Physics – Quantum Physics
Scientific paper
2010-10-21
Phys. Rev. A 84, 012333 (2011)
Physics
Quantum Physics
12 pages, 12 figures, the second version has been significantly expanded, and author ordering changed and the third version is
Scientific paper
10.1103/PhysRevA.84.012333
In order to investigate distributed quantum computation under restricted network resources, we introduce a quantum computation task over the butterfly network where both quantum and classical communications are limited. We consider deterministically performing a two-qubit global unitary operation on two unknown inputs given at different nodes, with outputs at two distinct nodes. By using a particular resource setting introduced by M. Hayashi [Phys. Rev. A \textbf{76}, 040301(R) (2007)], which is capable of performing a swap operation by adding two maximally entangled qubits (ebits) between the two input nodes, we show that unitary operations can be performed without adding any entanglement resource, if and only if the unitary operations are locally unitary equivalent to controlled unitary operations. Our protocol is optimal in the sense that the unitary operations cannot be implemented if we relax the specifications of any of the channels. We also construct protocols for performing controlled traceless unitary operations with a 1-ebit resource and for performing global Clifford operations with a 2-ebit resource.
Kinjo Yoshiyuki
Murao Mio
Soeda Akihito
Turner Peter S.
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