Table 1 A table of prohibited qudit graph states.

From: Quantum LOSR networks cannot generate graph states with high fidelity

d

3

4

5, 7

Prime dimension

n

3,4,5,6

3,4,5

3,4

3

  1. For a given dimension d one can consider an n-partite graph state and ask whether Theorem 10 can be used to prove the impossibility of its preparation (see Supplementary Note 3 for discussions). This table identifies situations where alln-partite qudit graph states in dimension d cannot be prepared by the network.
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