The authors study an extension of the coupling method from classical probability theory to quantum probability. Given two normal states \(\varphi,\psi\), inspired by a method introduced by R. Duvenhage [J. Math. Anal. Appl. 343, No. 1, 175–181 (2008; Zbl 1151.37008)] and F. Fidaleo [Infin. Dimens. Anal. Quantum Probab. Relat. Top. 12, No. 2, 307–320 (2009; Zbl 1248.37010)], they define a coupling state \(\hat\varphi\) on \({\mathcal M}\otimes{\mathcal M}'\), where \({\mathcal M}'\) is the commutant of \({\mathcal M}\) in a standard representation in the standard Hilbert space, of \(\varphi\) and the opposite state \(\psi'\) on \({\mathcal M}'\). With their definition, they show that considering a suitable projection \(p_\Delta\) in \({\mathcal M}\otimes{\mathcal M}'\), called the diagonal projection, they obtain the inequality \(\| \varphi-\psi\| \leq 4 \left( 1-\hat\varphi(p_\Delta)\right)^{1/2}\). This allows them to estimate convergence rates by analyzing couplings. For a given tensor dilation, they construct a self-coupling Markov operator. It turns out that their coupling is a dual version of the extended dual transition operator studied by R. Gohm et al. [Ergodic Theory Dyn. Syst. 26, No. 5, 1521–1548 (2006; Zbl 1121.81087)]. They also show that this coupling is successful if and only if the dilation is asymptotically complete.