# Questions tagged [density-matrix]

For questions about density matrices and related concepts and ideas, e.g. procedures for computing properties of quantum states from their density matrices.

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### (Proof verification) Kaye Exercise 3.5.5, partial trace in larger system

This is the exercise as stated in Kaye's book, Introduction An Introduction to Quantum Computing: Show that for any density operator $\rho$ on a system $A$, there exists a pure state $|\psi\rangle$ ...
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### Why density matrix representation usually written in the following form?

The pure state $|\psi\rangle = \sum \alpha_i |i\rangle$, $\rho = \sum_{i,j}\alpha_i^*\alpha_j |j\rangle\langle i|$, why is the form not be $\rho = \sum_{i}\alpha_i^*\alpha_i |i\rangle\langle i|$ ???
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### Is Density Matrix simulation same as Tensor Network simulation?

I read that there are two major ways of simulating quantum circuits - State Vector Simulation and Tensor Network Simulation. But Qiskti provides a backend to simulate state-vectors and a backend for ...
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### Question about the probability of failure of the bit flip code

For the bit flip superoperator is $$\mathcal{E}_{BF}(\rho) = (1-p)\rho + p X \rho X$$ where the first term refers to no bit flip and the second term refers to the bit flipping. A single qubit pure ...
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### How to find initial quantum states from the density matrix?

Recently, I came across density matrix. Given a qubit $|\psi \rangle = \alpha |0\rangle + \beta |1\rangle$, we can find its density matrix by computing $\rho \equiv |\psi \rangle \langle \psi |$. My ...
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I want to use the reduced density matrix to compute the measurement probability: $prob(y)=\langle y|\rho|y\rangle$ for a 3-qubit simon algorithm, instead of measuring the ancilla qubits. Here \$\rho=...