物理讲义量子信息基础of quantum mechanics

1、1量子力学原理速成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量子力学描写微观粒子的运动量子力学的态 量子力学的力学量 量子力学的测量值 量子力学测量的结果 量子力学态的演化4Stern Gerlach Experiment (1922)量子力学5量子力学的态、力学量原子核的自旋，电子自旋，光子的偏振核自旋由一个

2、波函数表示|力学量由一个厄米算符表示（厄米矩阵）6量子力学测量值只能是本征值对自旋的三个分量进行测量得到的结果只能是7核自旋的状态可以是叠加态zx无论测量多么仔细，量子测量的结果使得体系的状态发生改变。只有在体系处在被测量量的本征态时，测量才不会改变波函数。zxzxxz测量得到z的几率|c |28测量后体系状态发生改变，塌缩到本征态测量结果为+z量子体系的状态的时间演化遵从Schrodinger方程量子计算的过程是开启不同的H,完成量子计算9量子力学原理-2量子资源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量子纠缠和薛定谔猫薛定谔猫的理论与实验量子退相干Nature 427, 711-714 (2004)19薛定谔想要借此阐述的物理问题是：宏观世界是否也遵从适用于微观尺度的量子叠加原理。“薛定谔猫”佯谬巧妙地

6、把微观放射源和宏观的猫联系起来，旨在否定宏观世界存在量子叠加态。随着量子力学的发展，科学家已先后通过各种方案获得了宏观量子叠加态。此前，科学家最多使个离子或个光子达到“薛定谔猫”态。但如何使更多粒子构成的系统达到这种状态并保存更长时间，已成为实验物理学的一大挑战。 20EPR-量子纠缠态1935年 Einstein,Podolsky,Rosen. Bohm的简化表述t=0-21EPR佯缪2tT随着科学与技术的发展，这个理想实验被证实22The Greek LAOCOON量子纠缠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纠缠光子对实验相位