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arXiv · 2210.11100

The photodetector, the heterodyne instrument, and the principle of instrument autonomy

Christopher S. Jackson
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Abstract

Measuring instruments, especially ones that observe continually over time, have a reality to them that is independent of the states that stimulate their senses. This is the Principle of Instrument Autonomy. Although the mathematical concept of an instrument implicitly embodies this principle, the conventional analysis of continual observation has become overwhelmingly focused on state evolution rather than on descriptions of instruments themselves. Because of this, it can be hard to appreciate that an instrument that observes for a finite amount of time has an evolution of its own, a stochastic evolution that precedes the Born rule and Schr\"odinger equation of the measured system. In this article, the two most established of the continually observing instruments, the Srinivas-Davies photodetector and the Goetsch-Graham-Wiseman heterodyne detector, are reviewed with an emphasis on the autonomous instrument evolution they define, made explicit by application of the recently introduced Kraus-operator distribution function. It is then pointed out how the heterodyne instrument evolution is a complete alternative to the original idea of energy quantization, where the usual ideas of \emph{temperature} and \emph{energy} of a \emph{state} are replaced by the \emph{time} and \emph{positivity} of the \emph{instrument}.

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Christopher S. Jackson. 2022-10-20. The photodetector, the heterodyne instrument, and the principle of instrument autonomy. https://arxiv.org/abs/2210.11100

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