量子照明使用糾纏信號閑散 photo n 對可提高在具有明亮熱噪聲的環(huán)境中對低反射率物體的檢測效率。它的優(yōu)勢在低信號功率下尤為明顯，這對于無創(chuàng)生物醫(yī)學(xué)掃描或低功率短程雷達等應(yīng)用來說是一個很有前途的特性。在這里，我們通過實驗研究了微波頻率下量子照明的概念。我們在自由空間檢測設(shè)置中生成糾纏場以照亮距離為 1 m 的室溫物體。我們實現(xiàn)了一個基于線性正交測量的數(shù)字相位共軛接收器，它在相同條件下優(yōu)于對稱經(jīng)典噪聲雷達，盡管信號路徑會破壞糾纏。開始從實驗數(shù)據(jù)，我們還模擬的完美惰輪的情況下照片n個檢測，其結(jié)果在量子優(yōu)點，相對經(jīng)典基準進行比較。我們的研究結(jié)果突出了微波量子電路在室溫下首次應(yīng)用的機遇和挑戰(zhàn)。
量子感測為發(fā)達相片NIC的應(yīng)用程序（1（在線）與量子信息等先進區(qū)域2 - 5）。到目前為止，量子光學(xué)一直是實現(xiàn)量子通信、密碼學(xué)和計量學(xué)中大多數(shù)協(xié)議的最自然和最方便的設(shè)置 ( 6 )。在較長波長（例如四赫茲或微波）處情況有所不同，目前各種量子技術(shù)受到更多限制并僅限于低溫環(huán)境。除了超導(dǎo)量子處理（7)，沒有微波量子通常用于傳感和通信等應(yīng)用。對于這些任務(wù)，高能量和低損失的光學(xué)和電信頻率信號表示的第一選擇，并且形成在混合量子網(wǎng)絡(luò)（未來視覺通信主干8 - 10）。
盡管有這樣的總體情況，但量子傳感的一些應(yīng)用自然地嵌入了微波區(qū)域。釷是是恰與量子照明（QI）的情況下（11 - 17），用于其顯著魯棒性的背景噪聲，其中，在室溫下，相當于?10 3每模式熱量子在幾千兆赫。在 QI 中，目標是在存在非常明亮的熱噪聲的情況下檢測低反射率物體。釷是被完成由探測目標小于一個纏結(jié)照片牛每模式，在一個隱蔽的非侵入性的方式，這是不可能再現(xiàn)與經(jīng)典的裝置。在高斯 QI 協(xié)議 ( 12 ) 中，光準備在雙模壓縮真空狀態(tài) ( 3 ) 中，信號模式發(fā)送到探測目標，而空閑模式保持在接收器。雖然纏結(jié)在往返失去從該目標，幸存的信號惰相關(guān)性，當適當?shù)販y量，可強足以擊敗性能可實現(xiàn)由最強大的經(jīng)典檢測策略。在低照片?通量制度，其中Q我展示了最大的優(yōu)勢，它可以適用于將量子傳感技術(shù)擴展到短程雷達 ( 18 ) 和無創(chuàng)診斷掃描儀應(yīng)用 ( 19 )。
在微波域（以前的實驗20，21）證明所檢測到的協(xié)方差的量子增強用對稱古典噪聲雷達，即相比，具有大致相等的信號和閑散照片n個。通過適當?shù)南嗝魴z測，理想的經(jīng)典相關(guān)噪聲雷達可以達到同等水平，或者在明亮閑散器 ( 17 )的情況下，甚至優(yōu)于相干外差檢測方案，后者最大限度地提高了信噪比 (SNR)現(xiàn)實的（相位旋轉(zhuǎn)）目標。然而，如果反射信號的相位在相關(guān)范圍內(nèi)是穩(wěn)定的時間尺度或先驗已知，則零差檢測代表最強的經(jīng)典基準。
在這項工作中，我們實現(xiàn)了 ( 22 )的相位共軛接收器的數(shù)字版本，通過實驗研究微波狀態(tài)下的概念驗證 QI ( 23 )。我們在稀釋冰箱內(nèi)使用約瑟夫森參數(shù)轉(zhuǎn)換器 (JPC) ( 24 , 25 ) 來產(chǎn)生糾纏 ( 26 , 27 )。產(chǎn)生的信號微波模式，帶湮滅算子
( A ) 微波 QI 示意圖。量子源在兩條獨立的路徑中產(chǎn)生并發(fā)射固定的糾纏微波場。信號模式
Our digital approach to QI circumvents common practical problems such as finite idler storage time that can limit the range and fidelity of QI detection schemes. However, this advantage comes at the expense that the theoretically strongest classical benchmark in the same conditions—the coherent-state homodyne detector using the same signal power and signal path—can be approached in specific conditions such as quantum-limited amplification, but never be outperformed. To outperform coherent-state homodyne detection in practice, we will require low-temperature square law detection of microwave fields that can be realized with radiometer or photon counting measurements. Nevertheless, using calibration measurements of the idler path, we can simulate a situation with perfect idler photon number detection, extrapolating the case where the reflected mode is detected together with the idler mode using analog microwave photon counters. For this situation, we show that the SNR of coherent heterodyne detection and symmetric noise radars is exceeded by up to 4 dB and that of homodyne detection—the classical benchmark—by up to 1 dB for the same amplified signal path, measurement bandwidth, and signal power. We also note that the strong and noisy amplification of the signal path chosen to facilitate the detection with commercial analog-to-digital converters enables another classical receiver strategy, i.e., the detection of the amplifier noise in the presence of the target. Since the amplified noise exceeds the environmental noise at room temperature by orders of magnitude, this would be the most effective strategy for the implemented experiment. For the same reason, a low-noise coherent source at room temperature would outperform the relative benchmarks considered here. In practice, outperforming the room temperature benchmark depends on the chosen amount of gain, the type of amplifier, and the loss in the detection system and therefore does not pose a fundamental limitation to the presented measurement scheme that focuses on the relative comparison of the different illumination types.
The experimental setup, shown in Fig. 1B, is based on a frequency tunable superconducting JPC operated in the three-wave mixing regime and pumped at the sum of signal and idler frequencies ωp = ωS + ωI; see Materials and Methods for more details. The output of the JPC contains a nonzero phase-sensitive cross-correlation
A first important check for the experiment is to quantify the amount of entanglement at the output of the JPC at 7 mK. A sufficient condition for the signal and idler modes to be entangled is the nonseparability criterion
（甲）所測得的糾纏參數(shù)Δ為的JPC（藍色）的輸出和經(jīng)典噪聲（橙色）相關(guān)的推斷的信號的函數(shù)照片n個?小號在JPC的輸出和泵功率P p在JPC 的輸入。( B ) QI（實心藍色）、對稱經(jīng)典相關(guān)照明（CI、實心橙色）、帶零差（實心綠色）和外差檢測的相干態(tài)照明的測量單模信噪比 (SNR) 的比較（實心黃色），以及作為信號照片n 數(shù)N S的函數(shù)的校準 QI（藍色虛線）和 CI（橙色虛線）的推斷 SNR對于一個完全反射物體和5微秒測量添即 點是測量和推斷的數(shù)據(jù)點，實線和虛線是理論預(yù)測。對于 (A) 和 (B)，誤差條表示基于三組測量的 95% 置信區(qū)間，每組測量具有 380,000 個用于 QI/CI 的雙通道正交對和 192,000 個用于相干狀態(tài)照明的正交對。
然后，經(jīng)典相關(guān)信號和閑散模式從JPC反射回來（泵關(guān)閉）并通過連接到 JPC 輸出的測量線。這確保了經(jīng)典輻射和量子輻射在到達目標之前和以相同方式檢測之前在增益、損耗和噪聲方面都經(jīng)歷相同的條件。如圖所示圖2A，在低照片n個參數(shù)Δ低于一個，證明JPC的輸出被纏結(jié)，而在較大的相片n個（更大的泵功率），纏結(jié)在逐漸降解并消失? S = 4.5照片ns s -1 Hz -1. 我們將此歸因于 JPC 中的有限損耗，這會導(dǎo)致泵功率相關(guān)的加熱并導(dǎo)致輸出場的較大變化。另一方面，相同信號功率的經(jīng)典相關(guān)輻射（橙色數(shù)據(jù)點）不能滿足不可分離性標準，因此對于信號光子ns的整個范圍，Δ ≥ 1 。在后一種情況下，我們還觀察到作為信號光子n 數(shù)的函數(shù)的經(jīng)典相關(guān)性的緩慢相對退化，這可以通過更復(fù)雜的噪聲生成方案 ( 20 )得到改善。
QI 和經(jīng)典相關(guān)照明（CI）的實驗以類似的方式實現(xiàn)（見圖1B）。空閑模式的兩個放大正交
信號模式
或缺席
目標的
這意味著，在我們的驗證的原理的示范，運算添人古典策略實際上將基于檢測所述放大器的所述存在或不存在噪聲而非相干和信號惰路徑的相關(guān)性與測量的SNR被動= ( n 1 ? n 0 )/( n 0 + 1) ? 31.4 dB，用于我們設(shè)置中選擇的增益和接收器噪聲。然而，對于較低噪聲溫度的信號放大器和較低增益，以及在損耗增加的較長距離應(yīng)用中，檢測方案的這種無源特征將顯著減少，并最終在室溫下的環(huán)境噪聲中消失。
測量的最后一步是應(yīng)用數(shù)字版本的相位共軛接收器（22）。反射模式
在哪里
相干態(tài)照明的實驗進行通過生成在室溫下使用的微波源，隨后弱相干音由所述稀釋制冷機內(nèi)部熱化衰減器的低溫鏈。相干音的中心頻率為 ω S，與 QI 和 CI 實驗中使用的信號頻率完全匹配。相干音從非泵浦 JPC反射回來，并被引導(dǎo)到與 QI 和 CI 相同的測量鏈中（見圖1B）。發(fā)送信號以探測目標區(qū)域，并檢測到輻射
In the absence of a passive signature due to signal noise amplification, digital homodyne detection of a coherent state represents the optimal classical strategy in terms of the SNR, which is given by
while the SNR of the digital heterodyne detection is lower and given by
where
In Fig. 2B, we compare the SNR of QI and CI with and without idler calibration for a perfectly reflective object in a zero loss channel η = 1. For comparison, we also include the results of coherent-state illumination with homodyne and heterodyne detection. In all cases, the signal mode at room temperature is overwhelmed with amplifier noise. We use three sets of measurements to calculate the SD of the mean SNR of a single mode measurement with measurement time T = 1/B = 5 μs. Each set is based on M = 380,000 samples (192,000 for the coherent-state detection), corresponding to a measurement time of 1.87 s (0.93 s for the coherent-state detection). To get the total statistics, the measurement time takes 5.6 s (2.8 s for the coherent-state detection). For the same measurement bandwidth and using the raw data of the measured quadrature pairs (solid lines), QI (blue dots) outperforms suboptimum symmetric CI (orange dots) by up to 3 dB at low signal photon numbers, but it cannot compete with the SNR obtained with coherent-state illumination (yellow and green dots). Under the assumption of perfect idler photon number detection, i.e., applying the calibration discussed above (dashed lines), the SNR of QI is up to 4 dB larger than that of symmetric CI and coherent-state illumination with heterodyne detection, which does not require phase information, over the region where the outputs of the JPC are entangled. For signal photon numbers NS > 4.5, where there is no entanglement present in the signal source, the sensitivity of the coherent-state transmitter with heterodyne detection outperforms QI and CI, confirming the critical role of entanglement to improve the sensitivity of the detection.
QI with a phase-conjugate receiver is potentially able to outperform coherent-state illumination with homodyne detection by up to 3 dB, i.e., the optimum classical benchmark, in the regime of low signal photon numbers. In the region NS < 0.4, the experimentally inferred SNR of QI is approximately 1 dB larger, in agreement with the theoretical prediction taking into account experimental nonidealities like the finite squeezing of the source. In practice though, i.e., without the applied idler calibration, the quantum advantage compared with coherent homodyne detection is not accessible with a digital receiver based on heterodyne measurements, even in the case of quantum limited amplifiers, due to the captured idler vacuum noise, which lowers the optimal SNR by at least 3 dB (12, 16). The experimental results (dots) are in very good agreement with the theoretical prediction (solid and dashed lines). For the theory, we rewrite the SNRs Eqs. 3 to 5 in terms of the signal photon number
An important feature of a radar or short-range scanner is its resilience with respect to signal loss. To verify this, as shown in Fig. 1B, we use two microwave switches at room temperature in the signal line to select between a digitally controllable step attenuator to mimic an object with tunable reflectivity and a proof-of-principle radar setup. With this setup, we determine the effects of loss and object reflectivity as well as target distance on the efficiency of the quantum enhanced radar. In Fig. 3A, we plot the measured SNR of QI, CI, and coherent-state illumination with heterodyne detection as a function of the imposed loss on the signal mode. The calibrated QI protocol is always superior to calibrated symmetric CI and coherent-state illumination with heterodyne detection for a range of effective loss ?25 dB <η < 0 dB. The dashed lines are the theory predictions from Eqs. 3 and 5 for a fixed chosen signal photon number NS = 0.5. The shaded regions represent the confidence interval extracted from the SD of the measured idler photon numbers, and the cross-correlations as a function of η.
校準QI（藍色）和對稱的CI（橙色）的推斷的SNR，并與數(shù)字外差檢測（黃色）作為（的函數(shù)測得的相干態(tài)照明甲）的總的信號損失η和（乙）對象距離從所述用于自由空間照明的發(fā)射和接收天線。誤差條的計算類似于圖 2。對于 (A) 和 (B)，信號照片n 數(shù)為N S = 0.5。陰影區(qū)域是通過擬合實驗數(shù)據(jù)提取的理論不確定性。該圖中未顯示具有零差檢測的相干狀態(tài)的 SNR，因為所選N處的預(yù)期優(yōu)勢S小于該測量中的系統(tǒng)誤差。
在雷達的背景下，SNR 的微小改進導(dǎo)致錯誤概率呈指數(shù)級提高
在這項工作中，我們研究了微波域中的概念驗證 QI，這是目標檢測的最自然頻率范圍。假設(shè)完美惰照片N多的檢測，我們發(fā)現(xiàn)，量子優(yōu)點是可以盡管糾纏破信號路徑。由于最好的結(jié)果是小于一個平均實現(xiàn)照片牛每模式，我們的實驗表明QI的作為非侵入性掃描方法，例如電勢，用于生物醫(yī)學(xué)應(yīng)用，人體組織，或蛋白質(zhì)的無損旋轉(zhuǎn)光譜成像，除了它的潛在用作短程低功率雷達，例如用于安全應(yīng)用。然而，對于這一初步驗證的原理論證，目標區(qū)域被放大的亮聲淹沒了環(huán)境噪聲通過數(shù)量級，這排除了短距離目標的非侵入性特征，并提供了使用放大器噪聲的存在或不存在來檢測具有更高 SNR 的對象的機會。使用具有有限增益的量子限制參數(shù)放大器 ( 34 – 36 )，使得放大的真空不會顯著超過目標處的環(huán)境或典型電子噪聲，這將有助于在最低噪聲方面實現(xiàn)實際優(yōu)勢-在室溫下計算相干狀態(tài)外差接收器，并且直到真空噪聲，它們也會使閑散校準過時。使用靈敏輻射計或微波單的相片N個檢測器（37 - 39)，在毫開爾文溫度下，沒有信號放大，代表了在實際情況下以及相對于理想的相干態(tài)零差接收器而言實現(xiàn)優(yōu)勢的有希望的途徑。所提出的數(shù)字實現(xiàn)QI的一個優(yōu)點是，它并沒有遭受從依賴于模擬接收機的惰存儲問題光電檢測方案，本質(zhì)上限制了活動范圍的雷達使用時。基于最先進的超導(dǎo)電路技術(shù)和數(shù)字信號處理，在微波域中可以實現(xiàn)哪些其他類型的接收器（40）是一個有趣的懸而未決的問題。
我們使用非簡并三波混頻 JPC 作為非線性量子限制放大器，其信號、空閑和泵端口在空間上是分開的，如圖4所示。JPC 的非線性源于約瑟夫森環(huán)調(diào)制器 (JRM) ，該調(diào)制器由排列在矩形環(huán)上的四個約瑟夫森結(jié)和環(huán)內(nèi)的四個大的分流約瑟夫森結(jié)組成 ( 41 )。總幾何支持兩種差模和一種共模。正確的偏置點是通過引入一個 fl來選擇的UX在所述JRM環(huán)路通過使用外部磁鐵IC領(lǐng)域。連接到JRM中心的兩對微波半波長微帶傳輸線諧振器用作信號和閑散微波諧振器。這些諧振器耦合到 JRM 的兩個差分模式，并通過電容連接到兩個外部饋線，將微波信號輸入和輸出耦合到 JPC。
The Josephson parametric amplifier (JPC) contains a Josephson ring modulator (JRM) consisting of four Josephson junctions, and four large Josephson junctions inside the ring act as a shunt inductance for the JRM (41). Two microwave resonators are coupled to the JRM forming idler and signal resonators with resonance frequencies ωI and ωS, respectively. These resonators are capacitively coupled to the input and output ports. To use the JPC in the three-wave mixing condition, the device is biased using an external magnetic field and pumped at frequency ωp = ωI + ωS. Two broadband 180° hybrids are used to feed-in and feed-out the pump, idler, and signal. In this configuration, the second port of the signal is terminated using a 50-ohm cold termination.
The entanglement between signal mode with frequency ωS and idler mode with frequency ωI is generated by driving the nonresonant common mode of the JRM at frequency ωp = ωI + ωS. Two off-chip, broadband 180° hybrids are used to add the idler or signal modes to the pump drive. In our configuration, we apply the pump to the idler side and terminate the other port of the signal hybrid with a 50-ohm cold termination. The frequency of the signal mode is ωS = 10.09 GHz, and the frequency of the idler mode is ωI = 6.8 GHz. The maximum dynamical bandwidth and gain of our JPC are 20 MHz and 30 dB, respectively. The 1-dB compression point corresponds to the power ?128 dBm at the input of the device at which the device gain drops by 1 dB and the amplifier starts to saturate. The frequency of the signal and idler modes can be varied over the 100-MHz span by applying a direct current to the flux line.
The system gain Gi and system noise nadd, i of both signal and idler measurement chains are calibrated by injecting a known amount of thermal noise using two temperature-controlled 50-ohm cold loads (26, 42). The calibrators are attached to the measurement setup with two copper coaxial cables of the same length and material as the cables used to connect the JPC via two latching microwave switches (Radiall R573423600). A thin copper braid was used for weak thermal anchoring of the calibrators to the mixing chamber plate. By measuring the noise density in V2/Hz at each temperature as shown in Fig. 5 and fitting the obtained data with the expected scaling
where B = 200 kHz and R = 50 ohms, we accurately back out the total gain
and the number of added noise photons referenced to the JPC output
Calibration of signal (A) and idler (B) output channels. The measured noise density in units of quanta, Si = Ni/(?ωiBRGi) ? nadd, i, is shown as a function of the temperature T of the 50-ohm load. The error bars indicate the SD obtained from three measurements with 576,000 quadrature pairs each. The solid lines are fits to Eq. 5 in units of quanta, which yields the system gain and noise with the standard errors (95% confidence interval) as stated in section Results.
The 95% confidence values are taken from the standard error of the fit shown in Fig. 5.
In Fig. 6, we show the full measurement chain used in our experiment. The outputs of the JPC, the signal
where
where
是參考 JPC 輸出的總添加噪聲量。
JPC 的輸出在使用兩個本地振蕩器（LO 1和 LO 2）下變頻到 20 MHz 之前在不同的階段進行放大。在下變頻之后，信號被再次過濾和放大，然后使用模數(shù)轉(zhuǎn)換器 (ADC) 進行數(shù)字化。經(jīng)典的 CI 是通過使用任意波形（噪聲）發(fā)生器生成的相關(guān)白噪聲來執(zhí)行的。對于相干態(tài)照明，我們生成相干色調(diào)并將其發(fā)送到冰箱。信號從非泵浦 JPC反射并通過測量鏈。
信號模式用于探測目標區(qū)域。在目標存在H 1或不存在H 0的情況下，來自目標區(qū)域的反射信號分別由下式給出
其中 η 是總信號損失，并且
降頻轉(zhuǎn)換后的信號模式被給予由
與我= 0,1，
或目標缺席
在哪里
是 JPC 輸出處的總添加噪聲量。在靶的存在噪聲添加的總給出由
在本節(jié)中，我們將解釋如何執(zhí)行單模后處理。如圖7A所示，使用具有 8 位分辨率的雙通道 ADC 以 100 MS/s 連續(xù)記錄下轉(zhuǎn)換和放大的信號和空閑模式。總的測量添的QI / CI檢測（相干態(tài)檢測）的e是5.76秒（2.88 S），其中所述記錄的數(shù)據(jù)被短切到中號= 1.15×10 6（6×10 5）記錄; 每個包含 500 個樣本，對應(yīng)于 200 kHz 的濾波器帶寬。500 個樣本用于分別對每個記錄執(zhí)行 FFT，并提取復(fù)雜的正交電壓I I、Q I和IS , Q S為 20 MHz 處的中頻分量。我們計算檢測到的信號和閑散模式的場正交
( A )來自ADC的記錄數(shù)據(jù)被切割成M 個較短的陣列。我們在每個陣列上分別進行模擬下變頻后在閑散 (ω I ) 和信號頻率 (ω S )處應(yīng)用數(shù)字 FFT，以推斷信號和閑散模式正交的測量統(tǒng)計數(shù)據(jù)
JPC 和相關(guān)經(jīng)典源均生成具有非零互相關(guān)的零均值雙模高斯狀態(tài)
通過比較兩個探測器的總光子n計數(shù)（23）的差異來做出目標是否存在的決定，這相當于操作員的測量
在哪里
和
在哪里
和 ( 22 )
對于i = 0,1，我們采用校準后的無噪聲惰輪照片n 數(shù)
為了執(zhí)行相干態(tài)照明，我們在室溫下產(chǎn)生相干信號并將其發(fā)送到稀釋冰箱，其中模式
對于數(shù)字零差檢測，我們使用相位信息將信號旋轉(zhuǎn)到相關(guān)的正交方向并獲得改進的 SNR
我們感謝 C. Wilson，特別是 J. Shapiro，感謝他們提供了有益的批評性評論和討論。我們感謝 IBM 捐贈了這項工作中使用的 JPC，J. Chow 和 B. Abdo 提供了有用的建議，以及 M. Labendik 和 R. Sett 對表征 JPC 屬性的貢獻。資金：這項工作得到了奧地利科學(xué)技術(shù)研究所 (IST Austria)、歐洲研究委員會的資助協(xié)議號 758053 (ERC StG?? QUNNECT) 和歐盟地平線 2020 研究和創(chuàng)新計劃的資助協(xié)議號 862644 (FET打開四重奏）。SB確認支持從瑪麗羅多夫斯卡居里相交號707438（MSC-IF SUPEREOM）; DV承認支持從根據(jù)第 732894 號贈款協(xié)議（FET Proactive HOT）的歐盟地平線 2020 研究和創(chuàng)新計劃以及由QuantERA ERANET 量子技術(shù)聯(lián)合基金資助的 QuaSeRT項目；和 JMF來自奧地利科學(xué)基金 (FWF) 通過 BeyondC (F71)、NOMIS 基金會研究資助和歐盟地平線 2020 研究和創(chuàng)新計劃，資助協(xié)議編號為 732894 (FET Proactive HOT)。作者貢獻： SB、SP 和 DV 提出并發(fā)展了理論思想。SB 和 JMF 構(gòu)思了實驗，建立了實驗裝置，并分析了數(shù)據(jù)。SB 進行了理論計算和測量。所有作者都對手稿做出了貢獻。利益爭奪：作者聲明他們沒有相互競爭的利益。數(shù)據(jù)和材料可用性：用于生成本手稿結(jié)果的數(shù)據(jù)和代碼可在 Zenodo 上獲得：https ://doi.org/10.5281/zenodo.3745579 。
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