I am trying to understand the mathematics of quantum eraser experiments, in order to deepen my understanding of what is really happening. The paper I am currently working on is:(adsbygoogle = window.adsbygoogle || []).push({});

"A double-slit quantum eraser" by S. P. Walborn, M. O. Terra Cunha, S. Padua, and C. H. Monken (2001)

in which a quarter-wave plate is placed behind each slit, with the fast axis of one plate being perpendicular to that of the other. The photons passing through a slit have polarisations corresponding to either ##\vert x \rangle## or ##\vert y \rangle##, where the directions of those two polarisations are orthogonal. Each photon has been, prior to approaching the slit, entangled with a twin that has theotherpolarisation out of ##\vert x \rangle## and ##\vert y \rangle##.

The paper says, just after equation 9 on page 3, that the interference pattern, which is there if the quarter-wave plates are not in place, disappears when the quarter-wave plates are in place. Unfortunately it does not show the derivation by which that is deduced, contenting itself with the vague throwaway line that 'since ##\psi_1## and ##\psi_2## [the states representing transit through the first or second slit] have orthogonal polarizations, there is no possibility of interference'.

I have tried to confirm this result by mathematical derivation from the equations 1-9 in the paper. But in order to reach a result of non-interference, I have to make a couple of assumptions with which I am not comfortable. I am not very confident working with these states because I have not read about how to represent entangled states in bra-ket equations. My two texts - Shankar and Cohan-Tannoudji - do not mention entanglement at all, or at least the word does not appear anywhere in the index of either one.

I would be grateful if anybody could:

* point me to a derivation of the result that the interference disappears; and/or

* give me some hints that might help with my derivation; and/or

* point me towards a detailed explanation of how entangled states are represented by bra-ket equations.

Thank you

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# Mathematics of entanglement in quantum erasers

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