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Quantum Electronics and Laser Science Conference

Quantum cryptography with continuous variables

Kamel Bencheikh, A. Jankovic, Thomas Symul, Juan Ariel Levenson

Published Nov 13, 2002• 0 citations
Publisher

Abstract

Summary form only given. Quantum cryptography with continuous variables is an emerging field that consist in providing two communicating parties with a random secret key, using the quadrature components of electromagnetic fields as quantum carriers. According to quantum mechanics, the quantum states of the carriers used to establish the key are perturbed by the presence of unauthorized eavesdropping. Here, we present a new quantum cryptography protocol based on entangled quadratures of a two-mode electromagnetic field generated by phase sensitive parametric amplification (PSA).

DOI
10.1109/qels.2001.962180

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Summary form only given. Quantum cryptography with continuous variables is an emerging field that consist in providing two communicating parties with a random secret key, using the quadrature components of electromagnetic fields as quantum carriers. According to quantum mechanics, the quantum states of the carriers used to establish the key are perturbed by the presence of unauthorized eavesdropping. Here, we present a new quantum cryptography protocol based on entangled quadratures of a two-mode electromagnetic field generated by phase sensitive parametric amplification (PSA).
We study a new quantum cryptography protocol with continuous variables for the construction of secret quantum keys. The protocol is based on pairs of Einstein-Podolsky-Rosen entangled quadratures of a two-mode electromagnetic field generated by non-degenerate parametric amplification. Instantaneous measurements of the quantum fluctuations provide the random bits of the secret key. The irreversible alteration of the quadrature entanglement due to unauthorized measurements immunizes the quantum key distribution against eavesdropping attacks. Based on two identical non-degenerate parametric amplifiers, the protocol circumvents the usual 50% bits rejection due to base incompatibility during the key generation process, and avoids the need for homodyne detection schemes which are highly sensitive to the mode matching problems.
We study a new quantum cryptography protocol with continuous variables for the construction of secret quantum keys. The protocol is based on pairs of Einstein-Podolsky-Rosen entangled quadratures of a two-mode electromagnetic field generated by non-degenerate parametric amplification. Instantaneous measurements of the quantum fluctuations provide the random bits of the secret key. The irreversible alteration of the quadrature entanglement due to unauthorized measurements immunizes the quantum key distribution against eavesdropping attacks. Based on two identical non-degenerate parametric amplifiers, the protocol circumvents the usual 50% bits rejection due to base incompatibility during the key generation process, and avoids the need for homodyne detection schemes which are highly sensitive to the mode matching problems.
Scheme of quantum cryptography based on single mode quadrature phase and amplitude squeezed state lights is presented. The binary key is obtained by modulating the phase quadrature or amplitude quadrature of the quadrature squeezed coherent state. The uncertainty relation of quantum mechanics provides the quantum protection. Eavesdropping from optical tapping will degrade the signal to noise ratio of the results measured by the authorized receiver and hence be revealed. Comparing with that using a coherent state light, the application of the squeezed state light enhances the security significantly.
Correlations of the type discussed by EPR in their original 1935 paradox for continuous variables exist for the quadrature phase amplitudes of two spatially separated fields. These correlations were first experimentally reported in 1992. We propose to use such EPR beams in quantum cryptography, to transmit with high efficiency messages in such a way that the receiver and sender may later determine whether eavesdropping has occurred. The merit of the new proposal is in the possibility of transmitting a reasonably secure yet predetermined key. This would allow relay of a cryptographic key over long distances in the presence of lossy channels.
We analyze the distribution of secure keys using quantum cryptography based on the continuous variable degree of freedom of entangled photon pairs. We derive the information capacity of a scheme based on the spatial entanglement of photons from a realistic source, and show that the standard measures of security known for quadrature-based continuous variable quantum cryptography (CV-QKD) are inadequate. A specific simple eavesdropping attack is analyzed to illuminate how secret information may be distilled well beyond the bounds of the usual CV-QKD measures.
We consider the continuous-variable protocol of Pirandola et al. [arXiv:1312.4104] where the secret key is established by the measurement of an untrusted relay. In this network protocol, two authorized parties are connected to an untrusted relay by insecure quantum links. Secret correlations are generated by a continuous-variable Bell detection performed on incoming coherent states. In the present work we provide a detailed study of the symmetric configuration, where the relay is midway between the parties. We analyze symmetric eavesdropping strategies against the quantum links explicitly showing that, at fixed transmissivity and thermal noise, two-mode coherent attacks are optimal, manifestly outperforming one-mode collective attacks based on independent entangling cloners. Such an advantage is shown both in terms of security threshold and secret-key rate.