# XOR & AND equation in quantum computing ... is it correct?

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?

• 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.
– fgrieu
Sep 8, 2020 at 20:36
• 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. Sep 8, 2020 at 20:48
• @Serpent27: ∧ is AND, ^ is C's XOR. Different characters, different meanings. Sep 9, 2020 at 0:23
• Yes, but they still look basically the same if you're too used to seeing only ^ Sep 9, 2020 at 0:58
• Could you add the page and line, too? Sep 9, 2020 at 9:35