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Limits on the storage of quantum information in a volume of space

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Figure

Figure 1: Decomposition of the lattice in the definitions of local approximate quantum error correction.B shields A from C by a distance at least ℓ, and R represents the purifying space of the code.
Figure 2: Decomposition of the lattice in 2D leading to the tradeoff bound of Theorem 9.
Figure 3: Construction of the largest correctable square by successively adding rings of size at most d.
Figure 4: Decomposition of the lattice used for Theorem 13.
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