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Physica Scripta

Quantum nonlocality and quantum key distribution with the two-mode Gaussian equally squeezed state of continuous-variable systems

Shao-Hua Xiang, Shao Bin, Liu Jin, Kehui Song

Published Feb 1, 2009• 1 citation
Publisher

Abstract

We propose a scheme for generating the two-mode Gaussian equally squeezed state (GESS) by using the optical method and analyze the entanglement properties of this state by means of the logarithmic negativity. It is shown that such a two-mode GESS contains the same amount of entanglement as the two-mode squeezed vacuum state (TSVS). We investigate quantum nonlocality for this state by using two-mode Wigner function measurement. It is found that the operations of local squeezing and distancing can effectively enhance the degree of quantum nonlocality. We propose a quantum key distribution scheme based on the two-mode GESS, and we show that the proposed scheme is more secure against the partial interception attack strategy than one with Einstein–Podolsky–Rosen (EPR) pairs even though the transmission coefficient of the eavesdropping beam splitter is rather low.

DOI
10.1088/0031-8949/79/02/025002

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We propose a scheme for generating the two-mode Gaussian equally squeezed state (GESS) by using the optical method and analyze the entanglement properties of this state by means of the logarithmic negativity. It is shown that such a two-mode GESS contains the same amount of entanglement as the two-mode squeezed vacuum state (TSVS). We investigate quantum nonlocality for this state by using two-mode Wigner function measurement. It is found that the operations of local squeezing and distancing can effectively enhance the degree of quantum nonlocality. We propose a quantum key distribution scheme based on the two-mode GESS, and we show that the proposed scheme is more secure against the partial interception attack strategy than one with Einstein–Podolsky–Rosen (EPR) pairs even though the transmission coefficient of the eavesdropping beam splitter is rather low.
Abstract A class of non-Gaussian entangled states is introduced by applying the nonlocal single-photon addition to two-mode squeezed vacuum state and the properties of entanglement are numerically investigated according to linear entropy and Einstein–Podolsky–Rosen (EPR) steering. After the nonlocal single-photon addition operation, Wigner function of the generated state appears some negative region and loses its Gaussian property in phase space. In essence, non-Gaussian entangled states are generated after applying nonlocal single-photon addition. Additionally, by studying the linear entropy and EPR steering, we find that single-photon addition can enhance their entanglement degree and non-Gaussian steering can be witnessed in a large range of squeezing parameter for the second-order quadratures, which may provide a well application in the fields of quantum information processing.
We report the suitability of an Einstein–Podolsky–Rosen entanglement source for Gaussian continuous-variable quantum key distribution at 1550 nm. Our source is based on a single continuous-wave squeezed vacuum mode combined with a vacuum mode at a balanced beam splitter. Extending a recent security proof, we characterize the source by quantifying the extractable length of a composable secure key from a finite number of samples under the assumption of collective attacks. We show that distances in the order of 10 km are achievable with this source for a reasonable sample size despite the fact that the entanglement was generated including a vacuum mode. Our security analysis applies to all states having an asymmetry in the field quadrature variances, including those generated by superposition of two squeezed modes with different squeezing strengths.
We report the suitability of an Einstein-Podolsky-Rosen entanglement source for Gaussian continuous-variable quantum key distribution at 1550 nm. Our source is based on a single continuous-wave squeezed vacuum mode combined with a vacuum mode at a balanced beam splitter. Extending a recent security proof, we characterize the source by quantifying the extractable length of a composable secure key from a finite number of samples under the assumption of collective attacks. We show that distances in the order of 10 km are achievable with this source for a reasonable sample size despite the fact that the entanglement was generated including a vacuum mode. Our security analysis applies to all states having an asymmetry in the field quadrature variances, including those generated by superposition of two squeezed modes with different squeezing strengths.
Abstract In this work, we present a theoretical scheme for generating a new kind of tunable non-Gaussian entangled state, by means of beam splitters and multi-photon conditional measurement with two-mode squeezed vacuum state (TMSVS) inputs. The output state is proven to be two-variable Hermite polynomial excited squeezed vacuum states, whose success probability of detection relates to the Jacobi polynomials. We then mainly study the entanglement properties of the output state for the symmetric case quantified by the von Neumann entropy and Einstein–Podolsky–Rosen correlation. It is shown that the entropy of entanglement is valid for verifying the improvement of entanglement within a certain range of squeezing parameter and transmissivity, and the resulting state case may possess a stronger correlation than the initial TMSVS by increasing the transmissivity or photon number of detection. In addition, the violation of the Clauser–Horne–Shimony–Holt (CHSH) inequality for the output state is also evaluated in terms of Wigner representation in phase space. It is found that the negative region of Wigner function distribution becomes more visible with the increase of the photon number of detection, and the degree of the violation of the CHSH inequality significantly increases as the photon number of detection for the symmetrical case increases. The resulting state with highly nonclassical characteristics will provide a useful application in the fields of quantum information processing.
In this paper security of the quantum key distribution scheme using correlations of continuous variable Einstein–Podolsky–Rosen (EPR) pairs is investigated. A new approach for calculating the secret information rate Δ I is proposed by using the Shannon information theory. Employing an available parameter F which is associated with the entanglement of the EPR pairs, one can detect easily the eavesdropping. Results show that the proposed scheme is secure against individual beam splitter attack strategy with a proper squeeze parameter.
The distribution of deterministic keys is of significance in personal communications, but the existing continuous variable quantum key distribution protocols can only generate random keys. By exploiting the entanglement properties of two-mode squeezed states, a continuous variable quantum deterministic key distribution (CVQDKD) scheme is presented for handing over the pre-determined key to the intended receiver. The security of the CVQDKD scheme is analyzed in detail from the perspective of information theory. It shows that the scheme can securely and effectively transfer pre-determined keys under ideal conditions. The proposed scheme can resist both the entanglement and beam splitter attacks under a relatively high channel transmission efficiency.