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, 9 (1), 3711

Quantum Theory Cannot Consistently Describe the Use of Itself

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Quantum Theory Cannot Consistently Describe the Use of Itself

Daniela Frauchiger et al. Nat Commun.

Abstract

Quantum theory provides an extremely accurate description of fundamental processes in physics. It thus seems likely that the theory is applicable beyond the, mostly microscopic, domain in which it has been tested experimentally. Here, we propose a Gedankenexperiment to investigate the question whether quantum theory can, in principle, have universal validity. The idea is that, if the answer was yes, it must be possible to employ quantum theory to model complex systems that include agents who are themselves using quantum theory. Analysing the experiment under this presumption, we find that one agent, upon observing a particular measurement outcome, must conclude that another agent has predicted the opposite outcome with certainty. The agents' conclusions, although all derived within quantum theory, are thus inconsistent. This indicates that quantum theory cannot be extrapolated to complex systems, at least not in a straightforward manner.

Conflict of interest statement

The authors declare no competing interests.

Figures

Fig. 1
Fig. 1
Wigner’s and Deutsch’s arguments. Agent F measures the spin S of a silver atom in the vertical direction, obtaining outcome z. From F’s perspective, S is then in one of the two pure states ψS given in (1). Agent W, who is outside of F’s lab, may instead regard that lab, including the agent F, as a big quantum system L (orange box). Wigner argued that, having no access to z, he would assign a superposition state ΨL of the form (3) to L. Deutsch later noted that agent W could in principle test this state assignment by applying a carefully designed measurement to L
Fig. 2
Fig. 2
Illustration of the Gedankenexperiment. In each round n = 0, 1, 2, … of the experiment, agent F¯ tosses a coin and, depending on the outcome r, polarises a spin particle S in a particular direction. Agent F then measures the vertical polarisation z of S. Later, agents W¯ and W measure the entire labs L¯ and L (where the latter includes S) to obtain outcomes w¯ and w, respectively. For the analysis of the experiment, we assume that all agents are aware of the entire procedure as specified in Box 1, but they are located at different places and therefore make different observations. Agent F, for instance, observes z but has no direct access to r. She may however use quantum theory to draw conclusions about r
Fig. 3
Fig. 3
Consistent reasoning as required by Assumption (C). If a theory T (such as quantum theory) enables consistent reasoning (C) then it must allow any agent A to promote the conclusions drawn by another agent A' to his own conclusions, provided that A' has the same initial knowledge about the experiment and reasons within the same theory T. A classical example of such recursive reasoning is the muddy children puzzle (here T is just standard logic; see ref. for a detailed account). The idea of using a physical theory T to describe agents who themselves use T has also appeared in thermodynamics, notably in discussions around Maxwell's demon
Fig. 4
Fig. 4
Circuit diagram representation of the Gedankenexperiment. The actions of the agents during the protocol correspond to isometries (boxes) that act on particular subsystems (wires). For example, the measurement of S by agent F in the second protocol step, which starts at time n:10, induces an isometry USL1020 from S to F’s lab L, analogous to the one defined by (2). The subsystems labelled by F¯, F, W¯, and W contain the agents themselves. Similarly, D¯, D, E¯, and E are “environment” subsystems, which include the agents’ measurement devices. The states of these subsystems depend on the measurement outcome, which is indicated by their label. For example, +12F is the state of F when the agent has observed z=+12

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