  In this thesis, we investigate two different aspects of entanglement and
classical communication in distributed quantum computation (DQC).
  In the first part, we analyze implementable computation over a given quantum
network resource by introducing a new concept, quantum network coding for
quantum computation. We consider a setting of networks where quantum
communication for each edge of a network is restricted to sending one-qubit,
but classical communication is unrestricted. Specifically, we analyze
implementable $k$-qubit unitary operations over a certain class of networks,
called cluster networks. We show that any two-qubit unitary operation is
implementable over the butterfly network and the grail network, which are
fundamental primitive networks for network coding. We also obtain necessary and
sufficient conditions for the probabilistic implementability of unitary
operations over cluster networks.
  In the second part, we investigate resource tradeoffs in DQC. First, we show
that entanglement required for local state discrimination can be substituted by
less entanglement by increasing the rounds of classical communication. Second,
we develop a new framework of deterministic joint quantum operations by using a
causal relation between the outputs and inputs of the local operations without
predefined causal order, called "classical communication" without predefined
causal order (CC*). We show that local operations and CC* (LOCC*) is equivalent
to the separable operation (SEP). This result indicates that
entanglement-assisted LOCC implementing SEP can be simulated by LOCC* without
entanglement. We also investigate the relationship between LOCC* and another
formalism for deterministic joint quantum operations without assuming
predefined causal order based on the quantum process formalism. As a result, we
construct an example of non-LOCC SEP by using LOCC*.
