dorsal/arxiv
View SchemaEntanglement and the Power of One Qubit
| Authors | Animesh Datta, Steven T. Flammia, Carlton M. Caves |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0505213 |
| URL | https://arxiv.org/abs/quant-ph/0505213 |
| DOI | 10.1103/PhysRevA.72.042316 |
| Journal | Phys. Rev. A, 72, 042316 (2005) |
Abstract
The "Power of One Qubit" refers to a computational model that has access to only one pure bit of quantum information, along with n qubits in the totally mixed state. This model, though not as powerful as a pure-state quantum computer, is capable of performing some computational tasks exponentially faster than any known classical algorithm. One such task is to estimate with fixed accuracy the normalized trace of a unitary operator that can be implemented efficiently in a quantum circuit. We show that circuits of this type generally lead to entangled states, and we investigate the amount of entanglement possible in such circuits, as measured by the multiplicative negativity. We show that the multiplicative negativity is bounded by a constant, independent of n, for all bipartite divisions of the n+1 qubits, and so becomes, when n is large, a vanishingly small fraction of the maximum possible multiplicative negativity for roughly equal divisions. This suggests that the global nature of entanglement is a more important resource for quantum computation than the magnitude of the entanglement.
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"abstract": "The \"Power of One Qubit\" refers to a computational model that has access to\nonly one pure bit of quantum information, along with n qubits in the totally\nmixed state. This model, though not as powerful as a pure-state quantum\ncomputer, is capable of performing some computational tasks exponentially\nfaster than any known classical algorithm. One such task is to estimate with\nfixed accuracy the normalized trace of a unitary operator that can be\nimplemented efficiently in a quantum circuit. We show that circuits of this\ntype generally lead to entangled states, and we investigate the amount of\nentanglement possible in such circuits, as measured by the multiplicative\nnegativity. We show that the multiplicative negativity is bounded by a\nconstant, independent of n, for all bipartite divisions of the n+1 qubits, and\nso becomes, when n is large, a vanishingly small fraction of the maximum\npossible multiplicative negativity for roughly equal divisions. This suggests\nthat the global nature of entanglement is a more important resource for quantum\ncomputation than the magnitude of the entanglement.",
"arxiv_id": "quant-ph/0505213",
"authors": [
"Animesh Datta",
"Steven T. Flammia",
"Carlton M. Caves"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.72.042316",
"journal_ref": "Phys. Rev. A, 72, 042316 (2005)",
"title": "Entanglement and the Power of One Qubit",
"url": "https://arxiv.org/abs/quant-ph/0505213"
},
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