# Questions tagged [notation]

For questions about the usage of, origin of or reasons for specific notation used in the context of quantum computing.

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### What is meant by a "projection operator" in the book "Quantum Computation and Quantum Information"?

I've started reading the book "Quantum Computation and Quantum Information" by Michael A. Nielsen and Issac L. Chuang, specifically chapter 10 (about quantum error correction), and I'm ...
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### Is there any standard notation for two states being "equivalent up to a global phase"?

Is there any standard notation for two states "equivalent up to a global phase"? Currently, I use just an equal sign but I'd like to use a different symbol to distinguish between two phases ...
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### Elementary question: is $\langle a|b \rangle$ the same as $\langle a||b\rangle$?

In trying to learn more about quantum computing, one of the first things encountered is a definition of the inner product $\langle a|b\rangle$. If I interpret it correctly, and looking near the bottom ...
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### What is a term for a basis state along with its corresponding complex amplitude?

For some arbitrary state $|\psi\rangle = c_0|x_0\rangle + c_1|x_1\rangle + c_2|x_2\rangle ... + c_{2^n}|x_{2^n}\rangle$, where each of $|x_i\rangle$ is a basis state, and each of $c_i$ is the ...
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### What are QHT, QWT and QFT?

I am new to quantum computing. I am not able to understand QHT, QWT and QFT. I tried searching for a suitable material but still could not find them. It would be great if someone can explain and also ...
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### How is a classical bipartite state written in quantum notation?

As in the title, is a classical bipartite state on $AA'$ given by $$\sum_{ij} p_{ij} \vert i\rangle\langle i\vert_A \otimes \vert j\rangle\langle j\vert_{A'}$$ with $\sum_{ij}p_{ij} = 1$. In ...
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### What does it mean that 1 qubit can do the job of 1 ebit (entanglement bit)? (second Bennett's law)

I just came across Bennett's laws and I wonder what the second law mean. It states that 1 qubit "can do the job" of 1 ebit. However, the definition of ebit (entanglement bit, wiki just ...
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### What is the "quantum phase" of a quantum state?

On this page IMBQ docs, until the sentence '..and since the global phase of a quantum state is not detectable..' I follow everything. However 'quantum phase' is introduced without any explaination? ...
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### What is the correct notation to denote operations conditional on a measurement outcome?

What is the correct mathematical notation to describe the following setup? I have classical state in register $A$ which I can think of as $\sum_i p_i \vert i\rangle\langle i \vert_A$. I measure this ...
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### What is a bipartite unitary?

What is a 'bipartite unitary'? I saw it appearing in a paper "Efficient verification of quantum gates with local operations" (https://arxiv.org/pdf/1910.14032.pdf) A reference to the ...
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### In Dirac notation, why do we have $\langle cf|g\rangle = c^*\langle f\vert g\rangle$?
A Hilbert Space has this property $$\langle cf,g\rangle=c\langle f,g\rangle$$ where $f$ and $g$ are the vectors in the Hilbert Space and $c$ is a complex number. In Dirac Notation, \langle cf|g\...
### What are $|+\rangle$ and $|-\rangle$?
On a view places, I've seen kets that look like this $\left|+\right>$ or this $\left|-\right>$ but I don't seem to find any explanation of this base online. Is it just a different notation for \$...