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Quantum graphs as quantum relations. (arXiv:1506.03892v3 [math.OA] UPDATED)
来源于:arXiv
The "noncommutative graphs" which arise in quantum error correction are a
special case of the quantum relations introduced in [N. Weaver, Quantum
relations, Mem. Amer. Math. Soc. 215 (2012), v-vi, 81-140]. We use this
perspective to interpret the Knill-Laflamme error-correction conditions [E.
Knill and R. Laflamme, Theory of quantum error-correcting codes, Phys. Rev. A
55 (1997), 900-911] in terms of graph-theoretic independence, to give intrinsic
characterizations of Stahlke's noncommutative graph homomorphisms [D. Stahlke,
Quantum source-channel coding and non-commutative graph theory,
arXiv:1405.5254] and Duan, Severini, and Winter's noncommutative bipartite
graphs [R. Duan, S. Severini, and A. Winter, Zero-error communication via
quantum channels, noncommutative graphs, and a quantum Lovasz number, IEEE
Trans. Inform. Theory 59 (2013), 1164-1174], and to realize the noncommutative
confusability graph associated to a quantum channel as the pullback of a
diagonal relation.
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