Heisenberg’s uncertainty principle limits the precision with which two observables that do not commute with each other can be simultaneously measured. The Wigner-Araki-Yanase (WAY) theorem goes further. If observables A and B do not commute, and if observable A is conserved, observable B cannot be measured with arbitrary precision even if A is not measured at all. In its original 1960 formulation, the WAY theorem applied only to observables, such as spin, whose possible values are discrete and bounded. Now Yui Kuramochi of Kyushu University and Hiroyasu Tajima of the University of Electro-Communications—both in Japan—have proven that the WAY theorem also encompasses observables, such as position, that are continuous and unbounded [1]. Besides resolving the decades-long problem of how to deal with such observables, the extension will likely find practical applications in quantum optics.
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