量子信息简介

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量子信息简介

Basic Principles of Quantum Mechanics• The state of a quantum mechanical system iscompletely specified by wave function ψ ( x,t),*which has an important property that ψ( x,t)ψ ( x,t)dxis the probability that the particle lies in the3volume element dx at time t , satisfying thenormalized condition∞∫−∞ψ ( x,t)ψ*( x,t)dx3= 1• To every observable in classical mechanics therecorresponds a linear, Hermitian operator in quantummechanics (indicates superposition principle ).3PDF 文 件 使 用 "pdfFactory Pro" 试 用 版 本 创 建 Ì www.fineprint.com.cn


Quantum Superposition Principlep12φ =p1= | φφ1= | φ1||2+ φ2,2,, p2= |φ2|2.PDF 文 件 使 用 "pdfFactory Pro" 试 用 版 本 创 建 Ì www.fineprint.com.cn


Quantum Superposition Principlewhich slit?PDF 文 件 使 用 "pdfFactory Pro" 试 用 版 本 创 建 Ì www.fineprint.com.cn


Quantum Superposition PrincipleClassical Physics:“bit”Quantum Physics:“qubit”| 〉 or | 〉| 〉 + | 〉Quantum foundations: Bell’s inequality, quantum nonlocality…Quantum information processing: quantum communication,quantum computation, quantum simulation, and high precisionmeasurement etc …PDF 文 件 使 用 "pdfFactory Pro" 试 用 版 本 创 建 ÿ www.fineprint.com.cn


Zeno ParadoxOrigin of Zeno effectCan the rabbitovertake the turtle?PDF 文 件 使 用 "pdfFactory Pro" 试 用 版 本 创 建 蜀 www.fineprint.com.cn;


Quantum Zeno EffectPDF 文 件 使 用 "pdfFactory Pro" 试 用 版 本 创 建 www.fineprint.com.cn


Quantum Zeno EffectHΦH1 iϕ iϕ0 = (( e + 1) 0 + ( e −1)21)PDF 文 件 使 用 "pdfFactory Pro" 试 用 版 本 创 建 Ì www.fineprint.com.cn


Quantum Zeno EffectInteraction-free measurement !PDF 文 件 使 用 "pdfFactory Pro" 试 用 版 本 创 建 www.fineprint.com.cn


Quantum Zeno EffectupdownConsidering neutron spin evolving in magneticfield, the probability to find it still in spin upstate after time T isωpωT= cos 2 ( )2where is the Larmor frequency .PDF 文 件 使 用 "pdfFactory Pro" 试 用 版 本 创 建 1 www.fineprint.com.cn


Quantum Zeno EffectG (cake is good)=G0×1+cos2T,( ω=1)T=0 T=π/2 T=πT=0 T=π/2 T=πIf we cut the bad part of the cake at timeT=π/2 , then at T=π we haveG=1/4×G0PDF 文 件 使 用 "pdfFactory Pro" 试 用 版 本 创 建 www.fineprint.com.cn


Experimentπ NP = [cos 2 ( )]2NIn the limit of large N2π−2P = 1−+ O(N )4NP. Kwiat et. al., Phys. Rev. Lett. 74 4763 (1995)PDF 文 件 使 用 "pdfFactory Pro" 试 用 版 本 创 建 Ì www.fineprint.com.cn


Manipulation of Entanglement000→(0 + 1)00 = (00+10)0 → (00+11)0= 000+110→000+111→000+110= (00+11)0 → (00+10)0 = (0+1)00 → 000PDF 文 件 使 用 "pdfFactory Pro" 试 用 版 本 创 建 www.fineprint.com.cn


Einstein-Podolsky-Rosen Elements of RealityIn quantum mechanics in the case of two physicalquantities described by non-commuting operators,the knowledge of one precludes the knowledge ofthe other. Then either (1) the description of realitygiven by the wave function in quantum mechanics isnot complete or (2) these two quantities cannothave simultaneous reality.Quantum-mechanical description of physicalreality cannot be considered complete.non-commuting operators, i.e.,momentum P and position X of a particlePDF 文 件 使 用 "pdfFactory Pro" 试 用 版 本 创 建 Ì www.fineprint.com.cn


Bohm’s ArgumentBohm converted the original thought experiment intosomething closer to being experimentally testable.Polarization EntangledPhoton Pairs shared byAlice and Bob− 1| Ψ〉12= (| H〉 1| V〉− 2| V〉 1| H〉2)2= 1 (| H′ 〉 | | | )1V′ 〉−2V′ 〉1H′〉22= 1 (| R〉 | | | )1L〉− 2L〉 1R〉22H⎛1⎞⎛0⎞= ⎜ ⎟,V = ⎜ ⎟,⎝0⎠⎝1⎠H′=V′=R =L =1( H + V)2,1( H −V)21( H + iV )2,1( H − iV )2σσσxyzPDF 文 件 使 用 "pdfFactory Pro" 试 用 版 本 创 建 www.fineprint.com.cn


Bohm’s ArgumentAccording to the EPR argument, there exist threeσ ,elements of reality corresponding to and !xσ yσ zHowever, quantum mechanically, and arethree noncommuting operators !σ ,xσ yσ zPDF 文 件 使 用 "pdfFactory Pro" 试 用 版 本 创 建 Ì www.fineprint.com.cn


Bell’s Inequality and Violation of Local RealismThe limitation of the EPR !Both a local realistic (LR) picture and quantum mechanics(QM) can explain the perfect correlations observed.Non-testable![J. S. Bell, Physics 1, 195 (1964)]Bell’s inequality states that certain statisticalcorrelations predicted by QM for measurements ontwo-particle ensembles cannot be understood within arealistic picture based on local properties of eachindividual particle.PDF 文 件 使 用 "pdfFactory Pro" 试 用 版 本 创 建 Ì www.fineprint.com.cn


Sakurai's Bell InequlaityPick three arbitrarydirections a, b, and cP ( a+, b+) = P + PP ( a+, c+) = P + PP ( c+, b+) = P + P332474It is easy to seeP +3+ P4≤ P3+ P4+ P2P7PDF 文 件 使 用 "pdfFactory Pro" 试 用 版 本 创 建 Ì www.fineprint.com.cn


CHSH InequalityConsidering the imperfections in experiments,generalized Bell equality — CHSH equality,Local Reality prediction: S MAX≤ 2Quantum Mechanical prediction: S MAX= 2 2J. Clauser et al., Phys. Rev. Lett. 23, 880 (1969)PDF 文 件 使 用 "pdfFactory Pro" 试 用 版 本 创 建 Ì www.fineprint.com.cn


Experimental Test of Bell InequalityA. Aspect et al., Phys. Rev. Lett. 49, 1804 (1982)S = 0.101 0.020 violates a generalized inequality S ≤ 0exp±by 5 standard deviations.Drawbacks: 1. locality loop hole2. detection loop holePDF 文 件 使 用 "pdfFactory Pro" 试 用 版 本 创 建 Ì www.fineprint.com.cn


Experimental Test of Bell InequalityG. Weihs et al., Phys. Rev. Lett. 81, 5039 (1998)Sexp = 2.73±0.02by 30 standard deviations.violates CHSH inequality S ≤ 2Drawback: detection loop holePDF 文 件 使 用 "pdfFactory Pro" 试 用 版 本 创 建 Ì www.fineprint.com.cn

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