# Questions tagged [quantum-information]

This tag is related to Quantum information Theory.

85 questions
1answer
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### How to prove Shannon entropy inequality with something that seems to be some sort of taylor expansion

I'm slightly confused about some sort of "proof" (probably not a real proof since it's physics math) I have the formula $f(x) = f(y) + (x-y)f'(y) + \frac{f''(y)}{2\epsilon}, \quad \epsilon \in (x,y)$...
0answers
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### Prove that the operator of the Grover's algorithm 'inverts about the mean'

I'm trying to solve the following problems that I have found in the book An Introduction to Quantum Computing by Phillip Kaye, but I don't know exactly where should I start. I would appreciate any ...
0answers
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### Inequality between independence numbers(one-shot zero-error capacity)

I had a question when I was studying the Entanglement-Assisted Independence Number $\tilde{\alpha}(S)$, where $S$ is a operator system. In the inserted figure, the high-lighted sentence said that the ...
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1answer
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### Difference between operator defined on a space and operator represented in a space

I am quite confused about linear operators that are defined as acting on a Hilbert space $\mathcal{H}$ and their representations. The operators form an operator algebra and as such can be represented ...
2answers
147 views

### Does $\mathcal{B}(\mathcal{H})=H\otimes H^*$ in infinite dimensions?

In quantum information contexts (where in most cases finite dimensions are considered) I have often seen the statement that the space of bounded linear operators $\mathcal{B}(\mathcal{H})$ on a ...
1answer
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### Question concerning Stirling’s Approximation

From Nielsen & Chuang, page 55: The basic intuition for this decrease in resources required can be understood quite easily. Suppose the source emitting states $|0\rangle$ with probability $p$ ...
1answer
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### Characterizing families of $p^2$ orthogonal $p \times p$ unitaries?

Suppose I walk up with $2$-by-$2$ unitary matrices $U_1,U_2,U_3,U_4 \in \mathbb{C}^{2 \times 2}$ with the property that $\mathrm{Tr}(U_i U_j^\dagger) = 0$ for all $i \neq j$. One can show that there ...
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1answer
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### an example of stochastic matrix not derived from a unitary matrix

I solved (a) but cannot find an example for (b). Could anyone show me a stochastic matrix not derived from a unitary matrix?
0answers
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### How to compute the average value of an observable

This is from the p.116 of Nielsen and Chuang's quantum computation and quantum information book. The (2.229) equations are the ones I can't see how to calculate. In (2.227) and (2.228), the index 1 ...
1answer
113 views

### solving “Cascaded measurements are single measurements”

This is an exercise from p. 86 Quantum Computation and Quantum Information by Michael A. Nielsen and Isaac L. Chuang. Here I think I have to show that $p\left(l\right)p\left(m\right)=p\left(lm\right)$...
1answer
28 views

### what does it mean by “relabelling of the measurement outcomes”

This is an exercise from p.52 of An Introduction to Quantum Computing by P. Kaye, R. Laflamme and M. Mosca. The oberservable Z denotes Pauli Z matrix. What does it mean by relabelling of the ...