dorsal/arxiv
View SchemaVirtual Entanglement and Reconciliation Protocols for Quantum Cryptography with Continuous Variables
| Authors | F. Grosshans, N. J. Cerf, J. Wenger, R. Tualle-Brouri, Ph. Grangier |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0306141 |
| URL | https://arxiv.org/abs/quant-ph/0306141 |
Abstract
We discuss quantum key distribution protocols using quantum continuous variables. We show that such protocols can be made secure against individual gaussian attacks regardless the transmission of the optical line between Alice and Bob. This is achieved by reversing the reconciliation procedure subsequent to the quantum transmission, that is, using Bob's instead of Alice's data to build the key. Although squeezing or entanglement may be helpful to improve the resistance to noise, they are not required for the protocols to remain secure with high losses. Therefore, these protocols can be implemented very simply by transmitting coherent states and performing homodyne detection. Here, we show that entanglement nevertheless plays a crucial role in the security analysis of coherent state protocols. Every cryptographic protocol based on displaced gaussian states turns out to be equivalent to an entanglement-based protocol, even though no entanglement is actually present. This equivalence even holds in the absence of squeezing, for coherent state protocols. This ``virtual'' entanglement is important to assess the security of these protocols as it provides an upper bound on the mutual information between Alice and Bob if they had used entanglement. The resulting security criteria are compared to the separability criterion for bipartite gaussian variables. It appears that the security thresholds are well within the entanglement region. This supports the idea that coherent state quantum cryptography may be unconditionally secure.
{
"annotation_id": "60886b44-2062-4b92-9ebb-a11287cc7d7b",
"date_created": "2026-03-02T18:01:59.485000Z",
"date_modified": "2026-03-02T18:01:59.485000Z",
"file_hash": "9f68f0fc470b5ea1f21c0d82f99e1e19096a1828f06a4cbf1176962f5716a6cd",
"private": false,
"record": {
"abstract": "We discuss quantum key distribution protocols using quantum continuous\nvariables. We show that such protocols can be made secure against individual\ngaussian attacks regardless the transmission of the optical line between Alice\nand Bob. This is achieved by reversing the reconciliation procedure subsequent\nto the quantum transmission, that is, using Bob\u0027s instead of Alice\u0027s data to\nbuild the key. Although squeezing or entanglement may be helpful to improve the\nresistance to noise, they are not required for the protocols to remain secure\nwith high losses. Therefore, these protocols can be implemented very simply by\ntransmitting coherent states and performing homodyne detection. Here, we show\nthat entanglement nevertheless plays a crucial role in the security analysis of\ncoherent state protocols. Every cryptographic protocol based on displaced\ngaussian states turns out to be equivalent to an entanglement-based protocol,\neven though no entanglement is actually present. This equivalence even holds in\nthe absence of squeezing, for coherent state protocols. This ``virtual\u0027\u0027\nentanglement is important to assess the security of these protocols as it\nprovides an upper bound on the mutual information between Alice and Bob if they\nhad used entanglement. The resulting security criteria are compared to the\nseparability criterion for bipartite gaussian variables. It appears that the\nsecurity thresholds are well within the entanglement region. This supports the\nidea that coherent state quantum cryptography may be unconditionally secure.",
"arxiv_id": "quant-ph/0306141",
"authors": [
"F. Grosshans",
"N. J. Cerf",
"J. Wenger",
"R. Tualle-Brouri",
"Ph. Grangier"
],
"categories": [
"quant-ph"
],
"title": "Virtual Entanglement and Reconciliation Protocols for Quantum Cryptography with Continuous Variables",
"url": "https://arxiv.org/abs/quant-ph/0306141"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "a24c665c-9509-4d48-a63c-7ffbb21a9fba",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}