Stability of Consensus Quantum Networks in General Dimension

In this study, we deal with quantum networked systems consisting of
$N$
quantum subsystems having
$D$
states. In previous studies, it was proved that a symmetric-state consensus (SSC) can be attained by an algorithm composed of local measurements and a local feedback control in cases of
$D=2$
and 3. However, a proof for general
$D$
remained an open problem. In this study, we rigorously prove that an SSC can be attained by the same algorithm in the case of general
$D$
.