  We introduce and analyze a task that we call Markovianization, in which a
tripartite quantum state is transformed to a quantum Markov chain by a
randomizing operation on one of the three subsystems. We consider cases where
the initial state is the tensor product of $n$ copies of a tripartite state
$\rho^{ABC}$, and is transformed to a quantum Markov chain conditioned by $B^n$
with a small error, using a random unitary operation on $A^n$. In an asymptotic
limit of infinite copies and vanishingly small error, we analyze the
Markovianizing cost, that is, the minimum cost of randomness per copy required
for Markovianization. For tripartite pure states, we derive a single-letter
formula for the Markovianizing costs. Counterintuitively, the Markovianizing
cost is not a continuous function of states, and can be arbitrarily large even
if the state is close to a quantum Markov chain. Our results have an
application in analyzing the cost of resources for simulating a bipartite
unitary gate by local operations and classical communication.
