analiza aiqbench
This research addresses a fundamental tension in quantum formulations by introducing QPhys, a process theory that integrates classical systems and explores time symmetry through retrocausality constraints. The authors propose novel extensions to causality concepts, including a toy model linking causal/retrocausal systems to particles and anti-particles, while also defining a supertheory that relaxes standard constraints to avoid unphysical predictions. These theoretical advancements deepen our understanding of the foundational structure of quantum mechanics rather than offering immediate product applications.
Time symmetry in quantum theories and beyond
Quantum 10, 2221 (2026). https://doi.org/10.22331/q-2026-09-30-2221 There exists a stark tension among different formulations of quantum theory as some are inherently time-symmetric while others are time-asymmetric. This tension is crisply captured when considering physical theories as theories of processes. We present the process theory of quantum physics, QPhys, which treats classical systems as internal to quantum theory. We provide three ways to incorporate time symmetry in QPhys. The first restricts the process theory of QPhys to one that satisfies an additional retrocausality constraint. The second is a novel approach, which extends the notions of causality and retrocausality to apply to systems along with processes. Utilizing this approach, we create a toy model for particle physics , where the causal and retrocausal systems correspond to particles and anti-particles respectively. The third approach extends QPhys to a supertheory that satisfies neither a causality nor a retrocausality constraint. To avoid unphysical predictions we modify either its composition rule or its processes.
There exists a stark tension among different formulations of quantum theory as some are inherently time-symmetric while others are time-asymmetric. This tension is crisply captured when considering physical theories as theories of processes. We present the process theory of quantum physics, QPhys, which treats classical systems as internal to quantum theory. We provide three ways to incorporate time symmetry in QPhys. The first restricts the process theory of QPhys to one that satisfies an additional retrocausality constraint. The second is a novel approach, which extends the notions of causality and retrocausality to apply to systems along with processes. Utilizing this approach, we create a toy model for particle physics , where the causal and retrocausal systems correspond to particles and anti-particles respectively. The third approach extends QPhys to a supertheory that satisfies neither a causality nor a retrocausality constraint. To avoid unphysical predictions we modify either its composition rule or its processes.
[1] Eugene Paul Wigner. Gruppentheorie und ihre Anwendung auf die Quantenmechanik der Atomspektren. Springer, 1931. 10.1007/978-3-663-02555-9. https://doi.org/10.1007/978-3-663-02555-9
[2] Gerhart Lüders. On the equivalence of invariance under time reversal and under particle-antiparticle conjugation for relativistic field theories. Dan. Mat. Fys. Medd., 28: 1–17, 1954.
[3] John Stewart Bell. Time reversal in field theory. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 231 (1187): 479–495, 1955. 10.1142/9789812795854_0011. https://doi.org/10.1142/9789812795854_0011
[4] Yakir Aharonov, Peter G Bergmann, and Joel L Lebowitz. Time symmetry in the quantum process of measurement. Physical Review, 134 (6B): B1410, 1964. 10.1103/physrev.134.b1410. https://doi.org/10.1103/physrev.134.b1410
[5] Satosi Watanabe. Symmetry of physical laws. part iii. prediction and retrodiction. Reviews of Modern Physics, 27 (2): 179, 1955. 10.1103/revmodphys.27.179. https://doi.org/10.1103/revmodphys.27.179
[6] Andrew Thomas Holster. The criterion for time symmetry of probabilistic theories and the reversibility of quantum mechanics. New Journal of Physics, 5 (1): 130, 2003. 10.1088/1367-2630/5/1/130. https://doi.org/10.1088/1367-2630/5/1/130
[7] G. Chiribella, G. M. D'Ariano, and P. Perinotti. Probabilistic theories with purification. Physical Review A, 81 (6): 062348, 2010. 10.1103/physreva.81.062348. https://doi.org/10.1103/physreva.81.062348
[8] B. Coecke. Terminality implies non-signalling. arXiv:1405.3681, 2014. arXiv:1405.3681
[9] Bob Coecke, Stefano Gogioso, and John H Selby. The time-reverse of any causal theory is eternal noise. arXiv preprint arXiv:1711.05511, 2017. 10.48550/arXiv.1711.05511. https://doi.org/10.48550/arXiv.1711.05511 arXiv:1711.05511
[10] Ognyan Oreshkov and Nicolas J Cerf. Operational formulation of time reversal in quantum theory. Nature Physics, 11 (10): 853–858, 2015. 10.1038/nphys3414. https://doi.org/10.1038/nphys3414
[11] L. Hardy. Towards quantum gravity: a framework for probabilistic theories with non-fixed causal structure. J. Phys. A, 40 (12): 3081, 2007. 10.1088/1751-8113/40/12/s12. https://doi.org/10.1088/1751-8113/40/12/s12
[12] Matthew S Leifer and Robert W Spekkens. Towards a formulation of quantum theory as a causally neutral theory of bayesian inference. Physical Review A, 88 (5): 052130, 2013. 10.1103/physreva.88.052130. https://doi.org/10.1103/physreva.88.052130
[13] Robert Oeckl. General boundary quantum field theory: Foundations and probability interpretation. Advances in Theoretical and Mathematical Physics, 12 (2): 319–352, 2008. 10.4310/atmp.2008.v12.n2.a3. https://doi.org/10.4310/atmp.2008.v12.n2.a3
[14] Robert Oeckl. A local and operational framework for the foundations of physics. arXiv preprint arXiv:1610.09052, 2016. 10.4310/atmp.2019.v23.n2.a4. https://doi.org/10.4310/atmp.2019.v23.n2.a4 arXiv:1610.09052
[15] Ognyan Oreshkov and Nicolas J Cerf. Operational quantum theory without predefined time. New Journal of Physics, 18 (7): 073037, 2016. 10.1088/1367-2630/18/7/073037. https://doi.org/10.1088/1367-2630/18/7/073037
[16] Yakir Aharonov, Sandu Popescu, Jeff Tollaksen, and Lev Vaidman. Multiple-time states and multiple-time measurements in quantum mechanics. Physical Review A, 79 (5): 052110, 2009. 10.1103/physreva.79.052110. https://doi.org/10.1103/physreva.79.052110
[17] Yakir Aharonov and Lev Vaidman. The two-state vector formalism: an updated review. In Time in quantum mechanics, pages 399–447. Springer, 2008. 10.1007/978-3-540-73473-4_13. https://doi.org/10.1007/978-3-540-73473-4_13
[18] Andrea Di Biagio, Pietro Donà, and Carlo Rovelli. The arrow of time in operational formulations of quantum theory. Quantum, 5: 520, 2021. 10.22331/q-2021-08-09-520. https://doi.org/10.22331/q-2021-08-09-520
[19] Lucien Hardy. Time symmetry in operational theories. arXiv preprint arXiv:2104.00071, 2021. 10.48550/arXiv.2104.00071. https://doi.org/10.48550/arXiv.2104.00071 arXiv:2104.00071
[20] L. Hardy. Quantum theory from five reasonable axioms. arXiv:quant-ph/0101012, 2001. 10.48550/arXiv.quant-ph/0101012. https://doi.org/10.48550/arXiv.quant-ph/0101012 arXiv:quant-ph/0101012
[21] J. Barrett. Information processing in generalized probabilistic theories. Physical Review A, 75: 032304, 2007. 10.1103/physreva.75.032304. https://doi.org/10.1103/physreva.75.032304
[22] G. Chiribella, G. M. D'Ariano, and P. Perinotti. Informational derivation of quantum theory. Physical Review A, 84 (1): 012311, 2011. 10.1103/physreva.84.012311. https://doi.org/10.1103/physreva.84.012311
[23] Giacomo Mauro D'Ariano, Giulio Chiribella, and Paolo Perinotti. Quantum theory from first principles: an informational approach. Cambridge University Press, 2017. 10.1017/9781107338340.002. https://doi.org/10.1017/9781107338340.002
[24] Stefano Gogioso and Carlo Maria Scandolo. Categorical probabilistic theories. EPTCS, 266: 367–385, 2018. 10.4204/EPTCS.266.23. https://doi.org/10.4204/EPTCS.266.23
[25] S. Abramsky and B. Coecke. A categorical semantics of quantum protocols. In Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science (LICS), pages 415–425, 2004. 10.1109/lics.2004.1319636. arXiv:quant-ph/0402130. https://doi.org/10.1109/lics.2004.1319636 arXiv:quant-ph/0402130
[26] B. Coecke, B. Edwards, and R. W. Spekkens. Phase groups and the origin of non-locality for qubits. Electronic Notes in Theoretical Computer Science, 270 (2): 15–36, 2011. 10.1016/j.entcs.2011.01.021. arXiv:1003.5005. https://doi.org/10.1016/j.entcs.2011.01.021
[27] B. Coecke, R. Duncan, A. Kissinger, and Q. Wang. Generalised compositional theories and diagrammatic reasoning. In G. Chiribella and R. W. Spekkens, editors, Quantum Theory: Informational Foundations and Foils, Fundamental Theories of Physics. Springer, 2016a. 10.1007/978-94-017-7303-4_10. arXiv:1203.4988. https://doi.org/10.1007/978-94-017-7303-4_10 arXiv:1203.4988
[28] Stefano Gogioso. Fantastic quantum theories and where to find them. arXiv preprint arXiv:1703.10576, 2017a. 10.48550/arXiv.1703.10576. https://doi.org/10.48550/arXiv.1703.10576 arXiv:1703.10576
[29] Ralph Silva, Yelena Guryanova, Anthony J Short, Paul Skrzypczyk, Nicolas Brunner, and Sandu Popescu. Connecting processes with indefinite causal order and multi-time quantum states. New Journal of Physics, 19 (10): 103022, 2017. 10.1088/1367-2630/aa84fe. https://doi.org/10.1088/1367-2630/aa84fe
[30] Ralph Silva, Yelena Guryanova, Nicolas Brunner, Noah Linden, Anthony J Short, and Sandu Popescu. Pre-and postselected quantum states: Density matrices, tomography, and kraus operators. Physical Review A, 89 (1): 012121, 2014. 10.1103/physreva.89.012121. https://doi.org/10.1103/physreva.89.012121
[31] Ognyan Oreshkov, Fabio Costa, and Časlav Brukner. Quantum correlations with no causal order. Nature communications, 3 (1): 1–8, 2012. 10.1038/ncomms2076. https://doi.org/10.1038/ncomms2076
[32] Giulio Chiribella, G Mauro D’Ariano, and Paolo Perinotti. Quantum circuit architecture. Physical review letters, 101 (6): 060401, 2008. 10.1103/physrevlett.101.060401. https://doi.org/10.1103/physrevlett.101.060401
[33] Alessandro Bisio and Paolo Perinotti. Theoretical framework for higher-order quantum theory. Proceedings of the Royal Society A, 475 (2225): 20180706, 2019. 10.1098/rspa.2018.0706. https://doi.org/10.1098/rspa.2018.0706
[34] Sander Uijlen and Aleks Kissinger. A categorical semantics for causal structure. Logical Methods in Computer Science, 15, 2019. 10.23638/lmcs-15(3:15)2019. https://doi.org/10.23638/lmcs-15(3:15)2019
[35] Matt Wilson and Giulio Chiribella. A mathematical framework for transformations of physical processes. arXiv preprint arXiv:2204.04319, 2022. 10.48550/arXiv.2204.04319. https://doi.org/10.48550/arXiv.2204.04319 arXiv:2204.04319
[36] Bob Coecke. A universe of processes and some of its guises. Deep beauty: understanding the quantum world through mathematical innovation, pages 129–186, 2011. 10.1017/cbo9780511976971.004. https://doi.org/10.1017/cbo9780511976971.004
[37] B. Coecke and A. Kissinger. Categorical quantum mechanics I: causal quantum processes. In E. Landry, editor, Categories for the Working Philosopher. Oxford University Press, 2016a. 10.1093/oso/9780198748991.003.0012. arXiv:1510.05468. https://doi.org/10.1093/oso/9780198748991.003.0012
[38] B. Coecke and A. Kissinger. Picturing Quantum Processes. A First Course in Quantum Theory and Diagrammatic Reasoning. Cambridge University Press, 2016b. 10.1017/9781316219317.002. https://doi.org/10.1017/9781316219317.002
[39] John H Selby, Carlo Maria Scandolo, and Bob Coecke. Reconstructing quantum theory from diagrammatic postulates. Quantum, 5: 445, 2021. 10.22331/q-2021-04-28-445. https://doi.org/10.22331/q-2021-04-28-445
[40] John H Selby. A process theoretic triptych. PhD thesis, PhD thesis, Imperial College London, 2017.
[41] S. Abramsky and B. Coecke. Categorical quantum mechanics. In K. Engesser, D. Gabbay, and D. Lehmann, editors, Handbook of quantum logic and quantum structures: quantum logic, pages 261–324. Elsevier, 2009. ISBN 0444528695. 10.1016/b978-0-444-52869-8.50010-4. https://doi.org/10.1016/b978-0-444-52869-8.50010-4
[42] S. Mac Lane. Categories for the working mathematician. Springer-verlag, 1998. 10.1007/978-1-4612-9839-7. https://doi.org/10.1007/978-1-4612-9839-7
[43] Evan Patterson, David I Spivak, and Dmitry Vagner. Wiring diagrams as normal forms for computing in symmetric monoidal categories. arXiv preprint arXiv:2101.12046, 2021. 10.4204/EPTCS.333.4. https://doi.org/10.4204/EPTCS.333.4 arXiv:2101.12046
[44] John H Selby, Maria E Stasinou, Matt Wilson, and Bob Coecke. Generalised process theories. arXiv preprint arXiv:2502.10368, 2025. 10.48550/arXiv.2502.10368. https://doi.org/10.48550/arXiv.2502.10368 arXiv:2502.10368
[45] Bob Coecke, Chris Heunen, and Aleks Kissinger. Categories of quantum and classical channels. Quantum Information Processing, 15 (12): 5179–5209, 2016b. 10.1007/s11128-014-0837-4. https://doi.org/10.1007/s11128-014-0837-4
[46] John Selby and Bob Coecke. Leaks: quantum, classical, intermediate and more. Entropy, 19 (4): 174, 2017a. 10.3390/e19040174. https://doi.org/10.3390/e19040174
[47] Sean Tull. A categorical reconstruction of quantum theory. arXiv preprint arXiv:1804.02265, 2018. 10.48550/arXiv.1804.02265. https://doi.org/10.48550/arXiv.1804.02265 arXiv:1804.02265
[48] B. Coecke and R. Lal. Causal categories: relativistically interacting processes. Foundations of Physics, 43: 458–501, 2013. 10.1007/s10701-012-9646-8. arXiv:1107.6019. https://doi.org/10.1007/s10701-012-9646-8 arXiv:1107.6019
[49] Aleks Kissinger, Matty Hoban, and Bob Coecke. Equivalence of relativistic causal structure and process terminality. arXiv preprint arXiv:1708.04118, 2017. 10.48550/arXiv.1708.04118. https://doi.org/10.48550/arXiv.1708.04118 arXiv:1708.04118
[50] S. Abramsky and B. Coecke. Abstract physical traces. Theory and Applications of Categories, 14 (6): 111–124, 2005. 10.70930/tac/vgpjookq. arXiv:0910.3144. https://doi.org/10.70930/tac/vgpjookq arXiv:0910.3144
[51] P. Selinger. Dagger compact closed categories and completely positive maps. Electronic Notes in Theoretical Computer Science, 170: 139–163, 2007. 10.1016/j.entcs.2006.12.018. https://doi.org/10.1016/j.entcs.2006.12.018
[52] B. Coecke. Kindergarten quantum mechanics. In A. Khrennikov, editor, Quantum Theory: Reconsiderations of the Foundations III, pages 81–98. AIP Press, 2005. 10.1063/1.2158713. arXiv:quant-ph/0510032. https://doi.org/10.1063/1.2158713 arXiv:quant-ph/0510032
[53] John H Selby and Bob Coecke. A diagrammatic derivation of the hermitian adjoint. Foundations of Physics, 47 (9): 1191–1207, 2017b. 10.1007/s10701-017-0102-7. https://doi.org/10.1007/s10701-017-0102-7
[54] Stefano Gogioso. Categorical quantum dynamics. PhD thesis, University of Oxford, 2017b.
[55] Stefano Gogioso. A Diagrammatic Approach to Quantum Dynamics. In Markus Roggenbach and Ana Sokolova, editors, 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019), volume 139 of Leibniz International Proceedings in Informatics (LIPIcs), pages 19:1–19:23, Dagstuhl, Germany, 2019. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik. ISBN 978-3-95977-120-7. 10.4230/LIPIcs.CALCO.2019.19. URL http://drops.dagstuhl.de/opus/volltexte/2019/11447. https://doi.org/10.4230/LIPIcs.CALCO.2019.19 http://drops.dagstuhl.de/opus/volltexte/2019/11447
[56] Bob Coecke, Tobias Fritz, and Robert W Spekkens. A mathematical theory of resources. Information and Computation, 250: 59–86, 2016c. 10.1016/j.ic.2016.02.008. https://doi.org/10.1016/j.ic.2016.02.008
[57] John C Baez and Aaron Lauda. A prehistory of n-categorical physics. Deep Beauty: Understanding the Quantum World Through Mathematical Innovation, pages 13–128, 2011. 10.1017/cbo9780511976971.003. https://doi.org/10.1017/cbo9780511976971.003
[58] H. Scutaru. Some remarks on covariant completely positive linear maps on C*-algebras. Reports on Mathematical Physics, 16 (1): 79–87, 1979. ISSN 0034-4877. 10.1016/0034-4877(79)90040-5. URL https://www.sciencedirect.com/science/article/pii/0034487779900405. https://doi.org/10.1016/0034-4877(79)90040-5 https://www.sciencedirect.com/science/article/pii/0034487779900405
[59] Dominic Verdon. A covariant stinespring theorem. Journal of Mathematical Physics, 63 (9): 091705, 2022. 10.1063/5.0071215. https://doi.org/10.1063/5.0071215
[60] Markus P Müller and Cozmin Ududec. Structure of reversible computation determines the self-duality of quantum theory. Physical review letters, 108 (13): 130401, 2012. 10.1103/physrevlett.108.130401. https://doi.org/10.1103/physrevlett.108.130401
[61] Sandu Popescu and Daniel Rohrlich. Quantum nonlocality as an axiom. Foundations of Physics, 24 (3): 379–385, 1994. 10.1007/bf02058098. https://doi.org/10.1007/bf02058098
[62] Daniel Goldwater, Mauro Paternostro, and PF Barker. Testing wave-function-collapse models using parametric heating of a trapped nanosphere. Physical Review A, 94 (1): 010104, 2016. 10.1103/physreva.94.010104. https://doi.org/10.1103/physreva.94.010104
[63] Nicola Pinzani, Stefano Gogioso, and Bob Coecke. Categorical semantics for time travel. In 2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), pages 1–20. IEEE, 2019. 10.1109/LICS.2019.8785664. https://doi.org/10.1109/LICS.2019.8785664
[64] Aleks Kissinger and Sander Uijlen. A categorical semantics for causal structure. In Logic in Computer Science (LICS), 2017 32nd Annual ACM/IEEE Symposium on, pages 1–12. IEEE, 2017. 10.1109/lics.2017.8005095. https://doi.org/10.1109/lics.2017.8005095
[65] Matt Wilson and Giulio Chiribella. Causality in higher order process theories. arXiv preprint arXiv:2107.14581, 2021. 10.4204/EPTCS.343.12. https://doi.org/10.4204/EPTCS.343.12 arXiv:2107.14581
[66] David Schmid, John H Selby, and Robert W Spekkens. Unscrambling the omelette of causation and inference: The framework of causal-inferential theories. arXiv preprint arXiv:2009.03297, 2020. 10.48550/arXiv.2009.03297. https://doi.org/10.48550/arXiv.2009.03297 arXiv:2009.03297
[67] B. Coecke and R. Duncan. Interacting quantum observables: categorical algebra and diagrammatics. New Journal of Physics, 13: 043016, 2011. 10.1088/1367-2630/13/4/043016. arXiv:quant-ph/09064725. https://doi.org/10.1088/1367-2630/13/4/043016 arXiv:quant-ph/09064725
[68] Bob Coecke, Dominic Horsman, Aleks Kissinger, and Quanlong Wang. Kindergarden quantum mechanics graduates ...or how i learned to stop gluing lego together and love the zx-calculus. Theoretical Computer Science, 897: 1–22, 2022. ISSN 0304-3975. 10.1016/j.tcs.2021.07.024. URL https://www.sciencedirect.com/science/article/pii/S0304397521004308. https://doi.org/10.1016/j.tcs.2021.07.024 https://www.sciencedirect.com/science/article/pii/S0304397521004308
[69] Stefano Gogioso and Fabrizio Romano Genovese. Infinite-dimensional categorical quantum mechanics. EPTCS, 236: 51–69, 2017. 10.4204/EPTCS.236.4. https://doi.org/10.4204/EPTCS.236.4
[70] Razin A. Shaikh and Stefano Gogioso. Categorical semantics for feynman diagrams. arXiv preprint arXiv:2205.00466, 2022. 10.48550/arXiv.2205.00466. https://doi.org/10.48550/arXiv.2205.00466 arXiv:2205.00466
[71] Stefano Gogioso, Maria E Stasinou, and Bob Coecke. Functorial evolution of quantum fields. Frontiers of Physics, 9, 2020. 10.3389/fphy.2021.534265. https://doi.org/10.3389/fphy.2021.534265
[72] David I Spivak, Patrick Schultz, and Dylan Rupel. String diagrams for traced and compact categories are oriented 1-cobordisms. Journal of Pure and Applied Algebra, 221 (8): 2064–2110, 2017. 10.1016/j.jpaa.2016.10.009. https://doi.org/10.1016/j.jpaa.2016.10.009
[73] Bob Coecke, Ross Duncan, Aleks Kissinger, and Quanlong Wang. Strong complementarity and non-locality in categorical quantum mechanics. In 2012 27th Annual IEEE Symposium on Logic in Computer Science, pages 245–254. IEEE, 2012. 10.1109/LICS.2012.35. https://doi.org/10.1109/LICS.2012.35
[74] Stefano Gogioso and Aleks Kissinger. Fully graphical treatment of the quantum algorithm for the hidden subgroup problem. arXiv preprint arXiv:1701.08669, 2017. 10.48550/arXiv.1701.08669. https://doi.org/10.48550/arXiv.1701.08669 arXiv:1701.08669
[75] Stefano Gogioso and William Zeng. Generalised mermin-type non-locality arguments. Logical Methods in Computer Science, 15, 2019. 10.23638/LMCS-15(2:3)2019. https://doi.org/10.23638/LMCS-15(2:3)2019
[76] Jamie Vicary. Topological structure of quantum algorithms. In 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science, pages 93–102. IEEE, 2013. 10.1109/LICS.2013.14. https://doi.org/10.1109/LICS.2013.14
[77] Stefano Gogioso and William Zeng. Fourier transforms from strongly complementary observables. arXiv preprint arXiv:1501.04995, 2015. 10.48550/arXiv.1501.04995. https://doi.org/10.48550/arXiv.1501.04995 arXiv:1501.04995
Text integral sub licența deschisă a publicației · 2007 cuvinte
Subiecte conexe
Ergodicity broken in quantum systems even after long evolution
Quantum Zeitgeist · 11 sept. 2026
Symmetry-enriched topological order in tensor networks: Defects, gauging and anyon condensation
Quantum Journal · 1 sept. 2026
Quantum Asymmetry Breaks Time Symmetry with a Precise 2/3 Coupling
Quantum Zeitgeist · 15 iun. 2026
On the relation between perspective-neutral, algebraic, and effective quantum reference frames
Quantum Journal · 20 aug. 2026