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Lattice states are a class of quantum states that naturally generalize the fundamental set of Bell states. We apply recent results from quantum error correction and from one-way local operations and classical communication (LOCC) theory that are built on the structure theory of operator systems and operator algebras, to develop a technique for the construction of relatively small sets of lattice states not distinguishable by one-way LOCC schemes. We also present examples, show the construction extends to generalized Pauli states, and compare the construction to other recent work.

One-way LOCC indistinguishable lattice states via operator structures