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Classical and quantum cryptography in .NET Implement ECC200 in .NET Classical and quantum cryptography




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Classical and quantum cryptography using barcode printer for .net control to generate, create datamatrix 2d barcode image in .net applications. C# bases and the quantum bases {. 0 , . 1 } and {. + , . }, respectively. We m .net vs 2010 2d Data Matrix barcode ust notice that in order to reach this conclusion we did not need to make any assumption about the quantum nature of light.

Such an assumption will come into the picture later, when considering single-photon measurements. It will turn out, however, that the EM eld associated with the photon is essentially described by the same { , }, { , } bases and, therefore, the above conclusion remains fully valid at quantum scales. Next, I shall introduce an optical component referred to as a quarter-wave plate (QWP).

As the name suggests, it is a piece of at material, and it is transparent to light. The material, however, is a special type of crystal exhibiting the property of birefringence. A material is said to be birefringent if the speed of light varies according to the polarization orientation of the incident light ray (assumed linearly polarized).

Thus, the speed of light is faster in some polarization direction (referred to as the fast axis) and slower in the orthogonal direction (referred to as the slow axis). If the incident light ray is parallel to either the fast or slow axes, the light polarization remains unchanged. However, if the fast (or slow) axis forms a 45 angle with the incident polarization, the E- eld component that projects onto the fast axis propagates faster than the E- eld component that projects onto the slow axis, thus, introducing a phase delay between the two components and, hence, making the state of polarization of the ray evolve as it traverses the plate.

The additional feature of the QWP is that its thickness is precisely calculated in order for this net phase delay to be = /2 (corresponding to a quarter wavelength, hence, the name). Intuitively, we may already infer that the QWP transforms the input polarizations from linear to circular and the converse, and this inference is absolutely correct! Let us prove such a property now. Assuming a linearly polarized incident E- eld, as de ned in Eq.

(25.8), and the QWP axes oriented at 45 (cw) from the vertical axis, the incident E- eld is projected along the QWP fast and slow axes according to the de nition: 1 E in = ei 2 E1 + E2 E1 E2 ei t . (25.

16). After traversing the QW P, the output E- eld has become 1 E1 + E2 ei t E out = ei i 2 e (E 1 E 2 ) 1 E1 + E2 ei ei t . i (E 1 E 2 ) 2 Substituting E 1 = 1, E 2 = 0 (incident ray in the axis, or, conventionally, . 0 ), we obtain: 1 E out .net framework Data Matrix ECC200 = ei 2 1 = ei 2 1 i t e i 1 0 +i 0 1 ei t ,. (25.17). orientation, or aligned with the fast (25.18). which is immediately identi ed as the left-circular polarization state, or , or + . Clearly, the case E 1 = 0, E 2 = 1, corresponding to an incident ray in the orientation (or 25.8 Electromagnetic waves, polarization states, photons, and quantum measurements aligned with the slow a xis, or, conventionally, . 1 ), yields the right-circular polarization state, or , or . Thus, the QWP conve rts linear polarization states into circular polarization states, according to the transformations . 0 . + and 1 . . Let us show next th e converse operation. Assume an incident ray that is circularly polarized, according to the base or (equivalently, .

+ or ). It suf ces it to s ubstitute E 1 = 1 and E 2 = i in Eqs. (25.

16) and (25.17) to obtain for the output E- eld: 1 1 1 i i t 1 i ei t = ei e E out = ei 2 i (1 i) 2 i 1 1 1 + i i t 1 i t ei e ei + 4 e 1 2 1+i = i 1 1 i 1 ei t ei 4 ei t . e 1 2 (1 i).

(25.19). As expressed in the ver tical or horizontal basis (i.e., after rotating the reference axes by 45 ccw), the output E- eld is, nally, ei + 4 i e 4 1 i t e 0 0 i t e , 1.

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