TL;DR
This paper demonstrates that the Pryce photon position operator uniquely satisfies minimal properties for a one-photon position operator, and shows that states can be localized with arbitrary precision despite non-commuting components.
Contribution
It identifies the unique operator fulfilling minimal criteria for photon localization and analyzes its properties, including localization precision.
Findings
The Pryce operator is the unique minimal-property photon position operator.
States can be localized with arbitrary precision despite non-commuting components.
The operator's properties are consistent with photon localization requirements.
Abstract
We show that there is only one operator having some minimal properties enabling it to be a one photon position operator. These proerties are stated, and the solution is shown to be the photon position operator proposed by Pryce. This operator has non-commuting components. Nevertheless, it is shown that one can find states localized with an arbitrary precision.
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