# Any modification of the Born rule leads to a violation of the purification and local tomography principles

Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom

### Abstract

Using the existing classification of all alternatives to the measurement postulates of quantum theory we study the properties of bi-partite systems in these alternative theories. We prove that in all these theories the purification principle is violated, meaning that some mixed states are not the reduction of a pure state in a larger system. This allows us to derive the measurement postulates of quantum theory from the structure of pure states and reversible dynamics, and the requirement that the purification principle holds. The violation of the purification principle implies that there is some irreducible classicality in these theories, which appears like an important clue for the problem of deriving the Born rule within the many-worlds interpretation. We also prove that in all such modifications the task of state tomography with local measurements is impossible, and present a simple toy theory displaying all these exotic non-quantum phenomena. This toy model shows that, contrarily to previous claims, it is possible to modify the Born rule without violating the no-signalling principle. Finally, we argue that the quantum measurement postulates are the most non-classical amongst all alternatives.

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### Cited by

[1] Pei Wang, "Derive the Born’s rule from environment-induced stochastic dynamics of wave functions in an open system", The European Physical Journal Plus 135 11, 927 (2020).

[2] Marc-Oliver Pleinert, Joachim von Zanthier, and Eric Lutz, "Many-particle interference to test Born's rule", Physical Review Research 2 1, 012051 (2020).

[3] Lluís Masanes, Thomas D. Galley, and Markus P. Müller, "The measurement postulates of quantum mechanics are operationally redundant", Nature Communications 10 1, 1361 (2019).

[4] Marius Krumm and Markus P. Müller, "Quantum computation is the unique reversible circuit model for which bits are balls", npj Quantum Information 5, 7 (2019).

[5] Carlo Maria Scandolo, "Information-theoretic foundations of thermodynamics in general probabilistic theories", arXiv:1901.08054.

[6] Giulio Chiribella, "Agents, Subsystems, and the Conservation of Information", Entropy 20 5, 358 (2018).

The above citations are from Crossref's cited-by service (last updated successfully 2021-01-24 01:00:04) and SAO/NASA ADS (last updated successfully 2021-01-24 01:00:06). The list may be incomplete as not all publishers provide suitable and complete citation data.