The notorious quantum measurement problem brings out the difficulty to reconcile two quantum postulates: the unitary evolution of closed quantum systems and the wave-function collapse after a measurement. This problematics is particularly highlighted in the Wigner's friend thought experiment, where the mismatch between unitary evolution and measurement collapse leads to conflicting quantum descriptions for different observers. A recent no-go theorem has established that the (quantum) statistics arising from an extended Wigner's friend scenario is incompatible when one try to hold together three innocuous assumptions, namely no-superdeterminism, parameter independence and absoluteness of observed events. Building on this extended scenario, we introduce two novel measures of non-absoluteness of events. The first is based on the EPR2 decomposition, and the second involves the relaxation of the absoluteness hypothesis assumed in the aforementioned no-go theorem. To prove that quantum correlations can be maximally non-absolute according to both quantifiers, we show that chained Bell inequalities (and relaxations thereof) are also valid constraints for Wigner's experiment.
To illustrate the problem, the Hungarian-American physicist Eugene Wigner proposed in 1961 an imaginary experiment, now called Wigner's friend experiment. Charlie, an isolated observer in his laboratory, performs a measurement on a quantum system in a superposition of two states. He randomly obtains one of two possible measurement results. In contrast, Alice acts as a superobserver, and describes her friend Charlie, the laboratory and the system being measured as a large composite quantum system. So, from Alice's perspective, her friend Charlie exists in a coherent superposition, entangled with the result of his measurement. That is, from Alice's point of view, the quantum state does not associate a well-defined value with the result of Charlie's measurement. Thus, these two descriptions, that of Alice or that of her friend Charlie, lead to different results, which in principle could be compared experimentally. It might seem a little strange, but here lies the problem: quantum mechanics doesn't tell us where to draw the line between the classical and quantum worlds. In principle, the Schrödinger equation applies to atoms and electrons as well as to macroscopic objects such as cats and human friends. Nothing in the theory tells us what is to be analyzed through unitary evolutions or the formalism of measurement operators.
If we now imagine two superobservers, described by Alice and Bob, each of them measuring their own laboratory containing their respective friends, Charlie and Debbie and the systems they measure, the statistics obtained by Alice and Bob should be classical, that is, should not be able to violate any Bell inequality. After all, by the measurement postulate, all non-classicality of the system should have been extinguished when Charlie and Debbie performed their measurements. Mathematically, we can describe this situation by a set of hypotheses. The first hypothesis is the absoluteness of events (AoE). As in a Bell experiment, what we have experimental access to is probability distribution p(a,b|x,y), the measurement results of Alice and Bob, given that they measured a certain observable. But if measurements made by observers really are absolute events, then this observable probability should come from a joint probability in which Charlie and Debbie's measurement results can also be defined. When combined with the assumptions of measurement independence and no-signalling, AoE leads to experimentally testable constraints, Bell inequalities that are violated by quantum correlations, thus proving the incompatibility of quantum theory with the conjunction of such assumptions.
In this paper, we show that we can relax the AoE assumption and still obtain quantum violations of the corresponding Bell inequalities. By considering two different and complementary manners to quantify the relaxation of AoE, we quantify how much the predictions from an observer and a superobserver should disagree in order to reproduce the quantum predictions for such an experiment. In fact, as we prove, to reproduce the possible correlations allowed by quantum mechanics, this deviation has to be maximum, corresponding to the case where the measurement results of Alice and Charlie or Bob and Debbie are completely uncorrelated. In other terms, quantum theory allows for maximally non-absolute events.
 D. Bohm and J. Bub, A proposed solution of the measurement problem in quantum mechanics by a hidden variable theory, Reviews of Modern Physics 38, 453 (1966).
 G. Hooft, The free-will postulate in quantum mechanics, arXiv preprint quant-ph/0701097 (2007).
 H. Price, Toy models for retrocausality, Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 39, 752 (2008).
 P. A. Guérin, V. Baumann, F. Del Santo, and Č. Brukner, A no-go theorem for the persistent reality of Wigner's friends perception, Communications Physics 4, 1 (2021).
 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).
 M. Żukowski and M. Markiewicz, Physics and metaphysics of Wigner's friends: Even performed premeasurements have no results, Physical Review Letters 126, 130402 (2021).
 K.-W. Bong, A. Utreras-Alarcón, F. Ghafari, Y.-C. Liang, N. Tischler, E. G. Cavalcanti, G. J. Pryde, and H. M. Wiseman, A strong no-go theorem on the Wigner's friend paradox, Nature Physics 16, 1199 (2020).
 Z.-P. Xu, J. Steinberg, H. C. Nguyen, and O. Gühne, No-go theorem based on incomplete information of Wigner about his friend (2021), arXiv:2111.15010 [quant-ph].
 Veronika Baumann, Flavio Del Santo, Alexander R. H. Smith, Flaminia Giacomini, Esteban Castro-Ruiz, and Caslav Brukner, Generalized probability rules from a timeless formulation of Wigner’s friend scenarios, Quantum 5, 594 (2021).
 J. S. Bell, On the einstein podolsky rosen paradox, Physics Physique Fizika 1, 195 (1964).
 M. J. Hall, Local deterministic model of singlet state correlations based on relaxing measurement independence, Physical review letters 105, 250404 (2010a).
 R. Chaves, R. Kueng, J. B. Brask, and D. Gross, Unifying framework for relaxations of the causal assumptions in bell's theorem, Phys. Rev. Lett. 114, 140403 (2015).
 M. J. Hall and C. Branciard, Measurement-dependence cost for bell nonlocality: Causal versus retrocausal models, Physical Review A 102, 052228 (2020).
 R. Chaves, G. Moreno, E. Polino, D. Poderini, I. Agresti, A. Suprano, M. R. Barros, G. Carvacho, E. Wolfe, A. Canabarro, R. W. Spekkens, and F. Sciarrino, Causal networks and freedom of choice in bell's theorem, PRX Quantum 2, 040323 (2021).
 M. Fitzi, E. Hänggi, V. Scarani, and S. Wolf, The non-locality of n noisy popescu–rohrlich boxes, Journal of Physics A: Mathematical and Theoretical 43, 465305 (2010).
 J. I. De Vicente, On nonlocality as a resource theory and nonlocality measures, Journal of Physics A: Mathematical and Theoretical 47, 424017 (2014).
 E. Wolfe, D. Schmid, A. B. Sainz, R. Kunjwal, and R. W. Spekkens, Quantifying bell: The resource theory of nonclassicality of common-cause boxes, Quantum 4, 280 (2020).
 I. Šupić, R. Augusiak, A. Salavrakos and A. Acín, Self-testing protocols based on the chained Bell inequalities, New Journal of Physics 18, 035013 (2016).
 Howard M. Wiseman, Eric G. Cavalcanti, and Eleanor G. Rieffel, "A "thoughtful" Local Friendliness no-go theorem: a prospective experiment with new assumptions to suit", Quantum 7, 1112 (2023).
 J. Allam and A. Matzkin, "From observer-dependent facts to frame-dependent measurement records in Wigner friend scenarios", Europhysics Letters 143 6, 60001 (2023).
 Davide Poderini, Giovanni Rodari, George Moreno, Emanuele Polino, Ranieri Nery, Alessia Suprano, Cristhiano Duarte, Fabio Sciarrino, and Rafael Chaves, "Device-independent witness for the nonobjectivity of quantum dynamics", Physical Review A 108 3, 032201 (2023).
 Thaís M. Acácio and Cristhiano Duarte, "Analysis of Neural Network Predictions for Entanglement Self-Catalysis", Brazilian Journal of Physics 52 6, 189 (2022).
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