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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In exercise 8.23 of Nielson and Chuang why is the quantum operation no longer trace-preserving?
My question is about this exercise from Nielsen & Chuang:
For context, $\mathcal{E}_{AD}$ is the quantum operation for amplitude damping on a single physical qubit, with operation elements given ...
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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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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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Why does it matter that Schmidt number is invariant under unitary transformations?
I am reading Nielsen & Chuang and they say this:
"The bases $|i_A\rangle$ and $|i_B\rangle$ are called the Schmidt bases for A and B, respectively, and the number of non-zero values $\...
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Why do we need/have the operator sum representation (Kraus representation)?
I am reading through Nielsen & Chuang, and I am on the section about operator sum representation. They performed this derivation.
Why is it important and useful for us to bundle together the ...
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Why do minimal ensemble decompositions for $\rho$ contain $|\psi⟩\in{\rm supp}(\rho)$ with probability $1/\langle\psi|\rho^{-1}|\psi⟩?$
I came across the following exercise (2.73) in Nielsen & Chuang and am trying to understand it intuitively.
Here is my reasoning of what is going on:
The purpose of this exercise:
Let’s say we are ...
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What is meant with "different ensembles can give rise to the same density matrix?"
I am reading the Nielsen & Chuang section on density matrices and I don't understand the example given to demonstrate a concept. Here is what I am reading:
First, they said these two different ...
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Reasoning behind unitary freedom in the ensemble for density matrices theorem
Although my question has the same title of a different question, it is not a duplicate. I am asking a different question. I don't care why it made it into the book.
Here is a theorem from Nielsen &...
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Why is a post-measurement state a valid quantum state?
Postulate 3 of the postulates of quantum mechanics in Nielsen & Chuang states that
Quantum measurements are described by a collection ${M_m}$ of measurement operators... and the state of the ...
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Quantum Error Correction Difficulties: "Measurements destroy quantum information" Intuition
Context: In section 10.1.1, Nielsen and Chuang describe the difficulties QEC faces compared to classical error correction. Particularly that
Measurements destroy quantum information.
Shor states in ...
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On the use of $\log(P\otimes Q)= \log P\otimes I+I\otimes\log Q$ for relations between entropic quantities. What if $P,Q$ are only semidefinite?
Many properties of entropic quantities are shown by resorting to related properties of the relative entropy of suitable quantities. For instance, subadditivity of entropy may follow from non ...
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Exercise 11.7 in Nielsen & Chuang and basic properties of Shannon entropy
I apologize in advance if this question is trivial, I'm aware I'm a total beginner in this field. This is the exercise I would like to solve:
As to the first point, what I get is that one should ...
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Question about fault-tolerant measurement in Nielsen&Chuang page 490
The fault-tolerant procedures for state preparation and logical operation consider the procedure successful if only a one-qubit error occurs in each encoded block of the output.
So, I thought that the ...
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