dorsal/arxiv
View SchemaLinking Classical and Quantum Key Agreement: Is There "Bound Information"?
| Authors | N. Gisin, S. Wolf |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0005042 |
| URL | https://arxiv.org/abs/quant-ph/0005042 |
| Journal | Proceedings of Crypto 2000, Lecture Notes in Computer Science, 1880, 482-500, 2000 |
Abstract
After carrying out a protocol for quantum key agreement over a noisy quantum channel, the parties Alice and Bob must process the raw key in order to end up with identical keys about which the adversary has virtually no information. In principle, both classical and quantum protocols can be used for this processing. It is a natural question which type of protocols is more powerful. We prove for general states but under the assumption of incoherent eavesdropping that Alice and Bob share some so-called intrinsic information in their classical random variables, resulting from optimal measurements, if and only if the parties' quantum systems are entangled. In addition, we provide evidence that the potentials of classical and of quantum protocols are equal in every situation. Consequently, many techniques and results from quantum information theory directly apply to problems in classical information theory, and vice versa. For instance, it was previously believed that two parties can carry out unconditionally secure key agreement as long as they share some intrinsic information in the adversary's view. The analysis of this purely classical problem from the quantum information-theoretic viewpoint shows that this is true in the binary case, but false in general. More explicitly, bound entanglement, i.e., entanglement that cannot be purified by any quantum protocol, has a classical counterpart. This "bound intrinsic information" cannot be distilled to a secret key by any classical protocol. As another application we propose a measure for entanglement based on classical information-theoretic quantities.
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"abstract": "After carrying out a protocol for quantum key agreement over a noisy quantum\nchannel, the parties Alice and Bob must process the raw key in order to end up\nwith identical keys about which the adversary has virtually no information. In\nprinciple, both classical and quantum protocols can be used for this\nprocessing. It is a natural question which type of protocols is more powerful.\nWe prove for general states but under the assumption of incoherent\neavesdropping that Alice and Bob share some so-called intrinsic information in\ntheir classical random variables, resulting from optimal measurements, if and\nonly if the parties\u0027 quantum systems are entangled. In addition, we provide\nevidence that the potentials of classical and of quantum protocols are equal in\nevery situation. Consequently, many techniques and results from quantum\ninformation theory directly apply to problems in classical information theory,\nand vice versa. For instance, it was previously believed that two parties can\ncarry out unconditionally secure key agreement as long as they share some\nintrinsic information in the adversary\u0027s view. The analysis of this purely\nclassical problem from the quantum information-theoretic viewpoint shows that\nthis is true in the binary case, but false in general. More explicitly, bound\nentanglement, i.e., entanglement that cannot be purified by any quantum\nprotocol, has a classical counterpart. This \"bound intrinsic information\"\ncannot be distilled to a secret key by any classical protocol. As another\napplication we propose a measure for entanglement based on classical\ninformation-theoretic quantities.",
"arxiv_id": "quant-ph/0005042",
"authors": [
"N. Gisin",
"S. Wolf"
],
"categories": [
"quant-ph"
],
"journal_ref": "Proceedings of Crypto 2000, Lecture Notes in Computer Science,\n 1880, 482-500, 2000",
"title": "Linking Classical and Quantum Key Agreement: Is There \"Bound Information\"?",
"url": "https://arxiv.org/abs/quant-ph/0005042"
},
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