dorsal/arxiv
View SchemaCryptographic Distinguishability Measures for Quantum Mechanical States
| Authors | Christopher A. Fuchs, Jeroen van de Graaf |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9712042 |
| URL | https://arxiv.org/abs/quant-ph/9712042 |
Abstract
This paper, mostly expository in nature, surveys four measures of distinguishability for quantum-mechanical states. This is done from the point of view of the cryptographer with a particular eye on applications in quantum cryptography. Each of the measures considered is rooted in an analogous classical measure of distinguishability for probability distributions: namely, the probability of an identification error, the Kolmogorov distance, the Bhattacharyya coefficient, and the Shannon distinguishability (as defined through mutual information). These measures have a long history of use in statistical pattern recognition and classical cryptography. We obtain several inequalities that relate the quantum distinguishability measures to each other, one of which may be crucial for proving the security of quantum cryptographic key distribution. In another vein, these measures and their connecting inequalities are used to define a single notion of cryptographic exponential indistinguishability for two families of quantum states. This is a tool that may prove useful in the analysis of various quantum cryptographic protocols.
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"abstract": "This paper, mostly expository in nature, surveys four measures of\ndistinguishability for quantum-mechanical states. This is done from the point\nof view of the cryptographer with a particular eye on applications in quantum\ncryptography. Each of the measures considered is rooted in an analogous\nclassical measure of distinguishability for probability distributions: namely,\nthe probability of an identification error, the Kolmogorov distance, the\nBhattacharyya coefficient, and the Shannon distinguishability (as defined\nthrough mutual information). These measures have a long history of use in\nstatistical pattern recognition and classical cryptography. We obtain several\ninequalities that relate the quantum distinguishability measures to each other,\none of which may be crucial for proving the security of quantum cryptographic\nkey distribution. In another vein, these measures and their connecting\ninequalities are used to define a single notion of cryptographic exponential\nindistinguishability for two families of quantum states. This is a tool that\nmay prove useful in the analysis of various quantum cryptographic protocols.",
"arxiv_id": "quant-ph/9712042",
"authors": [
"Christopher A. Fuchs",
"Jeroen van de Graaf"
],
"categories": [
"quant-ph"
],
"title": "Cryptographic Distinguishability Measures for Quantum Mechanical States",
"url": "https://arxiv.org/abs/quant-ph/9712042"
},
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