Translating Uncontrolled Systems in Time

David Trillo; Benjamin Dive; Miguel Navascués

doi:10.22331/q-2020-12-15-374

Translating Uncontrolled Systems in Time

David Trillo, Benjamin Dive, and Miguel Navascués

Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, Vienna 1090, Austria

Published:	2020-12-15, volume 4, page 374
Eprint:	arXiv:1903.10568v3
Doi:	https://doi.org/10.22331/q-2020-12-15-374
Citation:	Quantum 4, 374 (2020).

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Abstract

We show that there exist non-relativistic scattering experiments which, if successful, freeze out, speed up or even reverse the free dynamics of any ensemble of quantum systems present in the scattering region. This ``time translation'' effect is universal, i.e., it is independent of the particular interaction between the scattering particles and the target systems, or the (possibly non-Hermitian) Hamiltonian governing the evolution of the latter. The protocols require careful preparation of the probes which are scattered, and success is heralded by projective measurements of these probes at the conclusion of the experiment. We fully characterize the possible time translations which we can effect on multiple target systems through a scattering protocol of fixed duration. The core results are: a) when the target is a single system, we can translate it backwards in time for an amount proportional to the experimental runtime; b) when $n$ targets are present in the scattering region, we can make a single system evolve $n$ times faster (backwards or forwards), at the cost of keeping the remaining $n-1$ systems stationary in time. For high $n$ our protocols therefore allow one to map, in short experimental time, a system to the state it would have reached with a very long unperturbed evolution in either positive or negative time.

Featured image: Identical target systems with unknown Hamiltonians can be translated in time by: preparing probes in specific states in a laboratory, letting them interact (with an unknown Hamiltonian) with the targets, and then post selecting the probes. This enables the effective evolution time of the target systems to be reduced, reversed, or traded between them.

► BibTeX data

@article{Trillo2020translating,
  doi = {10.22331/q-2020-12-15-374},
  url = {https://doi.org/10.22331/q-2020-12-15-374},
  title = {Translating {U}ncontrolled {S}ystems in {T}ime},
  author = {Trillo, David and Dive, Benjamin and Navascu{\'{e}}s, Miguel},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {4},
  pages = {374},
  month = dec,
  year = {2020}
}

► References

[1] Y. Aharonov, J. Anandan, S. Popescu, and L. Vaidman, Phys. Rev. Lett. 64, 2965 (1990).
https://doi.org/10.1103/PhysRevLett.64.2965

[2] I. S. Sardharwalla, T. S. Cubitt, A. W. Harrow, and N. Linden, (2016), arXiv:1602.07963.
arXiv:arXiv:1602.07963

[3] E. L. Hahn, Phys. Rev. 80, 580 (1950).
https://doi.org/10.1103/PhysRev.80.580

[4] W.-J. Kuo and D. A. Lidar, Phys. Rev. A 84, 042329 (2011).
https://doi.org/10.1103/PhysRevA.84.042329

[5] M. T. Quintino, Q. Dong, A. Shimbo, A. Soeda, and M. Murao, Phys. Rev. Lett. 123, 210502 (2019).
https://doi.org/10.1103/PhysRevLett.123.210502

[6] K. Gödel, Rev. Mod. Phys. 21, 447 (1949).
https://doi.org/10.1103/RevModPhys.21.447

[7] K. Thorne, Black Holes and Time Warps: Einstein's Outrageous Legacy, Commonwealth Fund Book Program (W.W. Norton, 1994).

[8] S. Krasnikov, Back-in-Time and Faster-than-Light Travel in General Relativity (Springer AG, 2018).
https://doi.org/10.1007/978-3-319-72754-7

[9] M. Navascués, Phys. Rev. X 8, 031008 (2018).
https://doi.org/10.1103/PhysRevX.8.031008

[10] Y. Atia and D. Aharonov, Nat. Comm. 8, 1572 (2017).
https://doi.org/10.1038/s41467-017-01637-7

[11] C. Arenz, D. I. Bondar, D. Burgarth, C. Cormick, and H. Rabitz, Quantum 4, 271 (2020).
https://doi.org/10.22331/q-2020-05-25-271

[12] G. Chiribella, G. M. D'Ariano, and P. Perinotti, Phys. Rev. Lett. 101, 180504 (2008).
https://doi.org/10.1103/PhysRevLett.101.180504

[13] S. C. Burd, R. Srinivas, J. J. Bollinger, A. C. Wilson, D. J. Wineland, D. Leibfried, D. H. Slichter, and D. T. C. Allcock, Science 364, 1163 (2019).
https://doi.org/10.1126/science.aaw2884

[14] E. Formanek, Journal of Algebra 23, 129 (1972).
https://doi.org/10.1016/0021-8693(72)90050-6

[15] D. Trillo, B. Dive, and M. Navascués, work in progress.

[16] J. Gleick, Time Travel: A History (Pantheon, 2016).

[17] A. Knapp, Representation theory of semisimple groups (Princeton University Press, 1986).
https://doi.org/10.1515/9781400883974

[18] R. Orús, Annals of Physics 349, 117–158 (2014).
https://doi.org/10.1016/j.aop.2014.06.013

[19] R. Werner, in Encyclopedia of Mathematical Physics, edited by J.-P. Françoise, G. L. Naber, and T. S. Tsun (Academic Press, Oxford, 2006) pp. 334 – 340.
https://doi.org/10.1016/B0-12-512666-2/00379-5

[20] M. Navascues and T. Vertesi, Quantum 2, 50 (2018).
https://doi.org/10.22331/q-2018-01-31-50

Cited by

[1] Felix Huber, "Positive maps and trace polynomials from the symmetric group", Journal of Mathematical Physics 62 2, 022203 (2021).

[2] Kean Chen, Nengkun Yu, and Zhicheng Zhang, Proceedings of the 58th Annual ACM Symposium on Theory of Computing 1376 (2026) ISBN:9798400725364.

[3] Teodor Strömberg, Peter Schiansky, Marco Túlio Quintino, Michael Antesberger, Lee A. Rozema, Iris Agresti, Časlav Brukner, and Philip Walther, "Experimental superposition of a quantum evolution with its time reverse", Physical Review Research 6 2, 023071 (2024).

[4] P. Schiansky, T. Strömberg, D. Trillo, V. Saggio, B. Dive, M. Navascués, and P. Walther, "Demonstration of universal time-reversal for qubit processes", Optica 10 2, 200 (2023).

[5] Tatsuki Odake, Satoshi Yoshida, and Mio Murao, "Analytical Lower Bound on Query Complexity for Transformations of Unknown Unitary Operations", Physical Review Letters 135 23, 230603 (2025).

[6] Chengkai Zhu, Yin Mo, Yu-Ao Chen, and Xin Wang, "Reversing Unknown Quantum Processes via Virtual Combs for Channels with Limited Information", Physical Review Letters 133 3, 030801 (2024).

[7] Satoshi Yoshida, Akihito Soeda, and Mio Murao, "Reversing Unknown Qubit-Unitary Operation, Deterministically and Exactly", Physical Review Letters 131 12, 120602 (2023).

[8] Satoshi Yoshida, Akihito Soeda, and Mio Murao, "Universal adjointation of isometry operations using conversion of quantum supermaps", Quantum 9, 1750 (2025).

[9] Marco Túlio Quintino and Daniel Ebler, "Deterministic transformations between unitary operations: Exponential advantage with adaptive quantum circuits and the power of indefinite causality", Quantum 6, 679 (2022).

[10] Claudio Procesi, Contemporary Mathematics 800, 239 (2024) ISBN:978-1-4704-7613-7.

[11] D. Trillo, B. Dive, and M. Navascués, "Universal Quantum Rewinding Protocol with an Arbitrarily High Probability of Success", Physical Review Letters 130 11, 110201 (2023).

[12] Daniel Ebler, Michał Horodecki, Marcin Marciniak, Tomasz Młynik, Marco Túlio Quintino, and Michał Studziński, "Optimal Universal Quantum Circuits for Unitary Complex Conjugation", IEEE Transactions on Information Theory 69 8, 5069 (2023).

[13] Marco Túlio Quintino, Qingxiuxiong Dong, Atsushi Shimbo, Akihito Soeda, and Mio Murao, "Reversing Unknown Quantum Transformations: Universal Quantum Circuit for Inverting General Unitary Operations", Physical Review Letters 123 21, 210502 (2019).

[14] Marco Túlio Quintino, Qingxiuxiong Dong, Atsushi Shimbo, Akihito Soeda, and Mio Murao, "Probabilistic exact universal quantum circuits for transforming unitary operations", Physical Review A 100 6, 062339 (2019).

[15] Zheng-Da Li, Xu-Fei Yin, Zizhu Wang, Li-Zheng Liu, Rui Zhang, Yu-Zhe Zhang, Xiao Jiang, Jun Zhang, Li Li, Nai-Le Liu, Xiao-Bo Zhu, Feihu Xu, Yu-Ao Chen, and Jian-Wei Pan, "Photonic realization of quantum resetting", Optica 7 7, 766 (2020).

[16] Hlér Kristjánsson, Tatsuki Odake, Satoshi Yoshida, Philip Taranto, Jessica Bavaresco, Marco Túlio Quintino, and Mio Murao, "Exponential separation in quantum query complexity of the quantum switch with respect to simulations with standard quantum circuits", arXiv:2409.18420, (2024).

[17] Claudio Procesi, "Tensor fundamental theorems of invariant theory", arXiv:2011.10820, (2020).

[18] Qin Feng, Tianfeng Feng, Yuling Tian, Maolin Luo, and Xiaoqi Zhou, "Experimentally undoing an unknown single-qubit unitary", Physical Review A 102 1, 012602 (2020).

[19] Claudio Procesi, "A note on the Weingarten function", arXiv:2008.11129, (2020).

[20] Claudio Procesi, "A construction of swap or switch polynomials", arXiv:2102.10657, (2021).

The above citations are from Crossref's cited-by service (last updated successfully 2026-07-15 14:52:05) and SAO/NASA ADS (last updated successfully 2026-07-15 14:52:06). The list may be incomplete as not all publishers provide suitable and complete citation data.

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