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Entanglement is considered as resource in quantum
information processing tasks. However, computation of the quantity is
often challenging, particularly when the system is of large size, or
when it is described by a mixed state -- for example, in the presence
of noise. In this talk, we discuss how entanglement in a noisy
topological code of large size, such as the Kitaev's surface code, or
the topological color code, can be estimated. We demonstrate how
graph
states can be employed to determine entanglement between two distant
qubits in these systems, and discuss how insight about the distance
dependence of entanglement can be obtained. We also discuss an
experimentally accessible methodology to estimate non-trivial lower
bounds of entanglement in these systems. |