 Elaborating on this, let us take a composite system \(\alpha \beta\), whose component subsystems \(\alpha\) and \(\beta\) are represented by the Hilbert spaces \(\mathcal{H}^{\alpha}\) and \(\mathcal{H}^{\beta}\), respectively, and consider a property represented by the projector \(\Pi^{\alpha}\) defined on \(\mathcal{H}^{\alpha}\). It is usual to assume that \(\Pi^{\alpha}\) represents the same property as that represented by \(\Pi^{\alpha} \otimes I^{\beta}\) defined on \(\mathcal{H}^{\alpha} \otimes \mathcal{H}^{\beta}\), where \(I^{\beta}\) is the identity operator on \(\mathcal{H}^{\beta}\). This assumption is based on the observational indistinguishability of the magnitudes represented by \(\Pi^{\alpha}\) and \(\Pi^{\alpha} \otimes I^{\beta}\): if the \(\Pi^{\alpha}\)-measurement has a certain outcome, then the \(\Pi^{\alpha} \otimes I^{\beta}\)-measurement has exactly the same outcome.