ar X iv : q ua nt - p h / 03 11 00 5 v 1 2 N ov 2 00 3 Orthogonality of Biphoton Polarization States


Orthogonality, one of the basic mathematical concepts, plays an important role in physics, especially quantum physics and, in particular, quantum optics. A well-known example including both classical and quantum cases is orthogonality of two polarization modes of electromagnetic radiation. Physically, orthogonality of two arbitrary polarization states means that if light is prepared in a certain (in the general case, elliptic) polarization state it will not pass through a filter selecting the orthogonal state. (A filter selecting an arbitrary polarization state can be made of a rotatable quarter-wave plate and a rotatable linear polarization filter [1].) Orthogonality of polarization states has an explicit representation on the Poincaré sphere where each polarization state is depicted by a point. The state orthogonal to a given one is shown by a point placed on the opposite side of the same diameter. Examples are states with vertical and horizontal linear polarization, rightand leftcircularly polarized states, and any two elliptically polarized states with opposite directions of rotation and inverse axis ratios. This concept of orthogonality relates to both classical polarization states of light and single-photon quantum states of polarized light [2]. Mathematically, orthogonality of two polarization states means that the scalar product of two corresponding Jones vectors [1] is equal to zero. In quantum optics, this corresponds to zero scalar product of polarization state vectors, for instance, state vectors of single-photon states. This is a particular case of the general rule: orthogonality of quantum states means that their scalar product is equal to zero.

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@inproceedings{Chekhova2005arXI, title={ar X iv : q ua nt - p h / 03 11 00 5 v 1 2 N ov 2 00 3 Orthogonality of Biphoton Polarization States}, author={Maria Chekhova and Leonid Krivitsky and Sergei P. Kulik and G . A . Maslennikov}, year={2005} }