dorsal/arxiv
View SchemaOptimal conversion of non--local unitary operations
| Authors | W. Dür, G. Vidal, J. I. Cirac |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0112124 |
| URL | https://arxiv.org/abs/quant-ph/0112124 |
| DOI | 10.1103/PhysRevLett.89.057901 |
| Journal | Phys. Rev. Lett. 89, 057901 (2002) |
Abstract
We study when a non--local unitary operation acting on two $d$--level systems can probabilistically simulate another one when arbitrary local operations and classical communication are allowed. We provide necessary and sufficient conditions for the simulation to be possible. Probabilistic interconvertability is used to define an equivalence relation between gates. We show that this relation induces a finite number of classes, that we identify. In the case of two qubits, two classes of non--local operations exist. We choose the CNOT and SWAP as representatives of these classes. We show how the CNOT [SWAP] can be deterministically converted into any operation of its class. We also calculate the optimal probability of obtaining the CNOT [SWAP] from any operation of the corresponding class and provide a protocol to achieve this task.
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"abstract": "We study when a non--local unitary operation acting on two $d$--level systems\ncan probabilistically simulate another one when arbitrary local operations and\nclassical communication are allowed. We provide necessary and sufficient\nconditions for the simulation to be possible. Probabilistic interconvertability\nis used to define an equivalence relation between gates. We show that this\nrelation induces a finite number of classes, that we identify. In the case of\ntwo qubits, two classes of non--local operations exist. We choose the CNOT and\nSWAP as representatives of these classes. We show how the CNOT [SWAP] can be\ndeterministically converted into any operation of its class. We also calculate\nthe optimal probability of obtaining the CNOT [SWAP] from any operation of the\ncorresponding class and provide a protocol to achieve this task.",
"arxiv_id": "quant-ph/0112124",
"authors": [
"W. D\u00fcr",
"G. Vidal",
"J. I. Cirac"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevLett.89.057901",
"journal_ref": "Phys. Rev. Lett. 89, 057901 (2002)",
"title": "Optimal conversion of non--local unitary operations",
"url": "https://arxiv.org/abs/quant-ph/0112124"
},
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