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Tutorial
Orthogonal Quantum States
The examples of photons with vertical ("V") or horizontal ("H") polarization introduce the concept of orthogonal quantum states. A "V" photon will never pass a test for "H" polarization (and vice versa), and so using the language of vectors, we say that "V" and "H" are two orthogonal quantum states of a photon. It is a remarkable property of photons that any other single-photon polarization state can be formed from a suitable linear combination of "V" and "H" states, possibly with complex coefficients. We say that single-photon polarization is a two-state (or two-level) quantum system, and that "V" and "H" form a basis for the space of polarizations (an example of a Hilbert space).
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