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Optics Letters

Generation of Gaussian-modulated entangled states for continuous variable quantum communication

Ning Wang, Shanna Du, Wenyuan Liu, Xuyang Wang, Yongmin Li

Published Jul 17, 2019• 4 citations
Publisher

Abstract

We present and demonstrate a high-efficiency and compact scheme for generating Gaussian-modulated Einstein-Podolsky-Rosen (EPR) entangled optical fields by injecting a modulated signal field into a non-degenerate optical parametric amplifier (NOPA). We perform a quantum analysis of the scheme and derive the variance of the output signal (idler) mode and the quantum entanglement between the signal and idler modes from the NOPA. An experimental study is presented with different Gaussian modulation depths, showing that the modulation of the injected signal field successfully enlarges the distribution of the field quadratures of the EPR source in phase space and has a negligible effect on the entanglement quality. The experimental observations have good agreement with the theoretical analysis. Our scheme can be used readily in continuous variable quantum key distribution protocol.

DOI
10.1364/ol.44.003613

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We present and demonstrate a high-efficiency and compact scheme for generating Gaussian-modulated Einstein-Podolsky-Rosen (EPR) entangled optical fields by injecting a modulated signal field into a non-degenerate optical parametric amplifier (NOPA). We perform a quantum analysis of the scheme and derive the variance of the output signal (idler) mode and the quantum entanglement between the signal and idler modes from the NOPA. An experimental study is presented with different Gaussian modulation depths, showing that the modulation of the injected signal field successfully enlarges the distribution of the field quadratures of the EPR source in phase space and has a negligible effect on the entanglement quality. The experimental observations have good agreement with the theoretical analysis. Our scheme can be used readily in continuous variable quantum key distribution protocol.
A quantum secure communication protocol using correlations of continuous variable Einstein-Podolsky-Rosen (EPR) pairs is proposed. The proposed protocol may implement both quantum key distribution and quantum message encryption by using a nondegenerate optical parametric amplifier (NOPA). The general Gaussian-cloner attack strategy is investigated in detail by employing Shannon information theory. Results show that the proposed scheme is secure, which is guaranteed physically by the correlations of the continuous variable EPR entanglement pairs generated by the NOPA.
Quantum entanglement shared by more than two partites is the essential bases for developing quantum communication networks and quantum computation. The multipartite entanglement of continuous variables can be generated by distributing or combining squeezed states of light using linear optics. We experimentally obtained a tripartite entangled state of bright optical field by means of a nondegenerate optical parametric amplifier (NOPA) and optical beam-splitters. The NOPA is operated in the state of parametric deamplification by locking the relative phase between the pump laser and the injected seed wave to (2n+1)π, so the generated Einstein-Podolsky-Rosen (EPR) beam for continuous variables is an entangled state of light with the quantum correlation of phase quadratures and the quantum anticorrelation of amplitude quadratures [1]. The output EPR beam consists of two frequency-degenerate optical modes with horizontal and vertical polarizations which are distributed to three parties with two linear beam-splitters. We have theoretically and experimentally demonstrated the three parties are in a tripartite entangled state with three-mode “position” (amplitude quadrature) correlation and relative “momentum” (phase quadrature) correlation [2]-[4]. The obtained GHZ-like state is a fully inseparable tripartite continuous-variables state violating the three inequalities used for the criterion of the inseparability [5][6]. The controlled dense coding quantum communication is experimentally accomplished by exploiting the tripartite entanglement. The three entangled modes are sent to a sender (Alice), a receiver (Bob) and a controller (Claire), respectively. The information transmission capacity of the quantum channel between Alice and Bob is controlled by Claire. The channel capacity completed under Claire’s help is always larger than that without her help.
In this paper we show how Einstein-Podolski-Rosen (EPR)-like entanglement between a pair of spatially separated propagating continuous-mode Gaussian fields can be generated via a coherent feedback loop that connects two spatially distant nondegenerate optical parametric amplifiers (NOPAs) over two transmission channels. In particular, the scheme generates entanglement in a distributed manner using spatially distributed resources. It is shown that similar to a single NOPA, the coherent feedback scheme has parameters that determine the achievable frequency dependent two-mode squeezing and entanglement bandwidth between the pair of continuous-mode fields. It is shown that in ideal scenarios, in the absence and presence of transmission losses, the feedback connection is able to provide a moderate increase in the quality of entanglement while achieving this in a more efficient manner by consuming less power, compared to conventional distribution of entanglement using a single NOPA.
In this paper, we present the first experimental demonstration on continuous variable quantum key distribution using determinant Einstein-Podolsky-Rosen entangled states of optical field. By means of the instantaneous measurements of the quantum fluctuations of optical modes, respectively, distributed at sender and receiver, the random bits of secret key are obtained without the need for signal modulation. The post-selection boundaries for the presented entanglement-based scheme against both Gaussian collective and individual attacks are theoretically concluded. The final secret key rates of 84 kbits/s and 3 kbits/s are completed under the collective attack for the transmission efficiency of 80% and 40%, respectively.
The bright Einsten-Podolsky-Rosen (EPR) beams with the quantum correlations between the quadrature-phase amplitudes of the spatially separated signal and idler beams have been experimentally generated from a cw nondegenerate optical parametric amplifier injected by seed waves with degenerate frequency but orthogonal polarization. The correlation degree of $0.853\ifmmode\pm\else\textpm\fi{}0.004$ between the quadrature-phase amplitudes of the output entangled beams is directly inferred from the measured quadrature-phase squeezing of the output vacuum squeezed-state light field formed from superposition of the original signal and idler modes. Our theoretical calculation and experimental measurements provide a reliable method to confirm the quadrature phase-squeezing and EPR correlation of bright light field.
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.