Local implementation of nonlocal operations of block forms

Abstract

We investigate the local implementation of nonlocal operations with the block matrix form, and propose a protocol for any diagonal or offdiagonal block operation. This method can be directly generalized to the two-party multiqubit case and the multiparty case. Especially, in the multiparty cases, any diagonal block operation can be locally implemented using the same resources as the multiparty control-U operation discussed in Ref. [Eisert et al., Phys. Rev. A 62, 052317(2000)]. Although in the bipartite case, this kind of operations can be transformed to control-U operation using local operations, these transformations are impossible in the multiparty cases. We also compare the local implementation of nonlocal block operations with the remote implementation of local operations, and point out a relation between them.

7 pages, 3 figures

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Cited by in corpus (6)

• Efficient implementation of bipartite nonlocal unitary gates using prior entanglement and classical communication
• Entanglement requirements for implementing bipartite unitary operations
• A Coding Theorem for Bipartite Unitaries in Distributed Quantum Computation
• Complexity of causal order structure in distributed quantum information processing and its trade-off with entanglement
• Investigating the implementation of restricted sets of multiqubit operations on distant qubits: a communication complexity perspective
• Asymptotic Compressibility of Entanglement and Classical Communication in Distributed Quantum Computation