  We consider two one-dimensional quantum $XX$ magnets linked by a periodically
driven quantum point contact (QPC). If magnets are initially polarized in
opposite directions, one expects that a spin current through the QPC will
establish. It has been shown recently [Phys. Rev. B 103, L041405 (2021)] that,
in fact, when the driving frequency exceeds a critical value, the current halts
completely, the QPC being effectively insulating. Here we enquire how this
picture is affected by quantum dephasing. Our findings reveal that any non-zero
dephasing restores the current.
