物理講義量子信息基礎(chǔ)of quantum mechanics

1、1量子力學(xué)原理速成2I think I can safely say that no body understands quantum mechanics. -Richard FeynmanAnyone who is not shocked by quantum theory has not understood it. -Niels Bohr3量子力學(xué)描寫微觀粒子的運(yùn)動量子力學(xué)的態(tài) 量子力學(xué)的力學(xué)量 量子力學(xué)的測量值 量子力學(xué)測量的結(jié)果 量子力學(xué)態(tài)的演化4Stern Gerlach Experiment (1922)量子力學(xué)5量子力學(xué)的態(tài)、力學(xué)量原子核的自旋，電子自旋，光子的偏振核自旋由一個

2、波函數(shù)表示|力學(xué)量由一個厄米算符表示（厄米矩陣）6量子力學(xué)測量值只能是本征值對自旋的三個分量進(jìn)行測量得到的結(jié)果只能是7核自旋的狀態(tài)可以是疊加態(tài)zx無論測量多么仔細(xì)，量子測量的結(jié)果使得體系的狀態(tài)發(fā)生改變。只有在體系處在被測量量的本征態(tài)時，測量才不會改變波函數(shù)。zxzxxz測量得到z的幾率|c |28測量后體系狀態(tài)發(fā)生改變，塌縮到本征態(tài)測量結(jié)果為+z量子體系的狀態(tài)的時間演化遵從Schrodinger方程量子計算的過程是開啟不同的H,完成量子計算9量子力學(xué)原理-2量子資源The Quantum Bit (Qubit)IWEPNM 2007, KirchbergQuantum states of a

3、Qubit (Spin ) The Spin Density Matrix SuperpositionPopulationPhase XPhase YThe Single QubitBasis: ororxyzBloch sphereSingle qubit operationsXXYZYZNOT?See: Quantum Computation and Quantum Information M. A. Nielsen and I. Chuang, Cambridge University Press 2000More Single Qubit GatesjjSTHHadamardHHHHA

4、rray of Quantum Dots with SpinsSingle spin in Q-dotDaniel LossproposalF. H. L. Koppens et. al. Nature, 442, 766 (2006)Other Qubits: Atoms and ions in traps, photons, Q-dots, superconductorsPhotons as flying qubitsQalgorithmSuperconducting qubit: Nakamura et al.Spin echo with sc-qubitBennet, Zeilinge

5、r, Zoller, Weinfurter et al.Two level systemFictitious spin 1/2Ion traps: J. I. Cirac and P. Zoller, Phys. Rev. Lett. 74, 4091 (1995)Two QubitsBasis: Bell states (entangled states): product state17量子糾纏和薛定諤貓薛定諤貓的理論與實驗量子退相干Nature 427, 711-714 (2004)19薛定諤想要借此闡述的物理問題是：宏觀世界是否也遵從適用于微觀尺度的量子疊加原理。“薛定諤貓”佯謬巧妙地

6、把微觀放射源和宏觀的貓聯(lián)系起來，旨在否定宏觀世界存在量子疊加態(tài)。隨著量子力學(xué)的發(fā)展，科學(xué)家已先后通過各種方案獲得了宏觀量子疊加態(tài)。此前，科學(xué)家最多使個離子或個光子達(dá)到“薛定諤貓”態(tài)。但如何使更多粒子構(gòu)成的系統(tǒng)達(dá)到這種狀態(tài)并保存更長時間，已成為實驗物理學(xué)的一大挑戰(zhàn)。 20EPR-量子糾纏態(tài)1935年 Einstein,Podolsky,Rosen. Bohm的簡化表述t=0-21EPR佯繆2tT隨著科學(xué)與技術(shù)的發(fā)展，這個理想實驗被證實22The Greek LAOCOON量子糾纏HHadamardUCNOTThe EPR PairEinstein, Podolsky and Rosen, Phy

7、s. Rev. 47, 777 (1935)Two Qubit GatesControlled NOT (CNOT)xCNOTHow to generate an entangled statexCNOTHQuanten computing in Hilbert space8 qubits span a256 dimensional HilbertspaceQuantum evolution in Hilbert spaceQuantum computing is: Preparation+Superposition+Entanglement+ProjectionTwo Qubit Algor

8、ithmsSuperdense coding:AliceBobAlice is allowed to send only a single qubit. Can she transmit one of four different bits of information?Suppose Alice and Bob share the entangled state:Alice performs one of the following single qubit operations on her qubit:Alice sends her qubit to Bob. Bob performs a Bell state measurement.I, Z, X, iY26Bell states (entangled states): 超光速通信?27糾纏光子對實驗相位