Continuous variable quantum cryptography using coherent states

Continuous variable quantum cryptography using coherent states

25 Sep 2001 | Frédéric Grosshans and Philippe Grangier
This paper proposes secure quantum key distribution (QKD) protocols using coherent states, which are secure against individual eavesdropping attacks. The protocols rely on the no-cloning theorem, which limits the signal-to-noise ratio of quantum measurements, rather than non-classical features like squeezing. These protocols use random distributions of coherent states and do not require squeezing or entanglement. They can be applied to various QKD protocols using Gaussian statistics. The security of these protocols is based on the no-cloning theorem, which ensures that any eavesdropping attempt cannot copy the quantum state. The protocols are analyzed using the Shannon formula for information rate, which is valid for Gaussian noise. The security condition is determined by the signal-to-noise ratio, which must be higher on the legitimate channel than on the eavesdropping channel. The paper discusses both coherent state and squeezed state protocols. For coherent states, the information rate is calculated based on the signal-to-noise ratio and the transmission loss. The security of the protocol is ensured as long as the signal-to-noise ratio on the legitimate channel is higher than that on the eavesdropping channel. The protocols can be extended to EPR beams, where the same security conditions apply. The paper also discusses the reconciliation protocol, which allows for efficient extraction of the secret key. The reconciliation protocol is optimized to approach the Shannon limit, ensuring that the information rate is maximized. The security of the protocol is further enhanced by privacy amplification, which reduces the amount of information that an eavesdropper can obtain. The paper concludes that coherent state protocols are secure against individual attacks and can be implemented using low-loss optical fibers. The protocols are asymptotically secure for losses smaller than 3 dB, and the information rate for the private key is determined by the transmission loss and the signal modulation. The paper also discusses the practical considerations of implementing these protocols, including detector noise and the limitations of computing power.This paper proposes secure quantum key distribution (QKD) protocols using coherent states, which are secure against individual eavesdropping attacks. The protocols rely on the no-cloning theorem, which limits the signal-to-noise ratio of quantum measurements, rather than non-classical features like squeezing. These protocols use random distributions of coherent states and do not require squeezing or entanglement. They can be applied to various QKD protocols using Gaussian statistics. The security of these protocols is based on the no-cloning theorem, which ensures that any eavesdropping attempt cannot copy the quantum state. The protocols are analyzed using the Shannon formula for information rate, which is valid for Gaussian noise. The security condition is determined by the signal-to-noise ratio, which must be higher on the legitimate channel than on the eavesdropping channel. The paper discusses both coherent state and squeezed state protocols. For coherent states, the information rate is calculated based on the signal-to-noise ratio and the transmission loss. The security of the protocol is ensured as long as the signal-to-noise ratio on the legitimate channel is higher than that on the eavesdropping channel. The protocols can be extended to EPR beams, where the same security conditions apply. The paper also discusses the reconciliation protocol, which allows for efficient extraction of the secret key. The reconciliation protocol is optimized to approach the Shannon limit, ensuring that the information rate is maximized. The security of the protocol is further enhanced by privacy amplification, which reduces the amount of information that an eavesdropper can obtain. The paper concludes that coherent state protocols are secure against individual attacks and can be implemented using low-loss optical fibers. The protocols are asymptotically secure for losses smaller than 3 dB, and the information rate for the private key is determined by the transmission loss and the signal modulation. The paper also discusses the practical considerations of implementing these protocols, including detector noise and the limitations of computing power.
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