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I'm trying to understand the following equality found in a paper of quantum key distribution Fully device independent quantum key distribution :

$$a \oplus b = x \wedge y$$

As far as I know;

  • $\oplus$ stands for lofic X-OR
  • $\wedge$ stands for logic AND

Using integers from a specific set $\{0,1\}$, how the above mentioned equality can be satisfied?

Example:

  • $a=1, b=1, x=1, y=1$

    $1 \oplus 1 = 0, \quad 1 \wedge 1 = 1 \quad 0 \neq 1$, therefore NOT satisfied

  • $a=1, b=0, x=1, y=1$

    $1 \oplus 0 = 1, \quad 1 \wedge 1 = 1 \quad 1 = 1$ therefore satisfied

Is that correct?

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    $\begingroup$ Yes this and the examples are correct: depending on values of $a$, $b$, $x$, $y$, the equality $a\oplus b=x\wedge y$ is satisfied, or not. $\endgroup$
    – fgrieu
    Sep 8, 2020 at 20:36
  • $\begingroup$ For a second I thought you were comparing XOR to XOR... I've been programming too much in C. Yes, the examples are correct, but be careful saying that to a C programmer. In C, ^ means XOR and & means AND. $\endgroup$
    – Serpent27
    Sep 8, 2020 at 20:48
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    $\begingroup$ @Serpent27: ∧ is AND, ^ is C's XOR. Different characters, different meanings. $\endgroup$ Sep 9, 2020 at 0:23
  • $\begingroup$ Yes, but they still look basically the same if you're too used to seeing only ^ $\endgroup$
    – Serpent27
    Sep 9, 2020 at 0:58
  • $\begingroup$ Could you add the page and line, too? $\endgroup$
    – kelalaka
    Sep 9, 2020 at 9:35

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