$\psi$-epistemic interpretations of quantum theory maintain that quantum states only represent incomplete information about the physical states of the world. A major motivation for this view is the promise to provide a reasonable account of state update under measurement by asserting that it is simply a natural feature of updating incomplete statistical information. Here we demonstrate that all known $\psi$-epistemic ontological models of quantum theory in dimension $d\geq3$, including those designed to evade the conclusion of the PBR theorem, cannot represent state update correctly. Conversely, interpretations for which the wavefunction is real evade such restrictions despite remaining subject to long-standing criticism regarding physical discontinuity, indeterminism and the ambiguity of the Heisenberg cut. This revives the possibility of a no-go theorem with no additional assumptions, and demonstrates that what is usually thought of as a strength of epistemic interpretations may in fact be a weakness.
 David Bohm. A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. I. Physical Review, 85 (2): 166–179, January 1952. ISSN 0031-899X. 10.1103/PhysRev.85.166.
 Hugh Everett. "Relative State" Formulation of Quantum Mechanics. Reviews of Modern Physics, 29 (3): 454–462, July 1957. ISSN 0034-6861. 10.1103/RevModPhys.29.454.
 Paul Dirac. The Principles of Quantum Mechanics. Oxford University Press, Oxford, 1958.
 G. C. Ghirardi, A. Rimini, and T. Weber. Unified dynamics for microscopic and macroscopic systems. Physical Review D, 34 (2): 470–491, July 1986. ISSN 0556-2821. 10.1103/PhysRevD.34.470.
 Philip Pearle. Combining stochastic dynamical state-vector reduction with spontaneous localization. Physical Review A, 39 (5): 2277–2289, March 1989. ISSN 0556-2791. 10.1103/PhysRevA.39.2277.
 Antony Valentini. On the Pilot-Wave Theory of Classical, Quantum, and Subquantum Physics. Ph.D. Thesis, SISSA, Trieste, 1991.
 E. G. Beltrametti and S. Bugajski. A classical extension of quantum mechanics. Journal of Physics A: Mathematical and General, 28 (12): 3329, 1995. ISSN 0305-4470. 10.1088/0305-4470/28/12/007.
 Dennis Dieks and Pieter E Vermaas. The Modal Interpretation of Quantum Mechanics. Springer Netherlands, Dordrecht, 1998. ISBN 978-94-011-5084-2. OCLC: 851391542.
 Philip Pearle. Collapse models. In Heinz-Peter Breuer and Francesco Petruccione, editors, Open Systems and Measurement in Relativistic Quantum Theory, volume 526, pages 195–234. Springer Berlin Heidelberg, 1999. ISBN 978-3-540-65978-5 978-3-540-48808-8. 10.1007/BFb0104404.
 Jeffrey A. Barrett. The Quantum Mechanics of Minds and Worlds. Oxford University Press, Oxford, 1999. 10.1093/acprof:oso/9780199247431.001.0001.
 Olimpia Lombardi and Dennis Dieks. Modal Interpretations of Quantum Mechanics. The Stanford Encyclopedia of Philosophy.
 Angelo Bassi, Kinjalk Lochan, Seema Satin, Tejinder P. Singh, and Hendrik Ulbricht. Models of wave-function collapse, underlying theories, and experimental tests. Reviews of Modern Physics, 85 (2): 471–527, April 2013. ISSN 0034-6861, 1539-0756. 10.1103/RevModPhys.85.471.
 A. Einstein, B. Podolsky, and N. Rosen. Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Physical Review, 47 (10): 777–780, May 1935. 10.1103/PhysRev.47.777.
 Simon Kochen and E. Specker. The Problem of Hidden Variables in Quantum Mechanics. Indiana University Mathematics Journal, 17 (1): 59–87, 1967. ISSN 0022-2518. 10.1512/iumj.1968.17.17004.
 L. E. Ballentine. The Statistical Interpretation of Quantum Mechanics. Reviews of Modern Physics, 42 (4): 358–381, October 1970. ISSN 0034-6861. 10.1103/RevModPhys.42.358.
 Don Howard. Einstein on locality and separability. Studies in History and Philosophy of Science Part A, 16 (3): 171–201, September 1985. ISSN 00393681. 10.1016/0039-3681(85)90001-9.
 L. E. Ballentine, Yumin Yang, and J. P. Zibin. Inadequacy of Ehrenfest's theorem to characterize the classical regime. Physical Review A, 50 (4): 2854–2859, October 1994. ISSN 1050-2947, 1094-1622. 10.1103/PhysRevA.50.2854.
 Robert W. Spekkens. In defense of the epistemic view of quantum states: A toy theory. Physical Review A, 75 (3), March 2007. ISSN 1050-2947, 1094-1622. 10.1103/PhysRevA.75.032110.
 Nicholas Harrigan and Robert W. Spekkens. Einstein, incompleteness, and the epistemic view of quantum states. Foundations of Physics, 40 (2): 125–157, February 2010. ISSN 0015-9018, 1572-9516. 10.1007/s10701-009-9347-0.
 M. S. Leifer. Is the quantum state real? An extended review of $\psi$-ontology theorems. Quanta, 3 (1): 67, November 2014. ISSN 1314-7374. 10.12743/quanta.v3i1.22.
 Rüdiger Schack. Participatory realism (talk), June 2016.
 Werner Heisenberg. Physics & Philosophy. Unwin University Books, 1958.
 Christopher A. Fuchs, N. David Mermin, and Rüdiger Schack. An introduction to QBism with an application to the locality of quantum mechanics. American Journal of Physics, 82 (8): 749–754, August 2014. ISSN 0002-9505, 1943-2909. 10.1119/1.4874855.
 Carlo Rovelli. Relational quantum mechanics. International Journal of Theoretical Physics, 35 (8): 1637–1678, August 1996. ISSN 0020-7748, 1572-9575. 10.1007/BF02302261.
 Richard Healey. Quantum Theory: A Pragmatist Approach. August 2010.
 Christopher A. Fuchs. Quantum Mechanics as Quantum Information (and only a little more). May 2002.
 D. Gross. Hudson's Theorem for finite-dimensional quantum systems. Journal of Mathematical Physics, 47 (12): 122107, December 2006. ISSN 0022-2488, 1089-7658. 10.1063/1.2393152.
 Alberto Montina. Dynamics of a qubit as a classical stochastic process with time-correlated noise: Minimal measurement invasiveness. Physical Review Letters, 108 (16), April 2012a. ISSN 0031-9007, 1079-7114. 10.1103/PhysRevLett.108.160501.
 Peter G. Lewis, David Jennings, Jonathan Barrett, and Terry Rudolph. Distinct Quantum States Can Be Compatible with a Single State of Reality. Physical Review Letters, 109 (15), October 2012. ISSN 0031-9007, 1079-7114. 10.1103/PhysRevLett.109.150404.
 Scott Aaronson, Adam Bouland, Lynn Chua, and George Lowther. $\psi$-epistemic theories: The role of symmetry. Physical Review A, 88 (3), September 2013. ISSN 1050-2947, 1094-1622. 10.1103/PhysRevA.88.032111.
 Joel J. Wallman and Stephen D. Bartlett. Nonnegative subtheories and quasiprobability representations of qubits. Physical Review A, 85 (6), June 2012. ISSN 1050-2947, 1094-1622. 10.1103/PhysRevA.85.062121.
 John S. Bell. On the Problem of Hidden Variables in Quantum Mechanics. Reviews of Modern Physics, 38 (3): 447–452, July 1966. ISSN 0034-6861. 10.1103/RevModPhys.38.447.
 Matthew F. Pusey, Jonathan Barrett, and Terry Rudolph. On the reality of the quantum state. Nature Physics, 8 (6): 476–479, May 2012. ISSN 1745-2473, 1745-2481. 10.1038/nphys2309.
 Roger Colbeck and Renato Renner. A system's wave function is uniquely determined by its underlying physical state. New Journal of Physics, 19 (1): 013016, January 2017. ISSN 1367-2630. 10.1088/1367-2630/aa515c.
 Lucien Hardy. Are quantum states real? International Journal of Modern Physics B, 27 (01n03): 1345012, January 2013. ISSN 0217-9792, 1793-6578. 10.1142/S0217979213450124.
 Shane Mansfield. Reality of the quantum state: Towards a stronger $\psi$ -ontology theorem. Physical Review A, 94 (4), October 2016. ISSN 2469-9926, 2469-9934. 10.1103/PhysRevA.94.042124.
 R. W. Spekkens. Contextuality for preparations, transformations, and unsharp measurements. Physical Review A, 71 (5), May 2005. ISSN 1050-2947, 1094-1622. 10.1103/PhysRevA.71.052108.
 Joseph Emerson, Dmitry Serbin, Chris Sutherland, and Victor Veitch. The whole is greater than the sum of the parts: On the possibility of purely statistical interpretations of quantum theory. December 2013. arXiv:1312.1345.
 Lorenzo Catani and Dan E. Browne. Spekkens' toy model in all dimensions and its relationship with stabilizer quantum mechanics. New Journal of Physics, 19 (7): 073035, July 2017. ISSN 1367-2630. 10.1088/1367-2630/aa781c.
 A. J. Leggett and Anupam Garg. Quantum mechanics versus macroscopic realism: Is the flux there when nobody looks? Physical Review Letters, 54 (9): 857–860, March 1985. 10.1103/PhysRevLett.54.857.
 Clive Emary, Neill Lambert, and Franco Nori. Leggett-Garg Inequalities. Reports on Progress in Physics, 77 (1): 016001, January 2014. ISSN 0034-4885, 1361-6633. 10.1088/0034-4885/77/1/016001.
 J. J. Sakurai and Jim Napolitano. Modern Quantum Mechanics. Addison-Wesley, Boston, 2nd edition, 2011. ISBN 978-0-8053-8291-4.
 Alberto Montina. Comment on math overflow question: `psi-epistemic theories' in 3 or more dimensions, December 2012b.
 Victor Veitch, Seyed Ali Hamed Mousavian, Daniel Gottesman, and Joseph Emerson. The Resource Theory of Stabilizer Computation. New Journal of Physics, 16 (1): 013009, January 2014. ISSN 1367-2630. 10.1088/1367-2630/16/1/013009.
 Christopher Ferrie. Quasi-probability representations of quantum theory with applications to quantum information science. Reports on Progress in Physics, 74 (11): 116001, November 2011. ISSN 0034-4885, 1361-6633. 10.1088/0034-4885/74/11/116001.
 David Gross. Non-negative Wigner functions in prime dimensions. Applied Physics B, 86 (3): 367–370, February 2007. ISSN 0946-2171, 1432-0649. 10.1007/s00340-006-2510-9.
 Nix Barnett and James P. Crutchfield. Computational Mechanics of Input-Output Processes: Structured transformations and the $\epsilon$-transducer. Journal of Statistical Physics, 161 (2): 404–451, October 2015. ISSN 0022-4715, 1572-9613. 10.1007/s10955-015-1327-5.
 Matthew S. Leifer and Matthew F. Pusey. Is a time symmetric interpretation of quantum theory possible without retrocausality? Proc. R. Soc. A, 473 (2202): 20160607, June 2017. ISSN 1364-5021, 1471-2946. 10.1098/rspa.2016.0607.
 Piers Lillystone and Joseph Emerson, "A Contextual $\psi$-Epistemic Model of the $n$-Qubit Stabilizer Formalism", arXiv:1904.04268.
 Iman Marvian, "Inaccessible information in probabilistic models of quantum systems, non-contextuality inequalities and noise thresholds for contextuality", arXiv:2003.05984.
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