# 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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### Density matrices for pure states and mixed states

What is the motivation behind density matrices? And, what is the difference between the density matrices of pure states and density matrices of mixed states? This is a self-answered sequel to What&#...
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### Purity of mixed states as a function of radial distance from origin of Bloch ball

@AHusain mentions here that the purity of a qubit state can be expressed as a function of the radius from the center of a Bloch sphere. The state corresponding to the origin is maximally mixed whereas ...
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### How to perform Quantum Process Tomography for three qubit gates?

I am trying to perform Quantum process tomography (QPT) on three qubit quantum gate. But I cannot find any relevant resource to follow and peform the experiment. I have checked Nielsen and Chuang's ...
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### Implementation of tomography on IBM Q

I wanted to ask how do you implement a circuit that finds the non-diagonal values of the density matrix of a quantum state on IBM Q?
Let's say I have more than one qbits $|0\rangle|1\rangle$ and I want to perform a $H$ on both of them. I know the matrix representation for the Hadamard on a single qbit is $$\frac{1}{\sqrt{2}}\begin{... • 215 3 votes 1 answer 210 views ### Is the partial trace \mathrm{Tr}_B(\rho) equal to \sum_k \mathrm{Tr}[(\sigma_k\otimes I)^\dagger \rho]\sigma_k? Assume a composite quantum systes with state |\psi_{AB}\rangle or better \rho=|\psi_{AB}\rangle\langle\psi_{AB}|. I want to know the state of system A only, i.e. \rho_A. Is there any ... • 658 2 votes 1 answer 245 views ### Why is a density operator defined the way it's defined? It's stated that the density operator is:$$\displaystyle \rho =\sum _{j}p_{j}|\psi _{j}\rangle \langle \psi _{j}|.$$But I don't understand why this is the way both in mixed state and pure state. ... • 881 2 votes 1 answer 42 views ### If states are close together does there always exist a channel close to the identity mapping one to the other? Question: Given states \rho,\omega\in\mathbb C^{n\times n} and \varepsilon>0 such that \rho and \omega are \varepsilon-close in trace norm does there exist a channel \Phi with \Phi(\... • 1,961 2 votes 1 answer 350 views ### Is there an algorithm that can decide if a state is a mixed state or a pure state? Given we are using the computational basis,is there a quantum algorithm that can decide if an arbitrary input state \vert A\rangle ( using N qubits) is a pure state or a mixed state? \vert A\... • 65 2 votes 1 answer 453 views ### How would I compute a density matrix of a 2 qubit mixed state? I am currently reading Nielsen & Chuang, and one of the questions asks to calculate a density matrix with the following mixed states, how would I do this?$$ |00> \;with \;probability \; 2/4 \\ ...
How can we find a Wigner function for the four maximally entangled Bell states $(|00\rangle \pm |11\rangle)/\sqrt{2}$, $(|01\rangle \pm |10\rangle)/\sqrt{2}$? I have used the basis where labels for ...