Ex10 13 / Discussion

This is the discussion related to the wiki page Ex10 13.

Local operations and classical communication (LOCC)

Anders B Madsen 25 Feb 2024 16:30

a)
LOCC operations are combinations of unitary operators and projections (measurement). So when applied to a subspace, LOCC operations can at most preserve the dimension of the subspace, never increase it.

b)
An unentangled state $\ket{\psi}$ has Schmidt rank 1, while any entangled state $\ket{\phi}$ has Schmidt rank at least 2, so no LOCC operation can convert $\ket{\psi}$ to $\ket{\phi}$.