1Centre for Quantum Computation and Communication Technology (Australian Research Council)
2Centre for Quantum Dynamics, Griffith University, Yuggera Country, Brisbane, Queensland 4111, Australia
3Centre for Quantum Dynamics, Griffith University, Yugambeh Country, Gold Coast, Queensland 4222, Australia
4QuAIL (Quantum Artifical Intelligence Laboratory), NASA Ames Research Center, Moffett Field, CA 94035, United States of America
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Abstract
A recent paper by two of us and co-workers [1], based on an extended Wigner’s friend scenario, demonstrated that certain empirical correlations predicted by quantum theory (QT) violate inequalities derived from a set of metaphysical assumptions we called “Local Friendliness” (LF). These assumptions are strictly weaker than those used for deriving Bell inequalities. Crucial to the theorem was the premise that a quantum system with reversible evolution could be an observer (colloquially, a “friend”). However, that paper was noncommittal on what would constitute an observer for the purpose of an experiment. Here, we present a new LF no-go theorem which takes seriously the idea that a system’s having $thoughts$ is a sufficient condition for it to be an observer. Our new derivation of the LF inequalities uses four metaphysical assumptions, three of which are thought-related, including one that is explicitly called “Friendliness”. These four assumptions, in conjunction, allow one to derive LF inequalities for experiments involving the type of system that “Friendliness” refers to. In addition to these four metaphysical assumptions, this new no-go theorem requires two assumptions about what is $technologically$ feasible: Human-Level Artificial Intelligence, and Universal Quantum Computing which is fast and large scale. The latter is often motivated by the belief that QT is universal, but this is $not$ an assumption of the theorem. The intent of the new theorem is to give a clear goal for future experimentalists, and a clear motivation for trying to achieve that goal. We review various approaches to QT in light of our theorem. The popular stance that “quantum theory needs no interpretation” does not question any of our assumptions and so is ruled out. Finally, we quantitatively discuss how difficult the experiment we envisage would be, and briefly discuss milestones on the paths towards it.
Featured image: Artist’s impression of QUALL-E, a quantum computer running a human-level artificial intelligence algorithm, who has observed a quantum system, perhaps about to be reversed at the whim of a human party. Credit: Tony Dunnigan.
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[1] Kok-Wei Bong, Aníbal Utreras-Alarcón, Farzad Ghafari, Yeong-Cherng Liang, Nora Tischler, Eric G. Cavalcanti, Geoff J. Pryde, and Howard M. Wiseman. “A strong no-go theorem on the Wigner’s friend paradox”. Nature Physics 16, 1199–1205 (2020).
https://doi.org/10.1038/s41567-020-0990-x
[2] E. P. Wigner. “Remarks on the mind-body question”. In I. J. Good, editor, The Scientist Speculates. Heinemann, London (1961).
https://doi.org/10.1007/978-3-642-78374-6_20
[3] J. S. Bell. “On the Einstein Podolsky Rosen paradox”. Physics Physique Fizika 1, 195–200 (1964).
https://doi.org/10.1103/PhysicsPhysiqueFizika.1.195
[4] Č. Brukner. “On the quantum measurement problem”. In R. Bertlmann and A. Zeilinger, editors, Quantum [un]speakables II: half a century of Bell’s theorem. Pages 95–117. The Frontiers Collection. Springer, Switzerland (2017).
https://doi.org/10.1007/978-3-319-38987-5_5
[5] Č. Brukner. “A no-go theorem for observer-independent facts”. Entropy 20, 350 (2018).
https://doi.org/10.3390/e20050350
[6] D. Frauchiger and R. Renner. “Quantum theory cannot consistently describe the use of itself”. Nature Communications 9, 3711 (2018).
https://doi.org/10.1038/s41467-018-05739-8
[7] M. Proietti, A. Pickston, F. Graffitti, P. Barrow, D. Kundys, C. Branciard, M. Ringbauer, and A. Fedrizzi. “Experimental test of local observer independence”. Science Advances 5, eaaw9832 (2019).
https://doi.org/10.1126/sciadv.aaw9832
[8] Veronika Baumann and Stefan Wolf. “On formalisms and interpretations”. Quantum 2, 99 (2018).
https://doi.org/10.22331/q-2018-10-15-99
[9] Richard Healey. “Quantum theory and the limits of objectivity”. Foundations of Physics 48, 1568–1589 (2018).
https://doi.org/10.1007/s10701-018-0216-6
[10] V. Baumann, F. Del Santo, and Č. Brukner. “Comment on Healey’s `Quantum theory and the limits of objectivity”’. Foundations of Physics 49, 741–749 (2019).
https://doi.org/10.1007/s10701-019-00276-w
[11] Andrea Di Biagio and Carlo Rovelli. “Stable facts, relative facts”. Foundations of Physics 51, 1–13 (2021).
https://doi.org/10.1007/s10701-021-00429-w
[12] Christopher A. Fuchs and Asher Peres. “Quantum theory needs no ‘interpretation’”. Physics Today 53, 70 (2000).
https://doi.org/10.1063/1.883004
[13] A. Shimony. “Controllable and uncontrollable non-locality”. In Susumu Kamefuchi, editor, Foundations of Quantum Mechanics in the Light of New Technology. Pages 225–230. Tokyo (1984). Physical Society of Japan.
https://doi.org/10.1017/CBO9781139172196.010
[14] Marwan Haddara and Eric G. Cavalcanti. “A possibilistic no-go theorem on the Wigner’s friend paradox” (2022) arXiv:2205.12223.
arXiv:2205.12223
[15] A. Peres. “Unperformed experiments have no results”. American Journal of Physics 46, 745–747 (1978).
https://doi.org/10.1119/1.11393
[16] Howard M. Wiseman and Eric G. Cavalcanti. “Causarum investigatio and the two Bell’s theorems of John Bell”. Pages 119–142. Springer International Publishing. Cham (2017).
https://doi.org/10.1007/978-3-319-38987-5_6
[17] Judea Pearl. “Causality: models, reasoning and inference”. Cambridge University Press. (2000).
https://doi.org/10.5555/1642718
[18] Eric G. Cavalcanti and Howard M. Wiseman. “Implications of Local Friendliness violation for quantum causality”. Entropy 23, 925 (2021).
https://doi.org/10.3390/e23080925
[19] Roger Colbeck and Renato Renner. “No extension of quantum theory can have improved predictive power”. Nature Communications 2, 411 (2011).
https://doi.org/10.1038/ncomms1416
[20] J. S. Bell. “The theory of local beables”. Epistemological Lett. 9, 11–24 (1976).
https://doi.org/10.1142/9789812795854_0078
[21] H. M. Wiseman. “The two Bell’s theorems of John Bell”. J. Phys. A 47, 424001 (2014).
https://doi.org/10.1088/1751-8113/47/42/424001
[22] Howard M. Wiseman and Eleanor G. Rieffel. “Reply to Norsen’s paper `are there really two different Bell’s theorems?”’. International Journal of Quantum Foundations 1, 85–99 (2015).
https://doi.org/10.48550/ARXIV.1503.06978
[23] Howard M. Wiseman, Eleanor G. Rieffel, and Eric G. Cavalcanti. “Reply to Gillis’s `on the analysis of Bell’s 1964 paper by Wiseman, Cavalcanti, and Rieffel”’. International Journal of Quantum Foundations 2, 143–154 (2016).
https://doi.org/10.48550/ARXIV.1608.04149
[24] Adrian Kent. “Causal quantum theory and the collapse locality loophole”. Phys. Rev. A 72, 012107 (2005).
https://doi.org/10.1103/PhysRevA.72.012107
[25] Adrian Kent. “Stronger tests of the collapse-locality loophole in Bell experiments”. Phys. Rev. A 101, 012102 (2020).
https://doi.org/10.1103/PhysRevA.101.012102
[26] Zhen-Peng Xu, Jonathan Steinberg, H. Chau Nguyen, and Otfried Gühne. “No-go theorem based on incomplete information of Wigner about his friend” (2021) arXiv:2111.15010.
https://doi.org/10.1103/PhysRevA.107.022424
arXiv:2111.15010
[27] George Moreno, Ranieri Nery, Cristhiano Duarte, and Rafael Chaves. “Events in quantum mechanics are maximally non-absolute”. Quantum 6, 785 (2022).
https://doi.org/10.22331/q-2022-08-24-785
[28] Mark Rowlands, Joe Lau, and Max Deutsch. “Externalism About the Mind”. In Edward N. Zalta, editor, The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University (2020). Winter 2020 edition.
[29] Rene Descartes. “Discourse on the method”. SMK Books. (2018).
[30] Gary Marcus. “What comes after the Turing test”. The New Yorker, 14 June 2014, https://www.newyorker.com/tech/annals-of-technology/what-comes-after-the-turing-test (2014).
https://www.newyorker.com/tech/annals-of-technology/what-comes-after-the-turing-test
[31] Guillaume Thierry. “GPT-3: new AI can write like a human but don’t mistake that for thinking – neuroscientist”. https://theconversation.com/gpt-3-new-ai-can-write-like-a-human-but-dont-mistake-that-for-thinking-neuroscientist-146082 (2020).
https://theconversation.com/gpt-3-new-ai-can-write-like-a-human-but-dont-mistake-that-for-thinking-neuroscientist-146082
[32] “DALL·E: creating Images from Text”. https://openai.com/blog/dall-e/ (accessed 2022).
https://openai.com/blog/dall-e/
[33] Charles H Bennett. “Logical reversibility of computation”. IBM journal of Research and Development 17, 525–532 (1973).
https://doi.org/10.1147/rd.176.0525
[34] E. G. Rieffel and W. Polak. “Quantum computing: A gentle introduction”. MIT Press. Cambridge, MA (2011).
https://doi.org/10.5555/1973124
[35] Thaddeus D Ladd, Fedor Jelezko, Raymond Laflamme, Yasunobu Nakamura, Christopher Monroe, and Jeremy Lloyd O’Brien. “Quantum computers”. Nature 464, 45–53 (2010).
https://doi.org/10.1038/nature08812
[36] Jamie Harris and Jacy Reese Anthis. “The moral consideration of artificial entities: a literature review”. Science and Engineering Ethics 27, 53 (2021).
https://doi.org/10.1007/s11948-021-00331-8
[37] David Deutsch. “Quantum theory as a universal physical theory”. International Journal of Theoretical Physics 24, 1–24 (1985).
https://doi.org/10.1007/BF00670071
[38] David Deutsch. “Quantum theory, the Church-Turing principle and the universal quantum computer”. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 400, 97–117 (1985).
https://doi.org/10.1098/rspa.1985.0070
[39] H. M. Wiseman and E. G. Cavalcanti. “How different approaches to quantum theory relate to the “thoughtful” Local Friendliness no-go theorem”. (in preparation) (2022).
[40] David Bohm. “A suggested interpretation of the quantum theory in terms of “hidden” variables. I”. Phys. Rev. 85, 166–179 (1952).
https://doi.org/10.1103/PhysRev.85.166
[41] David Bohm. “A suggested interpretation of the quantum theory in terms of “hidden” variables. II”. Phys. Rev. 85, 180–193 (1952).
https://doi.org/10.1103/PhysRev.85.180
[42] D. Dürr, S. Goldstein, and N. Zanghì. “Quantum physics without quantum philosophy”. Springer. Heidelberg (2013).
https://doi.org/10.1007/978-3-642-30690-7
[43] David Albert and Barry Loewer. “Interpreting the many-worlds interpretation”. Synthese 77, 195–213 (1988).
https://doi.org/10.1007/BF00869434
[44] Hugh Everett. “`Relative state’ formulation of quantum mechanics”. Rev. Mod. Phys. 29, 454–462 (1957).
https://doi.org/10.1103/RevModPhys.29.454
[45] Christopher A. Fuchs and Rüdiger Schack. “Quantum-bayesian coherence”. Rev. Mod. Phys. 85, 1693–1715 (2013).
https://doi.org/10.1103/RevModPhys.85.1693
[46] C. Rovelli. “Relational quantum mechanics”. International Journal of Theoretical Physics 35, 1637–1678 (1996).
https://doi.org/10.1007/BF02302261
[47] G. C. Ghirardi, A. Rimini, and T. Weber. “Unified dynamics for microscopic and macroscopic systems”. Phys. Rev. D 34, 470–491 (1986).
https://doi.org/10.1103/PhysRevD.34.470
[48] Valia Allori, Angelo Bassi, Detlef Dürr, and Nino Zanghi, editors. “Do wave functions jump?”. Fundamental Theories of Physics. Springer. Switzerland (2021).
https://doi.org/10.1007/978-3-030-46777-7
[49] Roger Penrose. “The emperor’s new mind: concerning computers, minds, and the laws of physics”. Oxford University Press, Inc. USA (1989).
https://doi.org/10.1093/oso/9780198519737.001.0001
[50] Roger Penrose. “Shadows of the mind: a search for the missing science of consciousness”. Oxford University Press, Inc. USA (1994). 1st edition.
[51] David J. Chalmers and Kelvin J. McQueen. “Consciousness and the collapse of the wave function”. In Shan Gao, editor, Consciousness and quantum mechanics. Oxford University Press (forthcoming). arXiv:2105.02314.
arXiv:2105.02314
[52] Anders Sandberg and Nick Bostrom. “Whole brain emulation: a roadmap”. http://www.fhi.ox.ac.uk/Reports/2008-3.pdf (2008).
http://www.fhi.ox.ac.uk/Reports/2008-3.pdf
[53] Joseph Carlsmith. “How much computational power does it take to match the human brain?”. https://www.openphilanthropy.org/brain-computation-report (2020).
https://www.openphilanthropy.org/brain-computation-report
[54] Steve B Furber, Francesco Galluppi, Steve Temple, and Luis A Plana. “The spinnaker project”. Proceedings of the IEEE 102, 652–665 (2014).
https://doi.org/10.1109/JPROC.2014.2304638
[55] TOP500 The List. “Top June 2022”. https://www.top500.org/lists/top500/2022/06/ (accessed 2022).
https://www.top500.org/lists/top500/2022/06/
[56] TOP500 The List. “Top #1 systems”. https://www.top500.org/resources/top-systems/ (accessed 2022).
https://www.top500.org/resources/top-systems/
[57] Sergey Bravyi, Oliver Dial, Jay M. Gambetta, Dario Gil, and Zaira Nazario. “The future of quantum computing with superconducting qubits” (2022). arXiv:2209.06841.
https://doi.org/10.1063/5.0082975
arXiv:2209.06841
[58] Noga Alon, F. R. K. Chung, and R. L. Graham. “Routing permutations on graphs via matchings”. SIAM Journal on Discrete Mathematics 7, 513–530 (1994).
https://doi.org/10.1137/S0895480192236628
[59] Naomi H. Nickerson, Joseph F. Fitzsimons, and Simon C. Benjamin. “Freely scalable quantum technologies using cells of 5-to-50 qubits with very lossy and noisy photonic links”. Phys. Rev. X 4, 041041 (2014).
https://doi.org/10.1103/PhysRevX.4.041041
[60] Robert Beals, Stephen Brierley, Oliver Gray, Aram W. Harrow, Samuel Kutin, Noah Linden, Dan Shepherd, and Mark Stather. “Efficient distributed quantum computing”. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, 20120686 (2013).
https://doi.org/10.1098/rspa.2012.0686
[61] Stephen Brierley. “Efficient implementation of quantum circuits with limited qubit interactions” (2015) arXiv:1507.04263.
arXiv:1507.04263
[62] Steven Herbert. “On the depth overhead incurred when running quantum algorithms on near-term quantum computers with limited qubit connectivity” (2018) arXiv:1805.12570.
arXiv:1805.12570
[63] Ryan Babbush, Jarrod R. McClean, Michael Newman, Craig Gidney, Sergio Boixo, and Hartmut Neven. “Focus beyond quadratic speedups for error-corrected quantum advantage”. PRX Quantum 2, 010103 (2021).
https://doi.org/10.1103/PRXQuantum.2.010103
[64] Austin G. Fowler, Matteo Mariantoni, John M. Martinis, and Andrew N. Cleland. “Surface codes: Towards practical large-scale quantum computation”. Phys. Rev. A 86, 032324 (2012).
https://doi.org/10.1103/PhysRevA.86.032324
[65] Michael Beverland, Vadym Kliuchnikov, and Eddie Schoute. “Surface code compilation via edge-disjoint paths” (2021).
https://doi.org/10.1103/PRXQuantum.3.020342
[66] Hector Bombin. “2D quantum computation with 3D topological codes” (2018) arXiv:1810.09571.
arXiv:1810.09571
[67] Benjamin J. Brown. “A fault-tolerant non-clifford gate for the surface code in two dimensions”. Science Advances 6, eaay4929 (2020).
https://doi.org/10.1126/sciadv.aay4929
[68] Yu He, SK Gorman, Daniel Keith, Ludwik Kranz, JG Keizer, and MY Simmons. “A two-qubit gate between phosphorus donor electrons in silicon”. Nature 571, 371–375 (2019).
https://doi.org/10.1038/s41586-019-1381-2
[69] Anasua Chatterjee, Paul Stevenson, Silvano De Franceschi, Andrea Morello, Nathalie P de Leon, and Ferdinand Kuemmeth. “Semiconductor qubits in practice”. Nature Reviews Physics 3, 157–177 (2021).
https://doi.org/10.1038/s42254-021-00283-9
[70] “Microprocessor chronology”. https://en.wikipedia.org/wiki/Microprocessor_chronology (accessed 2022).
https://en.wikipedia.org/wiki/Microprocessor_chronology
[71] Isabelle Dume. “Logic gate breaks speed record”. https://physicsworld.com/a/logic-gate-breaks-speed-record/ (accessed 2022).
https://physicsworld.com/a/logic-gate-breaks-speed-record/
[72] “Optical frequency combs”. https://www.nist.gov/topics/physics/optical-frequency-combs (accessed 2022).
https://www.nist.gov/topics/physics/optical-frequency-combs
[73] Steven T. Cundiff and Jun Ye. “Colloquium: Femtosecond optical frequency combs”. Rev. Mod. Phys. 75, 325–342 (2003).
https://doi.org/10.1103/RevModPhys.75.325
[74] S. Nandi et al. “Observation of Rabi dynamics with a short-wavelength free-electron laser”. Nature 608, 488–493 (2022).
https://doi.org/10.1038/s41586-022-04948-y
[75] Samuel C Smith, Benjamin J Brown, and Stephen D Bartlett. “A local pre-decoder to reduce the bandwidth and latency of quantum error correction” (2022). arXiv:2208.04660.
https://doi.org/10.1103/PhysRevApplied.19.034050
arXiv:2208.04660
[76] Anthony Leverrier and Gilles Zémor. “A parallel decoder for good quantum ldpc codes” (2022). arXiv:2208.05537.
arXiv:2208.05537
[77] Pavel Panteleev and Gleb Kalachev. “Asymptotically good quantum and locally testable classical LDPC codes”. In Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing. Pages 375–388. (2022).
https://doi.org/10.1145/3519935
[78] Anthony Leverrier and Gilles Zémor. “Quantum Tanner codes” (2022). arXiv:2202.13641.
arXiv:2202.13641
[79] Matthew B. Hastings and Jeongwan Haah. “Dynamically Generated Logical Qubits”. Quantum 5, 564 (2021).
https://doi.org/10.22331/q-2021-10-19-564
[80] Mihir K Bhaskar, Stuart Hadfield, Anargyros Papageorgiou, and Iasonas Petras. “Quantum algorithms and circuits for scientific computing” (2015). arXiv:1511.08253.
arXiv:1511.08253
[81] Stuart Andrew Hadfield. “Quantum algorithms for scientific computing and approximate optimization” (2018) arXiv:1805.03265.
arXiv:1805.03265
[82] Alex Parent, Martin Roetteler, and Krysta M Svore. “Reversible circuit compilation with space constraints” (2015). arXiv:1510.00377.
arXiv:1510.00377
[83] Thomas Häner, Martin Roetteler, and Krysta M Svore. “Optimizing quantum circuits for arithmetic” (2018). arXiv:1805.12445.
arXiv:1805.12445
[84] Andris Ambainis and Martins Kokainis. “Quantum algorithm for tree size estimation, with applications to backtracking and 2-player games”. In Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing. Page 989–1002. STOC 2017New York, NY, USA (2017). Association for Computing Machinery.
https://doi.org/10.1145/3055399.3055444
[85] Ashley Montanaro. “Quantum speedup of branch-and-bound algorithms”. Phys. Rev. Research 2, 013056 (2020).
https://doi.org/10.1103/PhysRevResearch.2.013056
[86] Kyle E. C. Booth, Bryan O’Gorman, Jeffrey Marshall, Stuart Hadfield, and Eleanor Rieffel. “Quantum-accelerated constraint programming”. Quantum 5, 550 (2021).
https://doi.org/10.22331/q-2021-09-28-550
[87] Paul Christiano. https://www.lesswrong.com/posts/TAbQHFwGD4E3jCMnt/is-it-a-coincidence-that-gpt-3-requires-roughly-the-same#: :text=Feb Comment on blog post “Is it a coincidence that GPT-3 requires roughly the same amount of compute as is necessary to emulate the human brain?” on Less Wrong blog, accessed 2023-03-20.
https://www.lesswrong.com/posts/TAbQHFwGD4E3jCMnt/is-it-a-coincidence-that-gpt-3-requires-roughly-the-same#:~:text=Febnewblock%20Comment%20on%20blog%20post%20I
[88] Tom B Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al. “Language models are few-shot learners” (2020). arXiv:2005.14165.
arXiv:2005.14165
[89] Tom Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al. “Language models are few-shot learners”. Advances in Neural Information Processing Systems 33, 1877–1901 (2020). url: proceedings.neurips.cc/paper/2020/hash/1457c0d6bfcb4967418bfb8ac142f64a-Abstract.html.
https://proceedings.neurips.cc/paper/2020/hash/1457c0d6bfcb4967418bfb8ac142f64a-Abstract.html
[90] Nuriya Nurgalieva, Simon Mathis, Lídia del Rio, and Renato Renner. “Thought experiments in a quantum computer” (2022). arXiv:2209.06236.
arXiv:2209.06236
[91] B. Schumacher. “Quantum coding”. Phys. Rev. A 51, 2738 (1995).
https://doi.org/10.1103/PhysRevA.51.2738
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[2] Jordan K. Taylor and Ian P. McCulloch, “Wavefunction branching: when you can’t tell pure states from mixed states”, arXiv:2308.04494, (2023).
[3] Adrian Kent, “The measurement postulates of quantum mechanics are not redundant”, arXiv:2307.06191, (2023).
[4] Aníbal Utreras-Alarcón, Eric G. Cavalcanti, and Howard M. Wiseman, “Allowing Wigner’s friend to sequentially measure incompatible observables”, arXiv:2305.09102, (2023).
[5] J. Allam and A. Matzkin, “From observer-dependent facts to frame-dependent measurement records in Wigner friend scenarios”, arXiv:2304.09289, (2023).
[6] Veronika Baumann and Caslav Brukner, “Observers in superposition and the no-signaling principle”, arXiv:2305.15497, (2023).
[7] Veronika Baumann, “Classical information and collapse in Wigner’s friend setups”, arXiv:2308.08260, (2023).
[8] Emanuel Schwarzhans, Felix C. Binder, Marcus Huber, and Maximilian P. E. Lock, “Quantum measurements and equilibration: the emergence of objective reality via entropy maximisation”, arXiv:2302.11253, (2023).
[9] David Schmid, Yìlè Yīng, and Matthew Leifer, “A review and analysis of six extended Wigner’s friend arguments”, arXiv:2308.16220, (2023).
The above citations are from SAO/NASA ADS (last updated successfully 2023-09-14 15:07:39). The list may be incomplete as not all publishers provide suitable and complete citation data.
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