# Questions tagged [linear-algebra]

For questions about vector spaces of all dimensions and linear transformations between them, including systems of linear equations, bases, dimensions, subspaces, matrices, determinants, traces, eigenvalues and eigenvectors, diagonalization, Jordan forms, etc.

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### How to write the joint action of a CP map that acts on a single qubit of a bipartite state?

The question Say I have a completely-positive (CP) map $\mathcal{A}_{ij}$ defined in terms of two projectors $\Pi_i = |i\rangle \langle i |$ and $\Pi_j = |j\rangle \langle j |$ that acts on a density ...
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Consider the task of distinguishing between the following two $n$ qubit quantum states. $$\rho = \frac{\mathbb{I}}{2^{n}}.$$ $$\sigma = \frac{1}{2^{n/2}}\sum_{x \in \{0, 1\}^{n/2}} |x\rangle\langle ... 0answers 81 views ### Is decomposing high-dimensional states in terms of Pauli matrices impossible? I've been trying to decompose a 3x3 density matrix with 3-dimensional Pauli matrices but it doesn't work for all matrices. For example, the density matrix of the state |0\rangle + |1\rangle + |2\... 0answers 82 views ### Matrix multiplication through Block Encodings For a project, I want to simulate a matrix multiplication on a simulated quantum circuit. Assuming that we have a matrix A\in \mathbb{R}^{m\times n} stored in a quantum superposition, i.e.$$|A\...
My goal would be to implement the unitary matrix $M=\begin{bmatrix}U_{1} &0\\0&U_{0}\end{bmatrix}$ as a circuit for arbitrary $N \mathrm{x} N$ unitary matrices. It is trivial to show that if ...
I am trying to repeat the results from Peng and Kowalski (Eq 11) which solves the analytical form of an equation consisting of powers of the Hamiltonian (moments): The $K$-th order PDS formalism is ...