  A restriction in the quality and quantity of available qubits presents a
substantial obstacle to the application of near-term and early fault-tolerant
quantum computers in practical tasks. To confront this challenge, some
techniques for effectively augmenting the system size through classical
processing have been proposed; one promising approach is quantum circuit
cutting. The main idea of quantum circuit cutting is to decompose an original
circuit into smaller sub-circuits and combine outputs from these sub-circuits
to recover the original output. Although this approach enables us to simulate
larger quantum circuits beyond physically available circuits, it needs
classical overheads quantified by the two metrics: the sampling overhead in the
number of measurements to reconstruct the original output, and the number of
channels in the decomposition. Thus, it is crucial to devise a decomposition
method that minimizes both of these metrics, thereby reducing the overall
execution time. This paper studies the problem of decomposing the parallel
$n$-qubit identity channel, i.e., $n$-parallel wire cutting, into a set of
local operations and classical communication; then we give an optimal
wire-cutting method comprised of channels based on mutually unbiased bases,
that achieves minimal overheads in both the sampling overhead and the number of
channels, without ancilla qubits. This is in stark contrast to the existing
method that achieves the optimal sampling overhead yet with ancilla qubits.
Moreover, we derive a tight lower bound of the number of channels in parallel
wire cutting without ancilla systems and show that only our method achieves
this lower bound among the existing methods. Notably, our method shows an
exponential improvement in the number of channels, compared to the
aforementioned ancilla-assisted method that achieves optimal sampling overhead.
