 In more detail, the state of \(S\) with respect to the reference system \(R\) is denoted by \(\varrho_{R}^{S}\). In the special case in which \(R\) coincides with \(S\), the state \(\varrho_{S}^{S}\) is called “the state of S with respect to itself”. If the system \(S\) is contained in a system \(A\), the state \(\varrho_{A}^{S}\) is defined as the density operator that can be derived from \(\varrho_{A}^{A}\) by taking the partial trace over the degrees of freedom in \(A\) that do not pertain to \(S\):