work, as we have illustrated it on the APD and the HD. [1] J. Von Neumann, Mathematical fondations of quantum mechanics , Princeton University Press (1955). [2] J. A. Wheeler and W. H. Zurek, Quantum Theory and Measurement . Princeton University Press, NJ, 1983). [3] M. Brune et al., Phys. Rev. Lett. 101 , 240402 (2008); Mirko Lobino, et al., Science 24 , Vol. 322, no. 5901 (October 2008). [4] J. S. Lunden et al. Nature Physics 5 , 27-30 (2009); G. Puentes et al. Phys. Rev. Lett. 102 , 080404 (2009). [5] M. Nielsen and I. Chuang, Quantum Computation and Quantum Information , Cambridge University Press (2000). [6] J. Fiurasek, Phys. Rev. A 64 , 024102 (2001). [7] Y. Aharonov, P. G. Bergman and J. L. Lebowitz, Phys. Rev. 134 , B1410 (1964). [8] S. M. Barnett, et al. J. Mod. Opt. 47 , 1779 (2000). [9] P. Busch, Phys. Rev. Lett. 91 , 120403 (2003). [10] A.M. Gleason, J. Math. Mech. 6, 885 (1957). [11] M. A. Neumark, Compt. Rend. (Doklady) Acad. Sci. URSS, 41(9), 359 (1983). [12] Y. Aharonov and L. Vaidman, Resolution of a ”Retrodiction Paradox” , arXiv:quant-ph/9501002v2 (1995). [13] S. Haroche and J.M. Raimond, Exploring the quantum : Atoms, Cavities, and Photons , Oxford Graduate Texts (2006). [14] K. Hornberger, Introduction to decoherence theory. in Entanglement and Decoherence. Foun- dations and Modern Trends, Lecture Notes in Physics 768, 221-276. Springer, Berlin (2009). [15] K. Kraus, States, Effects and Operations , Lecture notes in Physics No. 190, Springer (1983). [16] A.I. Lvovsky et al. Phys. Rev. Lett. 87 , 050402 (2001); A. Ourjoumtsev, et al. Phys. Rev. Lett. 96 , 213601 (2006). [17] A. Ourjoumtsev et al. Science 312 , 83-86 (2006); A. Ourjoumtsev et al. Nature 448 , 784-486 (2007). [18] E. Wigner, Phys. Rev. 40,749 (1932). 19