dorsal/arxiv
View SchemaRemote control of restricted sets of operations: Teleportation of Angles
| Authors | S. F. Huelga, M. B. Plenio, J. A. Vaccaro |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0107110 |
| URL | https://arxiv.org/abs/quant-ph/0107110 |
| DOI | 10.1103/PhysRevA.65.042316 |
| Journal | Phys. Rev. A 65, 042316 (2002) |
Abstract
We study the remote implementation of a unitary transformation on a qubit. We show the existence of non-trivial protocols (i.e., using less resources than bidirectional state teleportation) which allow the perfect remote implementation of certain continuous sets of quantum operations. We prove that, up to a local change of basis, only two subsets exist that can be implemented remotely with a non-trivial protocol: Arbitrary rotations around a fixed direction $\vec{n}$ and rotations by a fixed angle around an arbitrary direction lying in a plane orthogonal to $\vec{n}$. The overall classical information and distributed entanglement cost required for the remote implementation depends on whether it is a priori known to which of the two teleportable subsets the transformation belongs to. If it is so, the optimal protocol consumes one e-bit of entanglement and one c-bit in each direction. If the subset is not known, two e-bits of entanglement need to be consumed while the classical channel becomes asymmetric, two c-bits are conveyed from Alice to Bob but only one from Bob to Alice.
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"abstract": "We study the remote implementation of a unitary transformation on a qubit. We\nshow the existence of non-trivial protocols (i.e., using less resources than\nbidirectional state teleportation) which allow the perfect remote\nimplementation of certain continuous sets of quantum operations. We prove that,\nup to a local change of basis, only two subsets exist that can be implemented\nremotely with a non-trivial protocol: Arbitrary rotations around a fixed\ndirection $\\vec{n}$ and rotations by a fixed angle around an arbitrary\ndirection lying in a plane orthogonal to $\\vec{n}$. The overall classical\ninformation and distributed entanglement cost required for the remote\nimplementation depends on whether it is a priori known to which of the two\nteleportable subsets the transformation belongs to. If it is so, the optimal\nprotocol consumes one e-bit of entanglement and one c-bit in each direction. If\nthe subset is not known, two e-bits of entanglement need to be consumed while\nthe classical channel becomes asymmetric, two c-bits are conveyed from Alice to\nBob but only one from Bob to Alice.",
"arxiv_id": "quant-ph/0107110",
"authors": [
"S. F. Huelga",
"M. B. Plenio",
"J. A. Vaccaro"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.65.042316",
"journal_ref": "Phys. Rev. A 65, 042316 (2002)",
"title": "Remote control of restricted sets of operations: Teleportation of Angles",
"url": "https://arxiv.org/abs/quant-ph/0107110"
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