dorsal/arxiv
View SchemaOn the role of entanglement and correlations in mixed-state quantum computation
| Authors | Animesh Datta, Guifre Vidal |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0611157 |
| URL | https://arxiv.org/abs/quant-ph/0611157 |
| DOI | 10.1103/PhysRevA.75.042310 |
| Journal | Phys. Rev. A 75, 042310 (2007) |
Abstract
In a quantum computation with pure states, the generation of large amounts of entanglement is known to be necessary for a speedup with respect to classical computations. However, examples of quantum computations with mixed states are known, such as the deterministic computation with one quantum qubit (DQC1) model [Knill and Laflamme, Phys. Rev. Lett. 81, 5672 (1998)], in which entanglement is at most marginally present, and yet a computational speedup is believed to occur. Correlations, and not entanglement, have been identified as a necessary ingredient for mixed-state quantum computation speedups. Here we show that correlations, as measured through the operator Schmidt rank, are indeed present in large amounts in the DQC1 circuit. This provides evidence for the preclusion of efficient classical simulation of DQC1 by means of a whole class of classical simulation algorithms, thereby reinforcing the conjecture that DQC1 leads to a genuine quantum computational speedup.
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"abstract": "In a quantum computation with pure states, the generation of large amounts of\nentanglement is known to be necessary for a speedup with respect to classical\ncomputations. However, examples of quantum computations with mixed states are\nknown, such as the deterministic computation with one quantum qubit (DQC1)\nmodel [Knill and Laflamme, Phys. Rev. Lett. 81, 5672 (1998)], in which\nentanglement is at most marginally present, and yet a computational speedup is\nbelieved to occur. Correlations, and not entanglement, have been identified as\na necessary ingredient for mixed-state quantum computation speedups. Here we\nshow that correlations, as measured through the operator Schmidt rank, are\nindeed present in large amounts in the DQC1 circuit. This provides evidence for\nthe preclusion of efficient classical simulation of DQC1 by means of a whole\nclass of classical simulation algorithms, thereby reinforcing the conjecture\nthat DQC1 leads to a genuine quantum computational speedup.",
"arxiv_id": "quant-ph/0611157",
"authors": [
"Animesh Datta",
"Guifre Vidal"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.75.042310",
"journal_ref": "Phys. Rev. A 75, 042310 (2007)",
"title": "On the role of entanglement and correlations in mixed-state quantum computation",
"url": "https://arxiv.org/abs/quant-ph/0611157"
},
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