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2

You're right, there should be 16 terms. But since they are tracing out Alice's system in the next step only 4 terms are relevant - those that correspond to $|00\rangle \langle 00|$, $|01\rangle \langle 01|$, $|10\rangle \langle 10|$ and $|11\rangle \langle 11|$. Tracing out $|00\rangle \langle 01|\cdot |\phi\rangle\langle\psi|$ will result in 0, because $\...


2

This picture can be confusing, since it makes some assumptions that are not clear when you quickly scan through the text. The picture of the oracle $U_f$ describes its effect on the basis states that go into it, not on arbitrary superposition states. If both $x$ and $y$ are basis states, the oracle will behave exactly as the rectangle says, but the ...


4

To answer your first question, the quantum oracles are defined by their effect on the basis states $|0\rangle$ and $|1\rangle$, and if the oracle has to be computed on a superposition of basis states, its effects are expressed using the fact that the oracle is a linear transformation. This means that you never compute $f(|+\rangle)$; instead, to compute the ...


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You've computed $\rho^{AC},\rho^{BC}$ incorrectly $-$ they are matrices of size $8\times 8$, also they are not equal to $I/8$. Nevertheless their entropy is equal, i.e. $S(A,C) = S(B,C)$. So $|\psi \rangle$ is indeed a counterexample to the statement. The inequality $S(A,B)\geq S(A|C)-S(B|C)$, which is equivalent to $$ S(A,B) + S(B,C) \geq S(A,C) $$ is ...


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I will try to link the two concepts in the following way. It is rough, descriptive, but contains the essential idea. Here we are talking about the so-called orbital angular momentum (OAM) of an electron orbiting around the nuclei. In classical mechanics, OAM is defined as $ \vec{L} \equiv \vec{r}\times\vec{p} $ where $\vec{r}$ is the position of the ...


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