Virtual Entanglement and Reconciliation Protocols for Quantum Cryptography with Continuous Variables

TL;DR

This work demonstrates that quantum key distribution with continuous-variable systems can be securely implemented using reverse reconciliation, even in the presence of arbitrarily high optical losses. By mapping prepare-and-measure protocols to entanglement-based equivalents (via virtual entanglement) and analyzing Eve's Gaussian attacks with an entangling cloner, the authors derive concrete bounds on Eve's information and achievable secret-key rates. They show that coherent-state protocols with homodyne detection suffice, and that squeezing or entanglement mainly improve resilience to excess noise rather than baseline security. The study further links security thresholds to the entanglement criterion for bipartite Gaussian states, supporting the prospect of unconditional security for coherent-state quantum cryptography within the Gaussian-attack model.

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.

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