NECESSITY OF SINE-COSINE JOINT MEASUREMENT

The quantum measurement of trigonometric variables is revisited. We sh ow that the probability distributions of the sine and cosine operators of Susskind and Glogower [Physics 1, 49 (1964)] suffer unphysical fea tures for nonclassical states. We suggest that any measurement of a tr igonometric variable needs necessarily a joint measurement of the two cosine-sine phase quadratures. In this way unphysical quantum statisti cs are avoided, and no violation of the trigonometric calculus occurs for expected values. We show that this trigonometric measurement can b e defined in general terms in the framework of quantum estimation theo ry.