| 姓名 |
陳韋銘(Wei-Ming Chen)
查詢紙本館藏 |
畢業系所 |
物理學系 |
| 論文名稱 |
(THEORETICAL STUDY OF OPTIMAL PROBE STATES FOR QUANTUM TARGET DETECTION)
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| 相關論文 | |
| 檔案 |
 [Endnote RIS 格式]
[Bibtex 格式]
 [相關文章]  [文章引用]  [完整記錄]  [館藏目錄]  至系統瀏覽論文 (2025-2-19以後開放)
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| 摘要(中) |
量子目標探測是量子感測技術的其中一種分支，主要是使用了非古典光源或者量子接收器來展現測量結果上相對於傳統目標感測的優勢。為了獲得最佳的量子優勢，如何去選擇一個最佳的探測量子態成為一個重要的問題。在這篇論文中，我們研究了在一個具損耗且具雜訊的環境下的單模量子目標物探測問題，並通過數值分析，找出了不只在任意目標物條件下以及任意目標物資訊下的最佳探測量子態。研究結果表明，在完全未掌握目標訊息的情況下，最佳探測態在大多數情況下都是非高斯態，但當目標反射率接近零時，它們會趨近於一個相干態。當目標反射率較高時，最佳探測態將是光子數壓縮態。有趣的是，當達到特定的反射率時，最佳探測態將再次回到相干態。除此之外，我們還將發展的理論模型擴展至對探測目標具有已知資訊的條件，並展示了最佳探測態在不同雜訊下對於每個具有最佳量子優勢點的行為。這個研究補足了在單模量子探測中所有參數空間下的最佳量子態之演算，並進一步根據分析給出了深刻的物理觀點。在未來，本分析方法將有可能擴展至糾纏探測源之演算，並在量子目標物探測中找到龐大的應用空間。 |
| 摘要(英) |
Quantum target detection (QTD) is a branch of quantum sensing technology using non-classical light source to demonstrate the advantages compared to conventional target detection. However, the conditional QTD has not yet been extensively researched by many people. Here a research for QTD deciding the existence of a target immersed in a lossy and noisy environment by using non-classical resources is presented. The analysis is based on the numerical calculation of continuous variables optimal probe states (OPSs) for single-mode QTD in the whole range of reflectivity. With the unknown target information, the OPSs are non-Gaussian states in most of the conditions, but they will be near a coherent state when the target reflectivity is close to zero. When it comes to high target reflectivity, the OPSs will be the photon number squeezed state. It′s intriguing that the OPS regains a nearly coherent state when reaching a particular point of reflectivity. As for the target with available information, we also show the behaviors of OPSs with respect to different noise conditions for each point with the best quantum advantage. In a nutshell, we demonstrate the OPSs for different kinds of external conditions and give physical viewpoints for some of these cases. Maybe the analysis method of this work could be applied in the double-mode or multi-mode QTD in the future. |
| 關鍵字(中) |
★ 量子光學
★ 最佳探測量子態
★ 量子目標探測
★ 維格納函數
★ 量子優勢 |
關鍵字(英) |
★ quantum optics
★ optimal probe state
★ Wigner function
★ quantum target detection
★ quantum advantage |
| 論文目次 |
1 Introduction
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 Basic theory 11
2.1 Density matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.1 Reduced Density Matrix . . . . . . . . . . . . . . . . . . . . 12
2.2 Wigner function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 Fundamental operator and Gaussian theory . . . . . . . . . . . . . 14
2.3.1 Quadrature operator . . . . . . . . . . . . . . . . . . . . . . 14
2.3.2 Gaussian state . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Vacuum state . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Thermal state . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Coherent state . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Displacement operator . . . . . . . . . . . . . . . . . . . . . 20
2.4 Beam-splitter process tensor . . . . . . . . . . . . . . . . . . . . . . 20
3 Quantum target detection 23
3.1 Brief Scheme of Target Detection . . . . . . . . . . . . . . . . . . . 23
3.2 Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.3 Helstrom theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.4 Optimal probe state . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.5 Simulation method . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.5.1 The process of SQP . . . . . . . . . . . . . . . . . . . . . . . 27
3.5.2 SQP in our case . . . . . . . . . . . . . . . . . .
. . . . 28
4 Results & Discussions for Equal Prior Probability 31
4.1 Quantum advantage . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2 Noise-Free environment . . . . . . . . . . . . . . . . . . . . . . . . 32
4.3 Noisy environment . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5 Results & Discussions for the target with available information 45
5.1 Fixed mean photon number of probe at ̄n = 0.04 . . . . . . . . . . 45
5.1.1 Noiseless environment . . . . . . . . . . . . . . . . . . . . . 46
5.1.2 Noisy environment . . . . . . . . . . . . . . . . . . . . . . . 47
6 Summary & Future works 55
Bibliography 57
A Derivation of the Wigner function in the Fock basis 59
B Simulation code for finding OPSs 63 |
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| 指導教授 |
蔡秉儒(Pin-Ju, Tsai)
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審核日期 |
2024-1-22 |
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