Universal linear Bogoliubov transformations through one-way quantum computation

Ukai, Ryuji; Yoshikawa, Jun-ichi; Iwata, Noriaki; van Loock, Peter; Furusawa, Akira

doi:10.1103/PhysRevA.81.032315

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Universal linear Bogoliubov transformations through one-way quantum computation

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van Loock, Peter
van Loock Research Group, Research Groups, Max Planck Institute for the Science of Light, Max Planck Society;

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Citation

Ukai, R., Yoshikawa, J.-i., Iwata, N., van Loock, P., & Furusawa, A. (2010). Universal linear Bogoliubov transformations through one-way quantum computation. PHYSICAL REVIEW A, 81(3): 032315. doi:10.1103/PhysRevA.81.032315.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002D-6B2D-B

Abstract

We show explicitly how to realize an arbitrary linear unitary Bogoliubov (LUBO) transformation on a multimode quantum state through homodyne-based one-way quantum computation. Any LUBO transformation can be approximated by means of a fixed, finite-sized, sufficiently squeezed Gaussian cluster state that allows for the implementation of beam splitters (in form of three-mode connection gates) and general one-mode LUBO transformations. In particular, we demonstrate that a linear four-mode cluster state is a sufficient resource for an arbitrary one-mode LUBO transformation. Arbitrary-input quantum states including non-Gaussian states could be efficiently attached to the cluster through quantum teleportation.