Entanglement cost of implementing controlled-unitary operations

Abstract

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.

5 pages + 13 pages of appendix, comments welcome (published version)

References in corpus (4)

• The Uniqueness Theorem for Entanglement Measures
• On the capacities of bipartite Hamiltonians and unitary gates
• Binary search trees for generalized measurement
• Entanglement requirements for implementing bipartite unitary operations

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