Definitions,principles,etc Corollaries Cor.2.1 Simultaneous measurability page 67 Cor.16.1 Bell Dispersion-free 583 Definitions Def 51 Entanglement 183 Def.9.1 Operation Def.16.1 Completeness Lemmas Lemma 9.1 Elby-Bub 29 Lemma 16.1 BellI 83 Lemma 16.2 BelⅡ 58 Principles P.11 Superposition 18 Pr.1.2 Complementarity Pt.2.1 Quantization Statistical algorithm 23 Correspondence P.71 Svmmetrization P.7.2 Pauli exclusion principle Separability 16.2 Criterion of physical reality Theorems Th.2.1 Hermitian operators Th.2.2 Finite-dimensional spectrum Th.2.3 Observables'equality Commuting observables Th.3.1 Stone Th.5.1 Schmidt decomposition 06121859 Th.6.1 Addition of angular momenta Spin and statistics Wigner
Definitions, principles, etc. Corollaries Cor. 2.1 Simultaneous measurability page 67 Cor. 16.1 Bell Dispersion-free 583 Definitions Def. 5.1 Entanglement 183 Def. 9.1 Operation 328 Def. 16.1 Completeness 568 Lemmas Lemma 9.1 Elby–Bub 299 Lemma 16.1 Bell I 583 Lemma 16.2 Bell II 584 Principles Pr. 1.1 Superposition 18 Pr. 1.2 Complementarity 19 Pr. 2.1 Quantization 44 Pr. 2.2 Statistical algorithm 57 Pr. 2.3 Correspondence 72 Pr. 7.1 Symmetrization 248 Pr. 7.2 Pauli exclusion principle 251 Pr. 16.1 Separability 568 Pr. 16.2 Criterion of physical reality 569 Theorems Th. 2.1 Hermitian operators 46 Th. 2.2 Finite-dimensional spectrum 47 Th. 2.3 Observables’ equality 60 Th. 2.4 Commuting observables 66 Th. 3.1 Stone 122 Th. 5.1 Schmidt decomposition 185 Th. 6.1 Addition of angular momenta 229 Th. 7.1 Spin and statistics 249 Th. 8.1 Wigner 262
xix Principles Th.82 Noether Th.9.1 Kraus Th.15.1 No-Cloning Th.15.2 D'Ariano-Yuen Th.15.3 Th.16.1 Th.16.2BelⅡ Th.16.3 Stapp Th.16.4 Eber Th.16.5 Th.17.1 Lindblad Th.17.2 Holevo
xix Principles Th. 8.2 Noether 264 Th. 9.1 Kraus 329 Th. 15.1 No-Cloning 548 Th. 15.2 D’Ariano–Yuen 549 Th. 15.3 Informational completeness of unsharp observables 564 Th. 16.1 Bell I 584 Th. 16.2 Bell II 589 Th. 16.3 Stapp 613 Th. 16.4 Eberhard 620 Th. 16.5 Tsirelson 624 Th. 17.1 Lindblad 631 Th. 17.2 Holevo 642
Boxes 1.1 Interferomentry page 15 21 Hermitian and bounded operator 47 Example of a Hermitian operator Unitary operators 2.4 Example of mean value 60 2.5 Commuation and product of Hermitian operators 2.6 Wave packet 40 3.1 Cyclic property of the trace 117 32 Einstein's box 132 4.1 Relativity and tunneling time 4.2 Scanning tunneling microscopy 4.3 Example of a harmonic oscillator's dynamics 163 7.1 Rasetti's discovery 250 8 Decoheringhistories 9.2 Recoil-free which path detectors? 9.3 Complementarity 9.4 Example of postselection 9.5 Example of operation 10.1 Remarks on the Fourier transform 11.1 Confluent hypergeometric functions 131 LASER 494 14.1 Coherent states and macroscopic distinguishability 17.1 Example of factorization
Boxes 1.1 Interferomentry page 15 2.1 Hermitian and bounded operators 47 2.2 Example of a Hermitian operator 48 2.3 Unitary operators 51 2.4 Example of mean value 60 2.5 Commutation and product of Hermitian operators 64 2.6 Wave packet 80 3.1 Cyclic property of the trace 117 3.2 Einstein’s box 132 4.1 Relativity and tunneling time 152 4.2 Scanning tunneling microscopy 152 4.3 Example of a harmonic oscillator’s dynamics 163 7.1 Rasetti’s discovery 250 8.1 Example of passive and active transformations 260 9.1 Decohering histories 288 9.2 Recoil-free which path detectors? 313 9.3 Complementarity 322 9.4 Example of postselection 326 9.5 Example of operation 327 10.1 Remarks on the Fourier transform 388 11.1 Confluent hypergeometric functions 408 13.1 LASER 494 14.1 Coherent states and macroscopic distinguishability 537 17.1 Example of factorization 663
Symbols Latin letters proposition,number à=品(oi+) annihilation operator annihilation operator of the k-th mode of the electromagnetic field =√亮(oi-) creation operator creation operator of the k-th mode of the electromagnetic field lai) A number A() Airy function vector potential A(r,1)=∑kk vector potential operator x akuk(r)e-iant +agu(r)ea! apparatus b proposition,number (polarization)state vector(along the direction b) bi) element vector of a discrete basisb) number,intensity of the magnetic field B=h/8π21 rotational constant of the rigid rotato B=V×A classical magnetic field =(益) magnetic field operator xiker-t)ie-i(kr-on)b speed of light.proposition cj.cj generic coefficients of the j-th element of given discrete expansion coefficient of the basis elementa) coefficient of the basis element coefficients of the expansion of a state vector in stationary state at an initial moment to =0
Symbols Latin letters a proposition, number aˆ = m 2h¯ω ωxˆ + ı ˆ x˙ annihilation operator aˆk annihilation operator of the k-th mode of the electromagnetic field aˆ † = m 2h¯ω ωxˆ − ıˆ x˙ creation operator aˆ † k creation operator of the k-th mode of the electromagnetic field |a (polarization) state vector (along the direction a) a j element of a discrete vector basis a j A number A(ζ ) Airy function A vector potential Aˆ (r, t) = k ck × aˆkuk(r)e−ıωkt + ˆa† ku∗ k(r)eıωkt vector potential operator A apparatus |A ket describing a generic state of the apparatus b proposition, number |b (polarization) state vector (along the direction b) bj element vector of a discrete basis b j B number, intensity of the magnetic field B = h/8π2I rotational constant of the rigid rotator B = ∇ × A classical magnetic field Bˆ (r, t) = ı k hk¯ 2cL30 1 2 × aˆkeı(k·r−ωkt) − ˆa† ke−ı(k·r−ωkt) bλ magnetic field operator c speed of light, proposition c j , c j generic coefficients of the j-th element of a given discrete expansion ca j coefficient of the basis element a j cb j coefficient of the basis element bj c (0) n coefficients of the expansion of a state vector in stationary state at an initial moment t0 = 0
xxii Symbols c(n,c(传) coefficient of the eigenkets of continuous observablesand,respectively lc) polarization state vector (along the C.c constants coulomb charge unit,correlation function cost function Cjk cost incurred by choosing the j-th hypothesis when the k-th hypothesis is true field of complex numbers electric dipole d distance D decoherence functional D(a)=eaat-a"a displacement operator exponential function e electric charge e=(ex.ev.ez) vector orthogonal to the propagation direction of the electromagnetic field le) excited state lex) k-th ket of the environment's eigenbasisej E energy E Eo E one-dimensional electric field E=-VVe-A classical electric field r,刊=∑（会）月 electric field operator ×aure-gre] environment effect 1E) ket describing a generic state of the environment ir arbitrary function arbitrary vectors 1f) final state vector force,arbitrary classical physical quantity . Fm classically magnetic force Fm(中) eigenfunctions of Fr)=传<x) distribution function of a random variable that can take values g arbitrary function,gravitational acceleration g ground state G(n) coherence of the n-th order
xxii Symbols c(η), c(ξ ) coefficient of the eigenkets of continuous observables ηˆ and ξˆ, respectively | c polarization state vector (along the direction c) C,C constants C coulomb charge unit, correlation function C cost function Cjk cost incurred by choosing the j-th hypothesis when the k-th hypothesis is true C( field of complex numbers d electric dipole d distance D decoherence functional Dˆ (α) = eαaˆ†−α∗aˆ displacement operator e exponential function e electric charge e = (ex , ey , ez) vector orthogonal to the propagation direction of the electromagnetic field | e excited state | ek k-th ket of the environment’s eigenbasis e j E energy En n-th energy level, energy eigenvalue E0 energy value of the ground state E one-dimensional electric field E = −∇Ve − ∂ ∂t A classical electric field Eˆ (r, t) = ı k h¯ωk 20 1 2 × aˆkuk(r)e−ıωkt − ˆa† ku∗ k(r)eıωkt electric field operator E environment Eˆ effect |E ket describing a generic state of the environment f arbitrary function f, f arbitrary vectors | f final state vector F force, arbitrary classical physical quantity Fe classically electrical force Fm classically magnetic force Fm(φ) eigenfunctions of ˆlz F(x) = ℘(ξ < x) distribution function of a random variable that can take values < x g arbitrary function, gravitational acceleration | g ground state G(n) coherence of the n-th order