Extending the Agent in QBism
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Extending the Agent in QBism Jacques Pienaar1 Received: 3 July 2020 / Accepted: 26 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract According to the subjective Bayesian interpretation of quantum mechanics (QBism), the instruments used to measure quantum systems are to be regarded as an extension of the senses of the agent who is using them, and quantum states describe the agent’s expectations for what they will experience through these extended senses. How can QBism then account for the fact that (i) instruments must be calibrated before they can be used to ‘sense’ anything; (ii) some instruments are more precise than others; (iii) more precise instruments can lead to discovery of new systems? Furthermore, is the agent ‘incoherent’ if they prefer to use a less precise instrument? Here we provide answers to these questions. Keywords Quantum information · Quantum foundations · Quantum measurement
1 Introduction QBism is an interpretation of quantum mechanics according to which quantum states quantify an Agent’s subjective degrees of belief about their future personal experiences (Events). According to QBism, quantum theory itself is not meant to describe an external world independently of observation; rather, quantum theory is best understood as a normative addition to standard probability theory, that is to say, it is a rule constraining an Agent’s subjective probability assignments for the results of measurements on quantum systems. Normative rules are founded upon the principle of coherence: an Agent must strive to hold beliefs that are ‘Dutch book coherent’ (that is, which would not imply a sure loss if the Agent were to make bets according to them), and that are coherent with the world (i.e. that accommodate lessons learned from past experiences). QBism is thereby able to avoid at least one aspect of the measurement problem, the ‘problem of definite results’, which seeks to explain why a measurement * Jacques Pienaar [email protected] 1
QBism group, University of Massachusetts Boston, 100 Morrissey Boulevard, Boston, MA 02125, USA
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of a quantum system leads to a single result. QBism takes the personal experience of any Agent as fundamental; as such, the occurrence of definite results is a basic postulate that does not need to be derived or explained within the theory. Moreover, by insisting that the relevant definite results are Events that are personal to the Agent who experiences them, QBism also evades the teeth of the dilemmas posed by the EPR ‘paradox’ and Bell’s theorem [1]. Despite these advantages, QBism’s radical stance on the nature of measurement renders it vulnerable to another line of attack, concerning the status of the measuring apparatus. The question is a simple and natural one: should the physical devices that we scientists employ in order to obtain the results of our measurements be themselves treated as measured systems external to the Agent who uses them, or should they be treated as bei
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