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The following equations are derived from Quantum information theory, which requires the use of Cauchy Schwarz inequality for a proof.

I am quite puzzled by the second term in the summation, which consists of a sum over the product of a square norm and an absolute value i.e. the product of two scalars!, my question is : isn't cauchy schwarz inequality strictly applied to vectors only?

I found the closest thing to the one i had is the Rn dimension from Wiki, but xi, yi there are component of a vector in which my case isn't.

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  • $\begingroup$ See math.stackexchange.com/q/1681300 $\endgroup$ – Tom Collinge Mar 27 '16 at 12:56
  • $\begingroup$ Do you mean it is true that n = 1 i.e. scalar? still works? $\endgroup$ – el psy Congroo Mar 27 '16 at 12:59
  • $\begingroup$ If $n = 1 $ then all it says is $(xy)^2 \le x^2y^2$ and since they are the same this is clearly true. $\endgroup$ – Tom Collinge Mar 27 '16 at 13:02

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