dorsal/arxiv
View SchemaOptimal Encoding of Classical Information in a Quantum Medium
| Authors | Noam Elron, Yonina C. Eldar |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0601010 |
| URL | https://arxiv.org/abs/quant-ph/0601010 |
Abstract
We investigate optimal encoding and retrieval of digital data, when the storage/communication medium is described by quantum mechanics. We assume an m-ary alphabet with arbitrary prior distribution, and an n-dimensional quantum system. Under these constraints, we seek an encoding-retrieval setup, comprised of code-states and a quantum measurement, which maximizes the probability of correct detection. In our development, we consider two cases. In the first, the measurement is predefined and we seek the optimal code-states. In the second, optimization is performed on both the code-states and the measurement. We show that one cannot outperform `pseudo-classical transmission', in which we transmit n symbols with orthogonal code-states, and discard the remaining symbols. However, such pseudo-classical transmission is not the only optimum. We fully characterize the collection of optimal setups, and briefly discuss the links between our findings and applications such as quantum key distribution and quantum computing. We conclude with a number of results concerning the design under an alternative optimality criterion, the worst-case posterior probability, which serves as a measure of the retrieval reliability.
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"abstract": "We investigate optimal encoding and retrieval of digital data, when the\nstorage/communication medium is described by quantum mechanics. We assume an\nm-ary alphabet with arbitrary prior distribution, and an n-dimensional quantum\nsystem. Under these constraints, we seek an encoding-retrieval setup, comprised\nof code-states and a quantum measurement, which maximizes the probability of\ncorrect detection. In our development, we consider two cases. In the first, the\nmeasurement is predefined and we seek the optimal code-states. In the second,\noptimization is performed on both the code-states and the measurement.\n We show that one cannot outperform `pseudo-classical transmission\u0027, in which\nwe transmit n symbols with orthogonal code-states, and discard the remaining\nsymbols. However, such pseudo-classical transmission is not the only optimum.\nWe fully characterize the collection of optimal setups, and briefly discuss the\nlinks between our findings and applications such as quantum key distribution\nand quantum computing. We conclude with a number of results concerning the\ndesign under an alternative optimality criterion, the worst-case posterior\nprobability, which serves as a measure of the retrieval reliability.",
"arxiv_id": "quant-ph/0601010",
"authors": [
"Noam Elron",
"Yonina C. Eldar"
],
"categories": [
"quant-ph"
],
"title": "Optimal Encoding of Classical Information in a Quantum Medium",
"url": "https://arxiv.org/abs/quant-ph/0601010"
},
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