed permutations, with applications to quantum information, arXiv e-prints (2023a), arXiv:2310.02252 [quant-ph]. arXiv:2310.02252 [43] D. Grinko, A. Burchardt, and M. Ozols, Efficient quantum circuits for port-based teleportation, arXiv e-prints (2023b), arXiv:2312.03188 [quant-ph]. arXiv:2312.03188 [44] D. Grinko and M. Ozols, Linear programming with unitary-equivariant constraints, arXiv e-prints (2022), arXiv:2207.05713 [quant-ph]. https://doi.org/10.1007/s00220-024-05108-1 arXiv:2207.05713 [45] M. Mozrzymas, M. Horodecki, and M. Studziński, Structure and properties of the algebra of partially transposed permutation operators, Journal of Mathematical Physics 55, 032202 (2014). https://doi.org/10.1063/1.4869027 [46] Y. Yang and M. Hayashi, Representation matching for remote quantum computing, PRX Quantum 2, 020327 (2021). https://doi.org/10.1103/PRXQuantum.2.020327Cited byCould not fetch Crossref cited-by data during last attempt 2026-05-13 07:02:48: Could not fetch cited-by data for 10.22331/q-2026-05-13-2105 from Crossref. This is normal if the DOI was registered recently. Could not fetch ADS cited-by data during last attempt 2026-05-13 07:02:48: No response from ADS or unable to decode the received json data when getting the list of citing works.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.