Einstein Relatively Easy

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                                      If we need to construct the tensor product of two operators, and we do already know the matrix elements of the building blocks, we can combine them directly.

Here is the rule for combining by example 2x2 matrices to form 4x4 matrices:

or

 

Remark 1: the same pattern works for matrices of any size. In general, the product of an m x n matrix and a p x q matrix is a mp x nq matrix.

Remark 2: All of this applies perfectly well to column and rows vectors, which are just some kind of matrices.

so we would write by example for the basis vector |uu> of a qubit system:

 

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"The essence of my theory is precisely that no independent properties are attributed to space on its own. It can be put jokingly this way. If I allow all things to vanish from the world, then following Newton, the Galilean inertial space remains; following my interpretation, however, nothing remains.."
Letter from A.Einstein to Karl Schwarzschild - Berlin, 9 January 1916

"Quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. The theory says a lot, but does not really bring us any closer to the secret of the 'old one'. I, at any rate, am convinced that He is not playing at dice."
Einstein to Max Born, letter 52, 4th december 1926

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