xxvi Symbols 7 transmission coefficient temperature,classical kinetic energy kinetic energy operator time reversal operator generic transformation (v.T) energy density uo=音r k-th mode function of the electromagnetic field scalar potential unitary operator UBs beam splitting unitary operator UPBS polarization beam-splitting unitary operator unitary controlled-not operator Uf Boolean unitary transformation UE Fourier unitary transformation unitary Hadamard operato 0p(w) unitary momentum translation Up permutation operator 0R(p) rotation operator space-reflection operator 0 time translation unitary operator Ux(a) one-dimensional space translation unitary operator Ur(a) three-dimensional space translation unitary operator unitary rotation operator Ve unitary phase operator OSA=ekffisau) unitary operator coupling system and apparatus for time interval OsAe=e一isAt unitary operator which couples the environment Eto the system and apparatus S+Aat time antiunitary operato time reversal generic transformation that can be either unitary or antiunitary 1) state of vertical polarization element of a discrete basis potential energy scalar potential of the electromagnetic field V)=Ψ centrifugal-barrier potential energy classical potential energy potential energy operator xxvi Symbols T transmission coefficient T temperature, classical kinetic energy Tˆ kinetic energy operator Tˆ time reversal operator ˆ Tˆ , T generic transformation u(ν, T ) energy density uk(r) = e L 3 2 eık·r k-th mode function of the electromagnetic field U scalar potential Uˆ unitary operator UˆBS beam splitting unitary operator UˆPBS polarization beam-splitting unitary operator UˆCNOT unitary controlled-not operator Uˆ f Boolean unitary transformation Uˆ F Fourier unitary transformation Uˆ H unitary Hadamard operator Uˆp(v) unitary momentum translation Uˆ P permutation operator UˆR(φ) rotation operator UˆR space-reflection operator Uˆt time translation unitary operator Uˆ x (a) one-dimensional space translation unitary operator Uˆr(a) three-dimensional space translation unitary operator Uˆθ unitary rotation operator Uˆφ unitary phase operator Uˆ SA τ = e − ı h¯ τ 0 dt Hˆ SA(t) unitary operator coupling system and apparatus for time interval τ Uˆ SA,E t = e− ı h¯ t HˆSA,E unitary operator which couples the environment E to the system and apparatus S + A at time t ˜ Uˆ antiunitary operator ˜ UˆT time reversal Uˆ generic transformation that can be either unitary or antiunitary |v state of vertical polarization |vn element of a discrete basis V potential energy Ve scalar potential of the electromagnetic field Vc(r) = h¯ 2l(l+1) 2mr 2 centrifugal-barrier potential energy Vc classical potential energy Vˆ potential energy operator