# Tag Info

### What is the density matrix of a pure state?

You can determine whether a state is pure or mixed by considering the purity $\gamma$ which is defined as the trace (i.e. the sum of diagonal entries) of the density matrix squared. \...
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### Can a density operator be written equivalently as $\rho=\sum_i p_i|\psi_i〉\!\langle\psi_i|$ and $\rho=\sum_i\lambda_i|\psi_i\rangle\!\langle\psi_i|$?

The statement $\rho=\sum_ip_i|\psi_i\rangle\langle \psi_i|$ is a very general way of writing down the density matrix. It must be noted that if you are simply presented with the matrix $\rho$, there ...
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### Exercise 4.16 in the Nielsen & Chuang book

In my copy, we are asked to consider this action $$|x_1\rangle|x_2\rangle \rightarrow (I_1 \otimes H_2)|x_1\rangle|x_2\rangle$$ and to find the matrix representation of $I_1 \otimes H_2$. In matrix ...
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### In general, what is feasible quantum computation?

I'm guessing that each 'feasible operation' is meant to refer to a specific quantum gate that can be easily implemented on your particular quantum computer of interest, e.g. with one or a couple of ...
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### Why adding H-gate is referred as changing the basis of measurement?

There are many ways to see that (one can invoke group theory, for example), but the way that I find easier is the following. Let q denote a system of a single qubit. Consider then two situations: q ...
### The matrix norm $\|A\|=\max_{\langle u|u\rangle=1}|\langle u|A|u\rangle|$ in the proof of Lieb's theorem
The short answer is that there are two problems with your argument: The partial derivative of $u^TAu$ you state is wrong More gravely, the whole approach is flawed because you're treating $u$ as a ...
To add to the other answer: multiple such Hamiltonians are possible, in general. A simple way to see it is to notice that you are looking for Hermitians $H$ such that $e^{iH}=U$ for a given unitary $U$...