Connecting extended Wigner's friend arguments and noncontextuality
Laurens Walleghem, Yìlè Yīng, Rafael Wagner, David Schmid
备注：
20 pages + appendix, 16 figures, all comments welcome! The second half of this work is a follow-up work to arXiv:2310.06976v2. Main changes in v2 compared to v1 are: moved some parts to the appendix (mainly in Sections III.D and III.E)
The Local Friendliness argument is an extended Wigner's friend no-go theorem that provides strong constraints on the nature of reality -- stronger even than those imposed by Bell's theorem or by noncontextuality arguments. In this work, we prove a variety of connections between Local Friendliness scenarios and Kochen-Specker noncontextuality. Specifically, we first show how one can derive new Local Friendliness inequalities using known tools and results from the literature on Kochen-Specker noncontextuality. In doing so, we provide a new derivation for some of the facets of the Local Friendliness polytope, and we prove that this polytope is equal to the Bell polytope in a wide range of extended Wigner's friend scenarios with multipartite agents and sequential measurements. We then show how any possibilistic Kochen-Specker argument can be mathematically translated into a related proof of the Local Friendliness no-go theorem. In particular, we construct a novel kind of Local Friendliness scenario where a friend implements several compatible measurements (or joint measurements of these) in between the superobserver's operations on them. We illustrate this with the well-known 5-cycle and Peres-Mermin contextuality arguments.
We investigate the relationship between two properties of quantum transformations often studied in popular subtheories of quantum theory: covariance of the Wigner representation of the theory and the existence of a transformation noncontextual ontological model of the theory. We consider subtheories of quantum theory specified by a set of states, measurements and transformations, defined specifying a group of unitaries, that map between states (and measurements) within the subtheory. We show that if there exists a Wigner representation of the subtheory which is covariant under the group of uni…
Proietti et al. (arXiv:1902.05080) reported on an experiment designed to settle, or at least to throw light upon, the paradox of Wigner's friend. Without questioning the rigor or ingenuity of the experimental protocol, I argue that its relevance to the paradox itself is rather limited.
It is shown that the absence of an objective existence of the results of quantum measurements cannot be proved by known experiments. There are also general arguments confirming this conclusion.
This is a comment on the paper by Hagar and Hemmo (quant-ph/0512095) in which they suggest that information-theoretic approaches to quantum theory are incomplete.
The extended Wigner's friend problem deals with two Observers each measuring a sealed laboratory in which a friend is making a quantum measurement. We investigate this problem by relying on the basic rules of quantum mechanics as exposed by Feynman in the well-known "Feynman Lectures on Physics". Although recent discussions have suggested that the extended Wigner's friend problem cannot consistently be described by quantum theory, we show here that a straightforward application of these standard rules results in a non-ambiguous and consistent account of the measurement outcomes for all agents …
The quantum measurement problem can be regarded as the tension between the two alternative dynamics prescribed by quantum mechanics: the unitary evolution of the wave function and the state-update rule (or "collapse") at the instant a measurement takes place. The notorious Wigner's friend gedankenexperiment constitutes the paradoxical scenario in which different observers (one of whom is observed by the other) describe one and the same interaction differently, one --the Friend-- via state-update and the other --Wigner-- unitarily. This can lead to Wigner and his friend assigning different prob…
In a joint paper Jeff Bub and Itamar Pitowski argued that the quantum state represents `the credence function of a rational agent [...] who is updating probabilities on the basis of events that occur'. In the famous thought experiment designed by Wigner, Wigner's friend performs a measurement in an isolated laboratory which in turn is measured by Wigner. Here we consider Wigner's friend as a rational agent and ask what her `credence function' is. We find experimental situations in which the friend can convince herself that updating the probabilities on the basis of events that happen solely in…
"Wigner's friend" refers to a quantum process of which different observers, following the rules of quantum mechanics, give contradictory descriptions. Lostaglio and Bowles have recently claimed to describe a classical system showing the same effect. It is argued that this claim is not justified. it fails to take into account the different meanings of probability in classical and quantum mechanics.
According to QBism, quantum states, unitary evolutions, and measurement operators are all understood as personal judgments of the agent using the formalism. Meanwhile, quantum measurement outcomes are understood as the personal experiences of the same agent. Wigner's conundrum of the friend, in which two agents ostensibly have different accounts of whether or not there is a measurement outcome, thus poses no paradox for QBism. Indeed the resolution of Wigner's original thought experiment was central to the development of QBist thinking. The focus of this paper concerns two very instructive mod…
Recent developments in elementary quantum mechanics have seen a number of extraordinary claims regarding quantum behaviour, and even questioning internal consistency of the theory. These are, we argue, different disguises of what Feynman described as quantum theory's "only mystery".
The place and role of an Observer in quantum mechanics has been a subject of an ongoing debate since the theory's inception. Wigner brought this question to the fore in a celebrated scenario in which a super-Observer observes a Friend making a measurement. Here we briefly review why this \e{Wigner Friend scenario} has been taken to require the introduction of the Observer's consciousness, or alternatively to show the inconsistency of quantum measurement theory. We will argue that quantum theory can consistently leave observers outside its narrative, by making only minimal assumptions about how…
A general argument is presented against relativistic, unitary, single-outcome quantum mechanics. This is achieved by combining the Wigner's Friend thought experiment with measurements on a Greenberger-Horne-Zeilinger (GHZ) state, and describing the evolution of the quantum state in various inertial frames. Assuming unitary quantum mechanics and single outcomes, the result is that the Born rule must be violated in some inertial frame: in that frame, outcomes are obtained for which no corresponding term exists in the pre-measurement wavefunction.
Wigner Friend scenarios -- in which an external agent describes quantum mechanically a laboratory in which a Friend is making a measurement -- give rise to possible inconsistencies due to the ambiguous character of quantum measurements. In this work, we investigate Wigner Friend scenarios in which the external agents can probe in a non-invasive manner the dynamics inside the laboratories. We examine probes that can be very weakly coupled to the systems measured by the Friends, or to the pointers or environments inside the laboratories. These couplings, known as Weak Measurements, are asymptoti…
In 1962, Eugene P. Wigner introduced a thought experiment that highlighted the incompatibility in quantum theory between unitary evolution and wave function reduction in a measurement. This work resulted in a class of thought experiments often called Wigner's Friend Scenarios, which have been providing insights over many frameworks and interpretations of quantum theory. Recently, a no-go theorem obtained by Daniela Frauchiger and Renato Renner brought attention back to the Wigner's Friend and its potential of putting theories to test. Many answers to this result pointed out how timing in the t…
The purpose of this comment is to show that a reinterpretation of the results from the Letter: "Physics and Metaphysics of Wigner's Friends: Even performed pre-measurements have no results" allows for reaching the conclusion "pre-measurements have no resul" [arXiv:2003.07464] based only on postulates of quantum mechanics without additional assumptions on irreversibility. Additionally, with supplementary reasoning based on Bell's theorem, one can show that unitary decoherence cannot be solely responsible for the quantum-to-classical transition, and an additional irreversibility model is require…
Extended Wigner's Friend Scenarios with Agent-like Observers on Quantum Computers
Institute for Theoretical Physics, ETH Zürich（苏黎世联邦理工学院理论物理研究所）；Quantum and Advanced Technologies Research Institute, Griffith University（格里菲斯大学量子与先进技术研究院）
"The unambiguous account of proper quantum phenomena must, in principle, include a description of all relevant features of experimental arrangement" (Bohr). The measurement process is composed of pre-measurement (quantum correlation of the system with the pointer variable), and an irreversible decoherence via interaction with an environment. The system ends up in a probabilistic mixture of the eigenstates of the measured observable. For the pre-measurement stage, any attempt to introduce an 'outcome' leads, as we show, to a logical contradiction, $1=i$. This nullifies claims that a modified co…
The Wigner's friend paradox concerns one of the most puzzling problems of quantum mechanics: the consistent description of multiple nested observers. Recently, a variation of Wigner's gedankenexperiment, introduced by Frauchiger and Renner, has lead to new debates about the self-consistency of quantum mechanics. At the core of the paradox lies the description of an observer and the object it measures as a closed system obeying the Schrödinger equation. We revisit this assumption to derive a necessary condition on a quantum system to behave as an observer. We then propose a simple single-photon…
The notorious Wigner's friend thought experiment (and modifications thereof) has in recent years received renewed interest especially due to new arguments that force us to question some of the fundamental assumptions of quantum theory. In this paper, we formulate a no-go theorem for the persistent reality of Wigner's friend's perception, which allows us to conclude that the perceptions that the friend has of her own measurement outcomes at different times cannot "share the same reality", if seemingly natural quantum mechanical assumptions are met. More formally, this means that, in a Wigner's …
The original Wigner's friend paradox is a gedankenexperiment involving an observer described by an external agent. The paradox highlights the tension between unitary evolution and collapse in quantum theory, and is sometimes taken as requiring a reassessment of the notion of objective reality. In this note however we present a classical toy model in which (i) The contradicting predictions at the heart of the thought experiment are reproduced (ii) Every system is in a well-defined state at all times. The toy model shows how puzzles such as Wigner's friend's experience of being in a superpositio…
The notion of measurements is central for many debates in quantum mechanics. One critical point is whether a measurement can be regarded as an absolute event, giving the same result for any observer in an irreversible manner. Using ideas from the gedankenexperiment of Wigner's friend it has been argued that, when combined with the assumptions of locality and no-superdeterminism, regarding a measurement as an absolute event is incompatible with the universal validity of quantum mechanics. We consider a weaker assumption: is the measurement event realised relatively to the observer when he only …
This is an analysis of the recently published article `Quantum theory cannot consistently describe the use of itself' by D. Frauchiger and R. Renner~\cite{1}. Here I decipher the paradox and analyze it from the point of view of de Broglie-Bohm hidden variable theory (i.e., Bohmian mechanics). I also analyze the problem from the perspective obtained by the Copenhagen interpretation (i.e., the Bohrian interpretation) and show that both views are self consistent and do not lead to any contradiction with a `single-world' description of quantum theory.
It is well-known that the law of total probability does not hold in general in quantum theory. However, the recent arguments on some of the fundamental assumptions in quantum theory based on the extended Wigner's Friend scenario show a need to clarify how the law of total probability should be formulated in quantum theory and under what conditions it still holds. In this work, the definition of conditional probability in quantum theory is extended to POVM measurements. Rule to assign two-time conditional probability is proposed for incompatible POVM operators, which leads to a more general and…
The decoherence interpretation of quantum measurements is applied to Wigner's friend experiments. A framework in which all the experimental outcomes arise from unitary evolutions is proposed. Within it, a measurement is not completed until an uncontrolled environment monitorizes the state composed by the system, the apparatus and the observer. The (apparent) wave-function collapse and the corresponding randomness result from tracing out this environment; it is thus the ultimate responsible for the emergence of definite outcomes. Two main effects arise from this fact. First, external interferen…
In a recent paper, Żukowski and Markiewicz showed that Wigner's Friend (and, by extension, Schrödinger's Cat) can be eliminated as physical possibilities on purely logical grounds. I validate this result and demonstrate the source of the contradiction in a simple experiment in which a scientist S attempts to measure the position of object $|O\rangle = |A\rangle_S + |B\rangle_S$ by using measuring device M chosen so that $|A\rangle_M \approx |A\rangle_S$ and $|B\rangle_M \approx |B\rangle_S$. I assume that the measurement occurs by quantum amplification without collapse, in which M can entangle…
We argue that Wigner's friend thought experiment does not support observer dependence of quantum states. An analysis in terms of history vectors suggests that quantum collapse is to be understood as collapse of histories rather than collapse of states.
The measurement problem is seen as an ambiguity of quantum mechanics, or, beyond that, as a contradiction within the theory: Quantum mechanics offers two conflicting descriptions of the Wigner's-friend experiment. As we argue in this note there are, however, obstacles from within quantum mechanics and regarding our perspective onto doing physics towards fully describing a measurement. We conclude that the ability to exhaustively describe a measurement is an assumption necessary for the common framing of the measurement problem and ensuing suggested solutions.
Does quantum theory apply at all scales, including that of observers? New light on this fundamental question has recently been shed through a resurgence of interest in the long-standing Wigner's friend paradox. This is a thought experiment addressing the quantum measurement problem -- the difficulty of reconciling the (unitary, deterministic) evolution of isolated systems and the (non-unitary, probabilistic) state update after a measurement. Here, by building on a scenario with two separated but entangled friends introduced by Brukner, we prove that if quantum evolution is controllable on the …
We present a discussion of the extended Wigner's friend thought experiment proposed by Frauchiger and Renner in [1]. We show by using various arguments, including textbook quantum mechanics and the ontological approach of Contexts, Systems, Modalities (CSM), that no contradiction arises if one admits that agents must agree on what is considered as a system and what is not. In such a contextually objective approach of quantum mechanics, the apparent contradiction is automatically removed. We also discuss why this mutual agreement between agents is already implicit in the standard formulations o…
It is commonly expected that quantum theory is universal, in that it describes the world at all scales. Yet, quantum effects at the macroscopic scale continue to elude our experimental observation. This fact is commonly attributed to decoherence processes affecting systems of sufficiently large number of constituent subsystems leading to an effective macro-scale beyond which a quantum description of the whole system becomes superfluous. Here, we show both theoretically and experimentally that the existence of such a scale is unjustifiable from an information-theoretic perspective. We introduce…
