Suppose that you have a 2 times 2 pixel image, and you measure tomographic proje

Question

Suppose that you have a 2 times 2 pixel image, and you measure tomographic projections of it in the vertical and horizontal projections, as we did in class and in the previous homework (see figure below). Let's call the pixel values x1, x2, x3, and x4, as shown below. Remember that each projection value is the sum of the pixel values along a ray. As we have discussed, many imaging problems can be expressed in the form of g=Hf. Write down specifically how the projections shown in this figure can be written in this form. (Your answer should show the values for the elements of f, g, and H). Write down an equation that we learned about earlier, which would be a good solution for estimating f from the projections g, if there is a lot of noise in g.

Explanation / Answer

Quantum tomography or quantum state tomography is the process of reconstructing the quantum state (density matrix) for a source of quantum systems by measurements on the systems coming from the source.[1] The source may be any device or system which prepares quantum states either consistently into quantum pure states or otherwise into general mixed states. To be able to uniquely identify the state, the measurements must be tomographically complete. That is, the measured operators must form an operatorbasis on the Hilbert space of the system, providing all the information about the state. Such a set of observations is sometimes called a quorum.

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