As an application of the simultaneous and continuous measurement of noncommutative observables formulated in our previous paper [C. Jiang and G. Watanabe, Phys. Rev. A 102, 062216 (2020)], we propose a scheme to generate the pure ideal quadrature squeezed state in an one-dimensional harmonic oscillator system by the feedback control based on such type of measurement of noncommutative quadrature observables. We find that, by appropriately setting the strengths of the measurement and the feedback control, the pure ideal quadrature squeezed state with arbitrary squeezedness can be produced. This is in contrast to the scheme based on the single-observable measurement and the feedback control, where only nonideal squeezed state with squeezing of the measured quadrature are produced.
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