By Cherif Bendjaballah

ISBN-10: 3540591664

ISBN-13: 9783540591665

In recent times, growth within the iteration of squeezed states of sunshine, regularly characterised via a discounted noise estate, has prompted very important paintings when it comes to their capability use to enhance the sensitivity of optical communique platforms. those notes are dedicated to the detection and data processing of optical indications at very low degrees of strength. A survey of modern advancements from the quantum and classical issues of view is gifted. final limits of functionality lower than the standards of detection and knowledge are tested. a few of the effects are particular and will be applied for the layout of sensible platforms of communique utilizing current know-how. The textual content addresses physicists and engineers drawn to current and destiny advancements in optical conversation.

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22) J'P( a, a*)d(~e a )d(~m a) = 1. In this representation, the operators are normally ordered. In the case of antinormal ordering, a Q( a, a*) representation can be defined.. Plitkal ] Ja*kalP(a,a*)d(~ea)d(~ma). = There- fore P(a, a*) can be interpreted as a probability density. This function must be positive and its derivative should be smooth. Its conditions of existence are sometimes difficult to verify as in the case of the real squeezed states [26]. 23b) be the characteristic function normally ordered.

J 2lald(lal)lal 2m 2 exp (-l a I ) ] Im)(ml = L Im)(ml = ] m m which yield the probability that the energy is En of a Poisson form. 3) where {IPi)}, {Iqk)} are the corresponding complete sets of normal- ized eigenvectors of P, Q respectively, For a one dimensional particle X, Px in a Hilbert space 1t [23]. P, defined so that XIx) = - xix), Pip) = pip), we have (xlp) = Jxexp(~). Suppose I'l/J) be a given pure state. Setting 'l/Jl(X) = (xl'lf), it is easy to obtain 'l/Jl(X) = j (x Ip)(pl'l/J)dp = ~j exp( i~x )'l/J2(p)dp 'l/J2(p) = j(p1x) (x I'l/J) dx = ~j exp where J Ix)(xldx = 1, J Ip)(pldp = 1, 'l/J2(p) (-t x )'l/Jl(x)dx = (pl'l/J) , and (xIPI'l/J) = -ilitx(xl'lf).

Application, let us reproduce some elements of the demonstration of the quantum analog of the classical central limit theorem for a single mode of radiation [5]. I. Elements of Quantum Mechanics Let the state Iz} = Ivk- 2:m zm} 45 be composed of a large number M of independent identically distributed contributions Zm of distribution Tm(Zm). R(zm)d~(zm), the density operator is written ¥= J PM(Zm) ~ILZm}(LZmldJl(zm) m m where 'PM(Zm) is given by a multiple convolution integral PM(Zm) = J.. dJl(ZM -1) The Fourier transform W(x, k) of the equivalent form ofPM(zm) in the phase space W(p,q) is W(x, k) = n~=l W m wm(x, k) is the Fourier transform of the (k' k-) where distri~ution Tm(Z) in the phase space.

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