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Entanglement cost of implementing controlled-unitary operations

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arxiv 1008.1128 v2 pith:4MABK4TP submitted 2010-08-06 quant-ph

Entanglement cost of implementing controlled-unitary operations

classification quant-ph
keywords operationsentanglementcontrolled-unitarycostimplementingloccminimumarises
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We investigate the minimum entanglement cost of the deterministic implementation of two-qubit controlled-unitary operations using local operations and classical communication (LOCC). We show that any such operation can be implemented by a three-turn LOCC protocol, which requires at least 1 ebit of entanglement when the resource is given by a bipartite entangled state with Schmidt number 2. Our result implies that there is a gap between the minimum entanglement cost and the entangling power of controlled-unitary operations. This gap arises due to the requirement of implementing the operations while oblivious to the identity of the inputs.

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