  A quantum switch is a superoperator that, in general, creates a superposition
of various causal orders of two or more quantum dynamics that are all divisible
in the complete positivity (CP) sense. We introduce a process that we term as
the universal quantum switch (UQS), which unlike conventional quantum switches,
allows for the construction of a quantum switch that can superpose different
causal orders of any set of quantum dynamics, regardless of their
CP-divisibility. Our approach also enables the construction of a quantum switch
while considering a single environment connected with the system, in contrast
to the traditional one. Moreover, we show the UQS provides more advantages in
performance for a certain state discrimination task compared to traditional
quantum switches. The next question that we address is the following: What is
the CP-divisibility characteristic of a dynamics built by acting a quantum
switch on CP-divisible or -indivisible dynamics? In this regard, an example is
presented where the dynamics created by the action of the UQS on two
CP-indivisible dynamics is CP-indivisible. Additionally, we prove a necessary
and sufficient condition for the channel created by acting the traditional
quantum switch on two CP-divisible dynamics to be CP-divisible. Furthermore, we
present some examples of CP-divisible dynamics on which, when the usual quantum
switch is operated, the resulting dynamics not only becomes CP-indivisible but
also turns into P-indivisible. Our findings demonstrate that quantum switches
can build CP-divisible, CP-indivisible, and even P-indivisible dynamics from
CP-divisible dynamics, underscoring the versatility of this technique.
