dorsal/arxiv
View SchemaUnconditional fidelity thresholds in single copy distillation and some aspects of quantum error correction
| Authors | Pawel Horodecki, Maciej Demianowicz |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0501105 |
| URL | https://arxiv.org/abs/quant-ph/0501105 |
| DOI | 10.1016/j.physleta.2006.01.024 |
| Journal | Phys. Lett. A 354, 40-47 (2006) |
Abstract
Various aspects of distillation of noisy entanglement and some associated effects in quantum error correction are considered. In particular we prove that if only one--way classical communication (from Alice to Bob) is allowed and the shared $d \otimes d$ state is not pure then there is a threshold for optimal entanglement fraction $F$ of the state (being an overlap between the shared state and symmetric maximally entangled state) which can be obtained in single copy distillation process. This implies that to get (probabilistically) arbitrary good conclusive teleportation via mixed state at least one classical bit of backward communication (for Bob to Alice) has to be sent. We provide several other threshold properties in this context including in particular the existence of ultimate threshold of optimal $F$ for states of full rank. Finally the threshold results are linked to those of error correction. Namely it is pointed out that in quantum computer working on fixed number of quantum bits almost any kind of noise can be (probabilistically) corrected only to some threshold error bar though there are some (rare) exceptions.
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"abstract": "Various aspects of distillation of noisy entanglement and some associated\neffects in quantum error correction are considered. In particular we prove that\nif only one--way classical communication (from Alice to Bob) is allowed and the\nshared $d \\otimes d$ state is not pure then there is a threshold for optimal\nentanglement fraction $F$ of the state (being an overlap between the shared\nstate and symmetric maximally entangled state) which can be obtained in single\ncopy distillation process. This implies that to get (probabilistically)\narbitrary good conclusive teleportation via mixed state at least one classical\nbit of backward communication (for Bob to Alice) has to be sent. We provide\nseveral other threshold properties in this context including in particular the\nexistence of ultimate threshold of optimal $F$ for states of full rank. Finally\nthe threshold results are linked to those of error correction. Namely it is\npointed out that in quantum computer working on fixed number of quantum bits\nalmost any kind of noise can be (probabilistically) corrected only to some\nthreshold error bar though there are some (rare) exceptions.",
"arxiv_id": "quant-ph/0501105",
"authors": [
"Pawel Horodecki",
"Maciej Demianowicz"
],
"categories": [
"quant-ph"
],
"doi": "10.1016/j.physleta.2006.01.024",
"journal_ref": "Phys. Lett. A 354, 40-47 (2006)",
"title": "Unconditional fidelity thresholds in single copy distillation and some aspects of quantum error correction",
"url": "https://arxiv.org/abs/quant-ph/0501105"
},
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