FangWen Sun Key Laboratory of Quantum Information University

基于金刚石氮-空位色心体系的 超分辨成像及量子传感 Fang-Wen Sun(孙方稳)*, Key Laboratory of Quantum Information (量子信息重点实验室) University of Science and Technology of China， CAS (中国科学技术大学) *Email: fwsun@ustc. edu. cn

Outline Part I NV center based quantum sensor 1. Introduction to quantum sensor（Quantum metrology） 2. NV center based quantum sensor 3. NV center based magnetometer Part II NV center based nanoscopy 0. Introduction: Measurement of nearby emitters 1. Quantum statistical imaging (QSI) 2. Charge state depletion (CSD) nanoscopy 3. NV-based nanoscope Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 6

Outline Part I NV center based quantum sensor 1. Introduction to quantum sensor（Quantum metrology） 2. NV center based quantum sensor 3. NV center based magnetometer Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 7

量子力学 Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 9

量子态及其测量 Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 10

量子态测量—量子态层析技术 Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 11

量子计量（Quantum Metrology） 量子传感（Quantum Sensing） A. 应用量子特性突破物理量测量的经典极限 B. 量子态本身及量子操作的精密测量 Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 12

量子计量（Quantum Metrology） 量子传感（Quantum Sensing） A. 应用量子特性突破物理量测量的经典极限 B. 量子态本身及量子操作的精密测量 Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 13

例1：利用电子自旋量子态测量磁场 例2：利用光子测量相位 Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 15

A. 2 实验实现逼近海森堡极限的量子相位测量 NOON态 : 制备难度大； 丢失一个光子即完全消相干，导致测量完全失败； 概率投影测量导致失败； 需要NOON态投影测量； 无法实现海森堡极限 Sun FW, Ou ZY, Guo GC, Projection measurement of the maximally entangled N-photon state for a demonstration of the N -photon de Broglie wavelength, Physical Review A 73, 023808 (2006). Sun FW, Liu BH, Huang YF, Ou ZY, Guo GC, Observation of four-photon de Broglie wavelength by state projection measurement Physical Review A 74, 033812 (2006). Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 17

多光子态制备 相位改变 双模Fock态投影测量 经典散粒噪声 ~1/N 1/2 双模Fock态 海森堡极限 ~1/N Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 18

实验结果 完全可区分光子; 经典散射噪声极限; 部分可区分（两对不可区分）; 完全不可区分光子; 海森堡极限 1. 可以推广到任意多光子态的量子相位测量，突破了散射噪声极限，逼近海森堡极限。 2. 原则上克服了因为光子损耗所引起的测量精度下降。 Sun FW, Liu BH, Gong YX, Huang YF, Ou ZY, Guo GC, Experimental demonstration of phase measurement precision beating standard quantum limit by projection measurement, Europhysics Letters 82, 24001 (2008). Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 19

A. 3 用于量子传感的消相干与精度恢复 量子消相干降低测量精度及恢复： 量子消相干降低测量精度 Huelga, et. al, Phys. Rev. Lett. 79, 3865 (1997). Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 利用动力学去耦技术恢复测量精度 Dong, Sun, Guo, et. al, Phys. Rev. A 94, 052322 (2016). 2017 -9 -19 20

A. 4 量子计量—突破经典理论极限及实用化 压缩态应用于LIGO(红色曲线) 低于散粒噪声极限 3. 5 d. B The LIGO Scientific Collaboration, Nature Phys. 7, 962– 965 (2011). Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 量子统计测量用于相邻发光体测量 两点距离: 8. 5 nm; 分辨精度: 2. 4 nm Cui, Sun, Chen, Gong, & Guo Phys. Rev. Lett. 110, 153901 (2013). 2017 -9 -19 21

A. 5 利用量子态测量相关物理量—主要应用 q 量子光学相干层析 Phys. Rev. A 65, 053817 (2002); Phys. Rev. Lett. 91, 083601 (2003); Optics Letters 37, 4077(2012). q 量子定时定位, 量子雷达 Nature 412, 417(2001); Phys. Rev. A 65, 022309(2002); Appl. Phys. Lett. 85, 2655(2004); Arxiv: 1101. 2223(2011). q 量子生物检测 Nature Photonics 7, 229– 233 (2013); Phys. Rev. X 4, 011017 (2014). q 单量子体微纳尺度下物理量检测 Nature 455, 648 (2013); Science 339, 557 (2013); Science 339, 561 (2013). Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 22

量子计量（Quantum Metrology） 量子传感（Quantum Sensing） A. 应用量子特性突破物理量测量的经典极限 B. 量子态本身及量子操作的精密测量 Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 23

B. 3 量子态测量—方法 ü量子态层析技术 PRA 64, 052312（2001） (Maximal Likelihood Estimation, Bayesian Mean Estimation) 未知 ü量子操作层析技术 量子态 测量 PRL. 78, 390(1997); J. Mod. Opt. 44, 2455(1997) 已知 Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 量子态 测量 2017 -9 -19 27

B. 4 量子态测量—资源 4 qubits 5 qubits 6 qubits. . . N qubits 256 1024 4096. . . 计数率太低， 测量次数太多 8 qubits 65536 Huang, Liu, Peng, Li, Li, & Guo Nature Commun. 2, 546 (2011). Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 28

B. 4 量子态测量—减小实验复杂度策略 1. 利用压缩感知方法测量稀疏矩阵态 测量次数非指数增长 PRL 106, 100401 (2011) PRL 108, 170403 (2012) Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 29

B. 4 量子态测量—精度及提高 Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 31

Outline Part I NV center based quantum sensor 1. Introduction to quantum sensor（Quantum metrology） 2. NV center based quantum sensor 3. NV center based magnetometer Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 33

2. 2 NV色心量子传感-温度场传感 1. 电子自旋能级与温度的关系 2. 金刚石NV实现细胞中温度场测量， 当前实验精度 100 m. K，理论最高可达 1 m. K 1. Chen, Dong, Sun, Zou, Cui, Han, and Guo，Temperature dependent energy level shifts of nitrogen-vacancy centers in diamond, Applied Physics Letters 99, 161903(2011). 2. Kucsko G, Maurer P C, Yao N Y, et al. Nanometre-scale thermometry in a living cell. Nature, 500, 54 (2013). Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 35

2. 3 NV色心量子传感-压力传感 1. 最高可测60 GPa 2. 当前实验灵敏度 0. 6 MPa/Hz-1/2， 3. 理论灵敏度 68 Pa/Hz-1/2 Marcus W. Doherty et al, Electronic Properties and Metrology Applications of the Diamond NV− Center under Pressure，PRL 112, 047601 (2014) Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 36

2. 4 NV色心量子传感-磁场测量 金刚石NV色心用于磁场测量原理 能级及哈密顿量： 637 nm 532 nm D MW Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 37

2. 5 NV色心量子传感-磁场测量灵敏度及提高 Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 39

2. 6 NV色心量子传感-磁场强度测量 利用单个NV测量 104核自旋的磁场（ ~1 n. T, d=7 nm） Science 339, 561 (2013) 对磁畴的测量 (~30 nm, 1 m. T) Science 344, 1366{2014) Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 单蛋白质自旋共振： Science 347, 06226 2015. 2017 -9 -19 40

2. 7 NV色心量子传感-磁场矢量测量 Chen, Sun, Zou, Cui, Zhou, and Guo, Vector magnetic field sensing by a single nitrogen vacancy center in diamond, Europhysics Letters 101, 67003(2013). Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 41

Outline Part I NV center based quantum sensor 1. Introduction to quantum sensor（Quantum metrology） 2. NV center based quantum sensor 3. NV center based magnetometer Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 42

Enhancement of the resolution- with AFM Magnetic field @nanocale Science 344, 1366(2014) Thermal field @nanoscale Nano Letters 16, 326 (2016) Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 45

Enhancement of the resolution- far-field nanoscopy STED: Nat. Photon. 3, 144 (2009) Best resolution: 5. 8 nm with 8. 6 GW/cm 2 Adv. Mater. 24, OP 309 (2012) Best resolution: 2. 4 nm with 5 W Resolution Record of far-field nanoscopy STORM: PNAS. 111, 14669 (2014) Best resolution: 27 nm with 200 k. W/cm 2 Nanoscopy for multi-functional nanoscale sensor: 1. High resolution 2. Low pump intensity 3. Deterministic Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 46

Outline Part II NV center based nanoscopy 0. Introduction: Measurement of nearby emitters 1. Quantum statistical imaging (QSI) for detection and distinguishing of NV centers 2. Charge state depletion (CSD) nanoscopy for manipulation of quantum state 3. NV-based nanoscope Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 48

Outline Part II NV center based nanoscopy 0. Introduction: Measurement of nearby emitters 0. 1 Resolution limit 0. 2 Super-resolution microscopy 0. 3 Quantum metrology 1. Quantum statistical imaging (QSI) for detection and distinguishing of NV centers 2. Charge state depletion (CSD) nanoscopy for manipulation of quantum state 3. NV-based nanoscope Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 49

0. 1 Measurement of nearby emitters ---Resolution limit A B First order (single-photon) image IA(x, y) IB(x, y) Classical optical limit Abbe/Rayleigh diffraction limit Resolution improvement 1. Improvement of NA : oil/solid immersion lens 2. Decrease of l: ultraviolet, electron 3. Nonlinear process 4. Super/perfect lens Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 50

0. 2 Measurement of nearby emitters ---Super-resolution microscopy Beyond diffraction limit: 1. Spatial difference (structured excitation/collection): NSOM & nanostructured; SIM; STED & related 2. Temporal/ Lifetime difference: PALM; STORM; FLIM… 3. Statistics: SOFI; … 2. 4 nm http: //www. nobelprize. org/nobel_prizes/chemistry/l aureates/2014/ Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC X. Hao, C. Kuang, Z. i Gu, Y. Wang, S. Li, Y. Ku, Y. Li, J. Ge and X. Liu, From microscopy to nanoscopy via visible light Light: Science & Applications 2, e 108 (2013) 2017 -9 -19 51

0. 3 Measurement of nearby emitters ---Quantum metrology Quantum enhanced image techniques: (1). Quantum superposition Quantum Lithography: A. N. Boto, et al. Phys. Rev. Lett. 85, 2733 (2000) G. Björk, et al. , Phys. Rev. Lett. 86, 4516 (2001) M. D'Angelo, et al. , Phys. Rev. Lett. 87, 013602 (2001) Quantum-enhanced microscope: T. Ono, R. Okamoto, and S. Takeuchi, Nat. Comms. 4, 2426 (2013). Y. Israel, Shamir Rosen, and Y. Silberberg Phys. Rev. Lett. 112, 103604 (2014). Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 52

Quantum enhanced image techniques: (2). Quantum statistics Quantum-enhanced sub-diffraction limit: O. Schwartz and D. Oron, Phys. Rev. A 85, 033812 (2012). O. Schwartz, J. M. Levitt, R. Tenne, S. Itzhakov, Z. Deutsch, and D. Oron, Nano Lett. 13, 5832 (2013). D. G. Monticone, et. al. Phys. Rev. Lett. 113, 143602 (2014) Quantum statistical imaging without restriction of the diffraction limit J. -M. Cui, F. -W. Sun, X. -D. Chen, Z. -J. Gong, and G. -C. Guo, Phys. Rev. Lett. 110, 153901 (2013) Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 53

Quantum enhanced image techniques: (3). Super-resolution microscopy with quantum control spin-RESOLFT , Charge state depletion microscopy; P. C. Maurer, et. al. Nature Phys. 6 912 (2010); X. D. Chen, C. L. Zou, C. H. Dong, Z. J. Gong, G. C. Guo, and F. W. Sun, Light-Sci. & Appl. 4, e 230 (2015). CSC FLIM P. Neumann, et. al. Nature Phys. 6 249 (2010); Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 54

Summary: Quantum enhanced image techniques: (1). Quantum superposition Current status: prototype, few photons; Resolution: sub-diffraction limit Critical technical requirements: multi-photon superposition generation and detection; (2). Quantum statistics Current status: prototype, few photons Resolution: sub-diffraction limit/ <10 nmwith QSI Critical technical requirements: high efficient photon collecting rate; (3). Super-resolution microscopy with quantum control Current status: practical applications in physics Resolution: <10 nm Critical technical requirements: system stability Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 55

Outline Part II NV center based nanoscopy 0. Introduction: Measurement of nearby emitters 1. Quantum statistical imaging (QSI) for detection and distinguishing of NV centers 2. Charge state depletion (CSD) nanoscopy for manipulation of quantum state 3. NV-based nanoscope Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 56

Nitrogen-Vacancy Center in Diamond: Application of NV Quantum Information (bulk or nanocrystal) Magnetical Detection (bulk or nanocrystal) Nature, Science, … Nature 455, 648 (2013) Biology Labeling (nanocrystal) Thermal Detection (nanocrystal) Nature Nanotechol. 3, 284 (2008) Nature 500, 54 (2013) Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 57

Diamond and NV center at Key Lab of Quantum Information NV Center Fabrication & Measurement Diamond Nanostructure Fabrication Diamond based Nanophoto nic QIT NV Center Quantum Control Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 58

1. 1 NV center Fabrication with ion implantation Rabi oscillation Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 59

1. 2 Measurement of single NV centers Auto-correlation measurement Single NV Two NVs Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 60

1. 3 Measurement of nearby NV centers ---quantum statistical image A B First order (single-photon) image Classical optical limit Abbe/Rayleigh diffraction limit (Scale of optical wavelength, hundreds of nanometers) IA(x, y) IB(x, y) Second-order（two-photon）quantum statistical image Photon anti-bunching IA and IB from single-photon counts: I 1 and two-photon counts: I 2 Genuine quantum phenomenon; Without the restriction of diffraction limit; Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 61

Pair A (Far) A：x=0. 6710(15)um; y=0. 4401(15)um B：x=0. 3343(15)um; y=0. 5835(16)um D=366. 1(2. 8)nm Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 62

Pair B (Near) A：x=0. 4059(11)um; y=0. 3900(11)um B：x=0. 4136(14)um; y=0. 3939(14)um D=8. 5(2. 4)nm Cui, Sun, Chen, et. al. Phys. Rev. Lett. 110, 153901 (2013) Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 63

Axes of Pair B (Near) [100] Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 64

QSI without restriction of diffraction limit 1. Any other single quantum particles (quantum dot, atom, molecule, …) 2. Other degrees of freedom (position, polarization, lifetime, spectrum, …) 3. Simultaneous measurement of the dynamics evolutions of two quantum particles (Rabi Oscillation, …) 4. Multi-particle image and distinguishability Improvement of photon collection 1. Pulsed laser pump (for multi-photon counts). 2. More single-photon detectors or gated CCDs. 3. Nano-photonic structure for high photon emission collection rate Cui, Sun, Chen, et. al. Phys. Rev. Lett. 110, 153901 (2013) Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 65

Experimental results Image and distinguish two-NV with nano-scale resolution Separately manipulate two-NV with nano-scale resolution? Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 66

Outline Part II NV center based nanoscopy 0. Introduction: Measurement of nearby emitters 1. Quantum statistical imaging (QSI) for detection and distinguishing of NV centers 2. Charge state depletion (CSD) nanoscopy for manipulation of quantum state 3. NV-based nanoscope Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 67

2. 1 Charge State of NV Center Neutral charge state NV 0 Negative charge state NV- QIT(single photon source, entangled state, quantum memory…), high resolution electronic and magnetic field sensing, biolabeling… Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 68

2. 2 Charge State Conversion in NV center Lose one electron Capture one electron Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 69

2. 3. Sub-diffraction limit resolution measurement with charge state depletion (CSD) STED, Nobel prize (2014) S. W. HELL Gaussian beam: diffraction limit >200 nm Donut beam for sub-diffraction limit measurement Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 70

CSD For detection For NV- generation NV-, bright NV 0, dark For NV 0 generation Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 71

The resolution Confocal CSD Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 72

4. 1 nm without oil immersion lens，50 mw; 1/86 diffraction limit； 28. 6 nm Compared with other groups： Hell, Nat. Photon. (2009); STED, 5. 8 nm Lukin, Nat. Phys. (2010); spin-RESOLFT, 50 nm Hell, Nano Lett. (2010); GSD, 12 nm(oil lens) Hell, Adv. Mater. (2012); STED, 2. 4 nm (oil lens, SIL, 5 W 775 nm) Wrachtrup, PNAS (2014); STORM, 30 nm Chen, Zou, Gong, Dong, Guo and Sun Light-Sci. & Appl. 4, e 230 (2015) Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 73

2. 4 Sub-diffraction limit resolution manipulation with charge state depletion (CSD) ODMR for two NVs with different axes For measurement of the vector of magnetic field with high spatial resolution: |B 1|≈25. 5 G q 1, A ≈ 73 o q 1, B ≈ 68 o |B 2|≈48. 8 G q 2, A ≈ 76 o q 2, B ≈ 42 o Chen, Zou, Gong, Dong, Guo and Sun Light-Sci. & Appl. 4, e 230 (2015) Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 74

ODMR, Rabi oscillation and Ramsey fringes for two NVs with same axis Rabi oscillation Ramsey fringes Chen, Zou, Gong, Dong, Guo and Sun Light-Sci. & Appl. 4, e 230 (2015) Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 75

2. 5 NIR enhanced CSD---decrease the pump intensity “single-photon process” at short wavelength, “two-photon process” at long wavelength. Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC Chen, et. al. , APL 103, 013112(2013) 2017 -9 -19 76

CSC processes 0. 13 m. W 532 nm R=14 nm @Pump intensity： 1. 2 MW/cm 2 1/1000 of STED Resolution of cascaded CSD Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 Chen, et. al, Submitted (2016) 77

Outline Part II NV center based nanoscopy 0. Introduction: Measurement of nearby emitters 1. Quantum statistical imaging (QSI) for detection and distinguishing of NV centers 2. Charge state depletion (CSD) nanoscopy for manipulation of quantum state 3. NV-based nanoscope Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 78

3. 0 NV-based nanoscaled detection Magnetic field @nanocale Science 344, 1366(2014) Thermal field @nanoscale Nano letters 16, 326 (2016) Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 79

3. 1 NV-based nanoscope NV center +AFM NV center +CSD Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 80

3. 1 NV-based nanoscope Images of NV centers in diamond Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 81

SEM image: width 180 nm-192 nm Next: detection of optical, electric, magnetic, thermal field at nanoscale Multi-function nanoscope Li, et. al. , APL 109, 111107 (2016) Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 82

Summary ü Quantum sensor with NV center ü Nanoscopy with NV center Quantum Statistical image (QSI); Charge State Depletion (CSD) NEXT NV based high-spatial resolution high sensitivity multifunctional quantum sensor ￥￥￥： 1. National Basic Research Program of China 2. Knowledge Innovation Project of Chinese Academy of Sciences 3. National Natural Science Foundation of China 4. Program for New Century Excellent Talents in University 5. Fundamental Research Funds for the Central Universities 6. Foundation for the Author of National Excellent Doctoral Dissertation of China Fang-Wen Sun (孙方稳) Key Lab of Quantum Information, USTC 2017 -9 -19 83