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arXiv:1808.10258 · Physical Review A

Measuring continuous-variable quantum entanglement with parametric-amplifier-assisted homodyne detection

Jiamin Li, Yuhong Liu, Nan Huo, Liang Cui, Sheng Feng, Xiaoying Li, Z. Y. Ou

Published May 1, 2020• 18 citations
arXivHTMLPDF

Abstract

The traditional method for measuring Einstein-Podolsky-Rosen-type continuous-variable quantum entanglement relies on balanced homodyne detections, which are sensitive to vacuum quantum noise coupled in through losses due to various factors such as detector quantum efficiency and mode mismatching between the detected field and the local oscillator. In this paper, we propose and analyze a measurement method, which is realized by assisting the balanced homodyne detections with a high-gain phase-sensitive parametric amplifier. The employment of the phase-sensitive amplifier helps us to tackle the vacuum quantum noise originating from detection losses. Moreover, because the high-gain phase-sensitive amplifier can couple two fields of different types, the proposed scheme can be used to reveal quantum entanglement between two fields of different types by using only one balanced homodyne detection. Furthermore, detailed analysis shows that in the multimode case, the proposed scheme is also advantageous over the traditional method. Such a measurement method should find wide applications in quantum information and quantum metrology involving measurement of continuous variables.

DOI
10.1103/physreva.101.053801

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The traditional method for measuring Einstein-Podolsky-Rosen-type continuous-variable quantum entanglement relies on balanced homodyne detections, which are sensitive to vacuum quantum noise coupled in through losses due to various factors such as detector quantum efficiency and mode mismatching between the detected field and the local oscillator. In this paper, we propose and analyze a measurement method, which is realized by assisting the balanced homodyne detections with a high-gain phase-sensitive parametric amplifier. The employment of the phase-sensitive amplifier helps us to tackle the vacuum quantum noise originating from detection losses. Moreover, because the high-gain phase-sensitive amplifier can couple two fields of different types, the proposed scheme can be used to reveal quantum entanglement between two fields of different types by using only one balanced homodyne detection. Furthermore, detailed analysis shows that in the multimode case, the proposed scheme is also advantageous over the traditional method. Such a measurement method should find wide applications in quantum information and quantum metrology involving measurement of continuous variables.
Balanced homodyne detection relies on a beam splitter to superpose the weak signal input and strong local oscillator. However, recent investigation shows that a high gain phase sensitive amplifier (PSA) can be viewed as homodyne detector, in which the strong pump of PSA serves as the local oscillator [1]. Here, we analyze a new method of measuring the continuous variable entanglement by assisting a balanced homodyne detector with the PSA and implement it experimentally. Before measuring quadrature amplitude with the balanced homodyne detectors, two entangled fields generated from a pulse pumped fiber optical parametric amplifier are simultaneously coupled into the PSA. We find that the normalized noise for both the difference and sum of the quadrature amplitudes of the two entangled fields fall below the shot noise limit by about 4.6 dB, which is the record degree of entanglement measured in optical fiber systems. The experimental results illustrate that the advantages of the new measurement method include but not limit to tolerance to detection loss and characterizing entanglement with only one homodyne detector. The influence of mode-mismatching due to multi-mode property of entanglement on the measured noise reduction can also be greatly mitigated, indicating the new method is advantageous over the traditional measurement in multi-mode case.
Quantum parameter estimation exploits quantum states to achieve estimation sensitivity beyond classical limit. In continuous variable (CV) regime, squeezed state has been exploited to implement deterministic phase estimation. It is however, often restricted by fragility of quantum states. The quantum phase estimation sensitivity of squeezed state is significantly affected by loss or detection inefficiency, which restrict its applications. This issue can be solved by using a method of parametric amplification of squeezed state \cite{OPA}. In this work, we implement multi-phase estimation with optical parametric amplification of entanglement generated from squeezed states. We find multi-phase estimation sensitivity is robust against loss or detection inefficiency, where we use two-mode Einstein-Podolsky-Rosen entangled state and four-mode cluster state for analysis. Our work provides a method for realizing large-scale quantum metrology in real-world applications against loss or detection inefficiency.
Mode matching plays an important role in measuring the continuous variable entanglement. For the signal and idler twin beams generated by a pulse pumped fiber optical parametric amplifier (FOPA), the spatial mode matching is automatically achieved in single mode fiber, but the temporal mode property is complicated because it is highly sensitive to the dispersion and the gain of the FOPA. We study the temporal mode structure and derive the input-output relation for each temporal mode of signal and idler beams after decomposing the joint spectral function of twin beams with the singular-value decomposition method. We analyze the measurement of the quadrature-amplitude entanglement, and find mode matching between the multi-mode twin beams and the local oscillators of homodyne detection systems is crucial to achieve a high degree of entanglement. The results show that the noise contributed by the temporal modes nonorthogonal to local oscillator may be much larger than the vacuum noise, so the mode mis-match can not be accounted for by merely introducing an effective loss. Our study will be useful for developing a source of high quality continuous variable entanglement by using the FOPA.
Mode matching plays an important role in measuring the continuous variable entanglement. For the signal and idler twin beams generated by a pulse pumped fiber optical parametric amplifier (FOPA), the spatial mode matching is automatically achieved in single mode fiber, but the temporal mode property is complicated because it is highly sensitive to the dispersion and the gain of the FOPA. We study the temporal mode structure and derive the input-output relation for each temporal mode of signal and idler beams after decomposing the joint spectral function of twin beams with the singular-value decomposition method. We analyze the measurement of the quadrature-amplitude entanglement, and find mode matching between the multi-mode twin beams and the local oscillators of homodyne detection systems is crucial to achieve a high degree of entanglement. The results show that the noise contributed by the temporal modes nonorthogonal to local oscillator may be much larger than the vacuum noise, so the mode mis-match can not be accounted for by merely introducing an effective loss. Our study will be useful for developing a source of high quality continuous variable entanglement by using the FOPA.
Quantum metrology exploits quantum states to achieve an estimation sensitivity beyond classical limits. In the continuous-variable (CV) regime, the squeezed state has been used to implement deterministic quantum sensing, but the quantum metrology sensitivity of this state is significantly affected by losses or detection inefficiencies, which restrict its applications. In this work, quantum distributed sensing is proposed using optical parametric amplified multimode entanglement generated from squeezed states. It is found that the sensitivity is robust to loss or detection inefficiency when large-gain optical parametric amplification (OPA) is introduced, where a two-mode Einstein--Podolsky--Rosen-entangled state and a four-mode cluster state are exploited for analysis. The quantum sensitivity is greatly improved compared to that without OPA in almost all loss scenarios. The quantum Fisher matrix is calculated for both states to obtain the optimal bound in comparison with our scheme, and it is found that even with a small or moderate OPA gain, quantum sensing can be improved compared with the traditional scheme. The states are also compared with corresponding single-mode squeezed states, finding the parameter ranges where entangled states perform better. This study provides a method for realizing large-scale quantum metrology in real-world applications despite losses or detection inefficiencies.
A squeezed state with higher-order sidebands is a valuable quantum resource for channel multiplexing quantum communication. However, balanced homodyne detection used in nonclassical light detection has a trade-off performance between the detection bandwidth and clearance, in which the verification of a highly squeezing factor faces a challenge. Here, we construct two optical parametric amplifiers with cavity enhancement; one is for the generation of a -10.5 dB squeezed vacuum state, and the other is for all-optical phase-sensitive parametric homodyne detection. Finally, -6.5 dB squeezing at the carrier with 17 pairs of squeezing sidebands (bandwidth of 156 GHz) is directly and simultaneously observed. In particular, for the cavity-enhanced parametric oscillation and detection processes, we analyze the limiting factors of the detectable bandwidth and measurement deviation from the generated value, which indicates that the length difference and propagation loss between two optical parametric amplifiers should be as small as possible to improve the detection performance. The experimental results confirm our theoretical analysis.