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arXiv:1605.03429 · Optics Letters

Gaussian entanglement distribution with gigahertz bandwidth

S. Ast, Melanie Ast, Moritz Mehmet, Roman Schnabel

Published Oct 31, 2016• 9 citations
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Abstract

The distribution of entanglement with Gaussian statistic can be used to generate a mathematically proven secure key for quantum cryptography. The distributed secret key rate is limited by the entanglement strength, the entanglement bandwidth, and the bandwidth of the photoelectric detectors. The development of a source for strongly bipartite entangled light with high bandwidth promises an increased measurement speed and a linear boost in the secure data rate. Here, we present the experimental realization of a Gaussian entanglement source with a bandwidth of more than 1.25 GHz. The entanglement spectrum was measured with balanced homodyne detectors and was quantified via the inseparability criterion introduced by Duan and coworkers with a critical value of 4 below which entanglement is certified. Our measurements yielded an inseparability value of about 1.8 at a frequency of 300 MHz to about 2.8 at 1.2 GHz, extending further to about 3.1 at 1.48 GHz. In the experiment we used two 2.6 mm long monolithic periodically poled potassium titanyl phosphate (KTP) resonators to generate two squeezed fields at the telecommunication wavelength of 1550 nm. Our result proves the possibility of generating and detecting strong continuous-variable entanglement with high speed.

DOI
10.1364/ol.41.005094

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The distribution of entanglement with Gaussian statistic can be used to generate a mathematically proven secure key for quantum cryptography. The distributed secret key rate is limited by the entanglement strength, the entanglement bandwidth, and the bandwidth of the photoelectric detectors. The development of a source for strongly bipartite entangled light with high bandwidth promises an increased measurement speed and a linear boost in the secure data rate. Here, we present the experimental realization of a Gaussian entanglement source with a bandwidth of more than 1.25 GHz. The entanglement spectrum was measured with balanced homodyne detectors and was quantified via the inseparability criterion introduced by Duan and coworkers with a critical value of 4 below which entanglement is certified. Our measurements yielded an inseparability value of about 1.8 at a frequency of 300 MHz to about 2.8 at 1.2 GHz, extending further to about 3.1 at 1.48 GHz. In the experiment we used two 2.6 mm long monolithic periodically poled potassium titanyl phosphate (KTP) resonators to generate two squeezed fields at the telecommunication wavelength of 1550 nm. Our result proves the possibility of generating and detecting strong continuous-variable entanglement with high speed.
Squeezed states can be employed for entanglement-based continuous-variable quantum key distribution, where the secure key rate is proportional to the bandwidth of the squeezing. We produced a nonclassical cw laser field at the telecommunication wavelength of 1550 nm, which showed squeezing over a bandwidth of more than 2 GHz. The experimental setup used parametric downconversion via a periodically poled potassium titanyl phosphate crystal. We did not use any resonant enhancement for the fundamental wavelength, which should in principle allow a production of squeezed light over the full phase-matching bandwidth of several nanometers. We measured the squeezing to be up to 0.3 dB below the vacuum noise from 50 MHz to 2 GHz limited by the measuring bandwidth of the homodyne detector. The squeezing strength was possibly limited by thermal lensing inside the nonlinear crystal.
We developed a high speed homodyne detector in the telecommunication wavelength region for a Gaussian-modulated coherent-state quantum key distribution experiment. We are able to achieve a 100 MHz bandwidth, ultra-low electronic noise and pulse-resolved homodyne detector. The bandwidth of this homodyne detector has reached the same order of magnitude of the best homodyne detectors reported. By overcoming photodiode response functions mismatch, choosing proper laser sources, ensuring the homodyne detector linearity and stabilizing the homodyne detection system, we demonstrate that the homodyne detector has a 10 dB shot-noise-to-electronic-noise ratio in the time domain at a local oscillator of 5.4*10^8 photons/pulse at a laser repetition rate of 10 MHz. With this homodyne detector, we expect to ncrease our GMCS QKD experiment speed by 100 times, which will improve the key generation rate by 1-2 orders of magnitude.
We report the generation of squeezed vacuum states of light at 1550 nm with a broadband quantum noise reduction of up to 4.8 dB ranging from 5 MHz to 1.2 GHz sideband frequency. We used a custom-designed 2.6 mm long biconvex periodically-poled potassium titanyl phosphate (PPKTP) crystal. It featured reflectively coated end surfaces, 2.26 GHz of linewidth and generated the squeezing via optical parametric amplification. Two homodyne detectors with different quantum efficiencies and bandwidths were used to characterize the non-classical noise suppression. We measured squeezing values of up to 4.8 dB from 5 to 100 MHz and up to 3 dB from 100 MHz to 1.2 GHz. The squeezed vacuum measurements were limited by detection loss. We propose an improved detection scheme to measure up to 10 dB squeezing over 1 GHz. Our results of GHz bandwidth squeezed light generation provide new prospects for high-speed quantum key distribution.
Einstein-Podolsky-Rosen (EPR) entanglement is a criterion that is more demanding than just certifying entanglement. We theoretically and experimentally analyze the low-resource generation of bipartite continuous-variable entanglement, as realized by mixing a squeezed mode with a vacuum mode at a balanced beam splitter, i.e., the generation of so-called vacuum-class entanglement. We find that in order to observe EPR entanglement the total optical loss must be smaller than 33.333.333.3 %. However, arbitrarily strong EPR entanglement is generally possible with this scheme. We realize continuous-wave squeezed light at 155015501550 nm with up to 9.99.99.9 dB of nonclassical noise reduction, which is the highest value at a telecom wavelength so far. Using two phase-controlled balanced homodyne detectors we observe an EPR covariance product of $0.502\ifmmode\pm\else\textpm\fi{}0.006<1$, where 111 is the critical value. We discuss the feasibility of strong Gaussian entanglement and its application for quantum key distribution in a short-distance fiber network.
We report the generation of squeezed vacuum states of light at 1550 nm with a broadband quantum noise reduction of up to 4.8 dB ranging from 5 MHz to 1.2 GHz sideband frequency. We used a custom-designed 2.6 mm long biconvex periodically-poled potassium titanyl phosphate (PPKTP) crystal. It featured reflectively coated end surfaces, 2.26 GHz of linewidth and generated the squeezing via optical parametric amplification. Two homodyne detectors with different quantum efficiencies and bandwidths were used to characterize the non-classical noise suppression. We measured squeezing values of up to 4.8 dB from 5 to 100 MHz and up to 3 dB from 100 MHz to 1.2 GHz. The squeezed vacuum measurements were limited by detection loss. We propose an improved detection scheme to measure up to 10 dB squeezing over 1 GHz. Our results of GHz bandwidth squeezed light generation provide new prospects for high-speed quantum key distribution.
Quantum key distribution with continuous variables already uses advantageous high-speed single-mode homodyne detection with low electronic noise at room temperature. Together with continuous-variable information encoding to nonclassical states, the distance for secure key transmission through lossy channels can approach 300 km in current optical fibers. Such protocols tolerate higher channel noise and also limited data processing efficiency compared to coherent-state protocols. The secret key rate can be further increased by increasing the system clock rates, and, further, by a suitable frequency-mode-multiplexing of optical transmission channels. However, the multiplexed modes couple together in the source or any other part of the protocol. Therefore, multiplexed communication will experience cross talk and the gain can be minuscule. Advantageously, homodyne detectors allow solving this cross-talk problem by proper data processing. It is a potential advantage over protocols with single-photon detectors, which do not enable similar data processing techniques. We demonstrate the positive outcome of this methodology on the experimentally characterized frequency-multiplexed entangled source of femtosecond optical pulses with natural cross talk between eight entangled pairs of modes. As the main result, we predict the almost 15-fold higher secret key rate. This experimental test and analysis of frequency-multiplexed entanglement source open the way for the field implementation of high-capacity quantum key distribution with continuous variables.