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arXiv:quant-ph/9909006 · Physical Review A

Quantum cryptography with squeezed states

Mark S. Hillery

Published Jan 14, 2000• 506 citations
arXivHTMLPDF

Abstract

A quantum key distribution scheme based on the use of squeezed states is presented. The states are squeezed in one of two field quadrature components, and the value of the squeezed component is used to encode a character from an alphabet. The uncertainty relation between quadrature components prevents an eavesdropper from determining both with enough precision to determine the character being sent. Losses degrade the performance of this scheme, but it is possible to use phase sensitive amplifiers to boost the signal and partially compensate for their effect.

DOI
10.1103/physreva.61.022309

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A quantum key distribution scheme based on the use of squeezed states is presented. The states are squeezed in one of two field quadrature components, and the value of the squeezed component is used to encode a character from an alphabet. The uncertainty relation between quadrature components prevents an eavesdropper from determining both with enough precision to determine the character being sent. Losses degrade the performance of this scheme, but it is possible to use phase sensitive amplifiers to boost the signal and partially compensate for their effect.
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.
A continuous key-distribution scheme is proposed that relies on a pair of conjugate quantum variables. It allows two remote parties to share a secret Gaussian key by encoding it into one of the two quadrature components of a single-mode electromagnetic field. The resulting quantum cryptographic information versus disturbance trade-off is investigated for an individual attack based on the optimal continuous cloning machine. It is shown that the information gained by the eavesdropper then simply equals the information lost by the receiver.
The possibility of using squeezed states in the recently suggested unidimensional continuous-variable quantum key distribution based on a single quadrature modulation is addressed. It is shown that squeezing of the signal states expands the physicality bounds of the effective entangled state shared between the trusted parties due to the antisqueezing noise in the unmodulated quadrature. Modulation of the antisqueezed quadrature, on the other hand, effectively shrinks the physicality bounds due to the squeezing in the unmodulated quadrature and also provides noise on the reference side of the protocol, thus limiting the possibility of eavesdropping in noisy channels. This strategy is practical for low-loss (i.e., short-distance) channels, especially if direct reconciliation scheme is applied.
By analogy to classical cryptography, we develop a "quantum public key" based cryptographic scheme in which the two public and private keys consist in each of two entangled beams of squeezed light. An analog message is encrypted by modulating the phase of the beam sent in public. The knowledge of the degree of non classical correlation between the beam quadratures measured in private and in public allows only the receiver to decrypt the message. Finally, in a view towards absolute security, we formally prove that any external intervention of an eavesdropper makes him vulnerable to any subsequent detection.
ABSTRACT This thesis explores the photon-number characteristics and quantum communication po tential of superposed squeezed vacuum states, emphasizing their relevance to Quantum Key Distribution (QKD). The analysis investigates how statistical indicators of the light field—such as the average photon number and its fluctuations—reveal nonclassical be havior, including reduced quadrature noise and altered photon-number distributions that support efficient quantum encoding. Secure communication performance is evaluated through conditional probability methods and mutual information calculations, while Q function phase-space representations illustrate interference patterns and deformation in amplitude distributions arising from squeezing and photon correlations. A Gaussian se curity model is applied to estimate the Holevo bound and quantify possible information gained by an eavesdropper. MATLAB simulations demonstrate that tuning the squeez ing strength and superposition parameters enhances the achievable key rate, showing that superposed squeezed states exhibit increased resilience to channel loss and common quantum attacks, making them strong candidates for secure, low-photon, long-distance QKDapplications. Keywords:-Photon number variation,Q-function analysis, Quadrature squeezing, Quantum Key Distribution (QKD),Secret key rate analysis,Superposed squeezed vac uum states i
ABSTRACT This thesis explores the photon-number characteristics and quantum communication po tential of superposed squeezed vacuum states, emphasizing their relevance to Quantum Key Distribution (QKD). The analysis investigates how statistical indicators of the light field—such as the average photon number and its fluctuations—reveal nonclassical be havior, including reduced quadrature noise and altered photon-number distributions that support efficient quantum encoding. Secure communication performance is evaluated through conditional probability methods and mutual information calculations, while Q function phase-space representations illustrate interference patterns and deformation in amplitude distributions arising from squeezing and photon correlations. A Gaussian se curity model is applied to estimate the Holevo bound and quantify possible information gained by an eavesdropper. MATLAB simulations demonstrate that tuning the squeez ing strength and superposition parameters enhances the achievable key rate, showing that superposed squeezed states exhibit increased resilience to channel loss and common quantum attacks, making them strong candidates for secure, low-photon, long-distance QKDapplications. Keywords:-Photon number variation,Q-function analysis, Quadrature squeezing, Quantum Key Distribution (QKD),Secret key rate analysis,Superposed squeezed vac uum states i