dorsal/arxiv
View SchemaCloning and Cryptography with Quantum Continuous Variables
| Authors | N. J. Cerf, S. Iblisdir, G. Van Assche |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0107077 |
| URL | https://arxiv.org/abs/quant-ph/0107077 |
| DOI | 10.1140/epjd/e20020025 |
| Journal | Eur. Phys. J. D 18, 211-218 (2002) |
Abstract
The cloning of quantum variables with continuous spectra is investigated. We define a Gaussian 1-to-2 cloning machine, which copies equally well two conjugate variables such as position and momentum or the two quadrature components of a light mode. The resulting cloning fidelity for coherent states, namely $F=2/3$, is shown to be optimal. An asymmetric version of this Gaussian cloner is then used to assess the security of a continuous-variable quantum key distribution scheme that allows two remote parties to share a Gaussian key. The information versus disturbance tradeoff underlying this continuous quantum cryptographic scheme is then analyzed for the optimal individual attack. Methods to convert the resulting Gaussian keys into secret key bits are also studied. The extension of the Gaussian cloner to optimal $N$-to-$M$ continuous cloners is then discussed, and it is shown how to implement these cloners for light modes, using a phase-insensitive optical amplifier and beam splitters. Finally, a phase-conjugated inputs $(N,N')$-to-$(M,M')$ continuous cloner is defined, yielding $M$ clones and $M'$ anticlones from $N$ replicas of a coherent state and $N'$ replicas of its phase-conjugate (with $M'-M=N'-N$). This novel kind of cloners is shown to outperform the standard $N$-to-$M$ cloners in some situations.
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"abstract": "The cloning of quantum variables with continuous spectra is investigated. We\ndefine a Gaussian 1-to-2 cloning machine, which copies equally well two\nconjugate variables such as position and momentum or the two quadrature\ncomponents of a light mode. The resulting cloning fidelity for coherent states,\nnamely $F=2/3$, is shown to be optimal. An asymmetric version of this Gaussian\ncloner is then used to assess the security of a continuous-variable quantum key\ndistribution scheme that allows two remote parties to share a Gaussian key. The\ninformation versus disturbance tradeoff underlying this continuous quantum\ncryptographic scheme is then analyzed for the optimal individual attack.\nMethods to convert the resulting Gaussian keys into secret key bits are also\nstudied. The extension of the Gaussian cloner to optimal $N$-to-$M$ continuous\ncloners is then discussed, and it is shown how to implement these cloners for\nlight modes, using a phase-insensitive optical amplifier and beam splitters.\nFinally, a phase-conjugated inputs $(N,N\u0027)$-to-$(M,M\u0027)$ continuous cloner is\ndefined, yielding $M$ clones and $M\u0027$ anticlones from $N$ replicas of a\ncoherent state and $N\u0027$ replicas of its phase-conjugate (with $M\u0027-M=N\u0027-N$).\nThis novel kind of cloners is shown to outperform the standard $N$-to-$M$\ncloners in some situations.",
"arxiv_id": "quant-ph/0107077",
"authors": [
"N. J. Cerf",
"S. Iblisdir",
"G. Van Assche"
],
"categories": [
"quant-ph"
],
"doi": "10.1140/epjd/e20020025",
"journal_ref": "Eur. Phys. J. D 18, 211-218 (2002)",
"title": "Cloning and Cryptography with Quantum Continuous Variables",
"url": "https://arxiv.org/abs/quant-ph/0107077"
},
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