dorsal/arxiv
View SchemaOn Protected Realizations of Quantum Information
| Authors | E. Knill |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0603252 |
| URL | https://arxiv.org/abs/quant-ph/0603252 |
| DOI | 10.1103/PhysRevA.74.042301 |
Abstract
There are two complementary approaches to realizing quantum information so that it is protected from a given set of error operators. Both involve encoding information by means of subsystems. One is initialization-based error protection, which involves a quantum operation that is applied before error events occur. The other is operator quantum error correction, which uses a recovery operation applied after the errors. Together, the two approaches make it clear how quantum information can be stored at all stages of a process involving alternating error and quantum operations. In particular, there is always a subsystem that faithfully represents the desired quantum information. We give a definition of faithful realization of quantum information and show that it always involves subsystems. This justifies the "subsystems principle" for realizing quantum information. In the presence of errors, one can make use of noiseless, (initialization) protectable, or error-correcting subsystems. We give an explicit algorithm for finding optimal noiseless subsystems. Finding optimal protectable or error-correcting subsystems is in general difficult. Verifying that a subsystem is error-correcting involves only linear algebra. We discuss the verification problem for protectable subsystems and reduce it to a simpler version of the problem of finding error-detecting codes.
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"abstract": "There are two complementary approaches to realizing quantum information so\nthat it is protected from a given set of error operators. Both involve encoding\ninformation by means of subsystems. One is initialization-based error\nprotection, which involves a quantum operation that is applied before error\nevents occur. The other is operator quantum error correction, which uses a\nrecovery operation applied after the errors. Together, the two approaches make\nit clear how quantum information can be stored at all stages of a process\ninvolving alternating error and quantum operations. In particular, there is\nalways a subsystem that faithfully represents the desired quantum information.\nWe give a definition of faithful realization of quantum information and show\nthat it always involves subsystems. This justifies the \"subsystems principle\"\nfor realizing quantum information. In the presence of errors, one can make use\nof noiseless, (initialization) protectable, or error-correcting subsystems. We\ngive an explicit algorithm for finding optimal noiseless subsystems. Finding\noptimal protectable or error-correcting subsystems is in general difficult.\nVerifying that a subsystem is error-correcting involves only linear algebra. We\ndiscuss the verification problem for protectable subsystems and reduce it to a\nsimpler version of the problem of finding error-detecting codes.",
"arxiv_id": "quant-ph/0603252",
"authors": [
"E. Knill"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.74.042301",
"title": "On Protected Realizations of Quantum Information",
"url": "https://arxiv.org/abs/quant-ph/0603252"
},
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