Events in quantum mechanics are maximally non-absolute

George Moreno1,2, Ranieri Nery1, Cristhiano Duarte1,3, and Rafael Chaves1,4

1International Institute of Physics, Federal University of Rio Grande do Norte, 59078-970, Natal, Brazil
2Departamento de Computação, Universidade Federal Rural de Pernambuco, 52171-900, Recife, Pernambuco, Brazil
3School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom
4School of Science and Technology, Federal University of Rio Grande do Norte, Natal, Brazil

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Abstract

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.

The measurement problem emerges from the incompatibility between two of the quantum postulates. On the one hand, we have the Schrödinger equation, which tells us that the evolution of the wave function is governed by a smooth and reversible unitary transformation. On the other side, we have the measurement postulate, telling us what is the probability of a certain result when a measurement is performed, implying the so-called collapse of the wavefunction, a non-unitary, abrupt and irreversible transformation.
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.

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