# Questions tagged [nielsen-and-chuang]

For questions about exercises or passages from the popular quantum computing textbook *Quantum Computation and Quantum Information* by Michael Nielsen and Isaac Chuang.

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### POVM and non distinguishibility

The fact that non orthogonal states can't be distinguished is the reason why Alice can't communicate information faster than the speed of light when they have a qubit each and they are in bell state ...
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### What is the origin of the term POVM?

In Nielsen Chuang section 2.2.6 as they are introducing POVMs they write “The acronym POVM stands for ‘Positive Operator-Valued Measure’, a technical term whose historical origins we won’t worry about....
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### Single-qubit quantum channel from the CNOT gate

I am studying quantum noise, chapter $8$ in Nielsen and Chuang. Section $8.2.2$ introduces an example for the definition of quantum operations, in particular the CX gate is introduced as an example. I ...
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### Some lemma proof related to shor algorithm

How to derive or prove Lemma A4.12 and Theorem A4.13 from appendix 4 (section 4.3) of the book Quantum Computation and Quantum Information by Michael A. Nielsen, ...
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### No-cloning theorem and distinguishing between two non-orthogonal quantum states revisited revisited

There are many posts to this question from Nielson and Chuang's Quantum Computation and Quantum Information Exercise 1.2 page 57. It is required to prove that if a hypothetical device exists, which ...
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### Can a density operator be written equivalently as $\rho=\sum_i p_i|\psi_i〉\!\langle\psi_i|$ and $\rho=\sum_i\lambda_i|\psi_i\rangle\!\langle\psi_i|$?

My doubt arises from page 99, 101 of the book Quantum Computation and Quantum Information by Michael A.Nielson and Issac L.Chung. Let {${p_{i}, | \psi_{i} \rangle }$} be an ensemble of pure states. ...
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### How to derive the expression for the probability in quantum phase estimation? ((5.27) Nielsen & Chuang)

I'm trying to understand the QPE algorithm that is presented in the Nielsen and Chuang textbook. More precisely, I do not understand Equation $(5.27)$. Context: In the following, let $b$ be a natural ...
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### How Does the Transformation $|x \rangle | 0 \rangle \rightarrow | x \rangle | Hx \rangle$ Avoid Violating the No-Cloning Theorem?
This question relates to Nielsen & Chuang, Exercise 10.26, which says Suppose $H$ is a parity check matrix. Explain how to compute the transformation \$|x \rangle | 0 \rangle \rightarrow | x \...