  Distributed quantum computing leverages the collective power of multiple
quantum devices to perform computations exceeding the capabilities of
individual quantum devices. A currently studied technique to enable this
distributed approach is wire cutting, which decomposes a quantum circuit into
smaller subcircuits by cutting their connecting wires. These subcircuits can
then be executed on distributed devices, and their results are classically
combined to reconstruct the original computation's result. However, wire
cutting requires additional circuit executions to preserve result accuracy,
with their number growing exponentially with each cut. Thus, minimizing this
sampling overhead is crucial for reducing the total execution time. Employing
shared non-maximally entangled (NME) states between distributed devices reduces
this overhead for single wire cuts, moving closer to ideal teleportation with
maximally entangled states. Extending this approach to jointly cutting multiple
wires using NME states remained unexplored. Our paper addresses this gap by
investigating the use of NME states for joint wire cuts, aiming to reduce the
sampling overhead further. Our three main contributions include (i) determining
the minimal sampling overhead for this scenario, (ii) analyzing the overhead
when using composite NME states constructed from smaller NME states, and (iii)
introducing a wire cutting technique that achieves the optimal sampling
overhead with pure NME states, paving the way towards wire cutting with
arbitrary NME states.
