# 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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### Can results about pure states be extended to convex sums of pure states?

Most results discussed in quantum computing textbooks are about pure states. I'm curious whether these result can be extend to convex sum of pure states. In the case of qubit states, pure states are ...
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### Complexity of Partial transpose operation

Let us take a general bipartite system $H = H_a \otimes H_b$, with $d_a$ = dim $H_a$, and similarly $d_b$ = dim $H_b$. My question is: what is the complexity of the partial transpose operation on a ...
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### Tests of entanglement between one and many qubits

I have a 5-qubit state $|\psi \rangle$, which has a physical interpretation that the middle qubit is the "impurity" with spin $s_{imp} = 1/2$. The rest 4 qubits highlight the presence of ...
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### What is the best way to model a polarizer?

If I have a photon reaching a polarizer, I can think of a polarizer as an operator of $P=a^\dagger_Va_V$ where $a^\dagger_V$ creates a photon with vertical polarization (V). However, on the other ...
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### Obtaining the reduced density matrices for both subsystems of a bipartite system [duplicate]

If we have a single copy of a bipartite quantum system with density matrix $\rho$, is it possible to extract the reduced density matrices of the constituent subsystems separately, i.e. to achieve the ...
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### Proving CLDM is in QMA, In particular why is it possible to assume that the given input is a product of copies in the soundness section?

I'm wondering about a specific proof for Consistency of Local Density Matrices (CLDM) $\in$ QMA appearing in "QMA-hardness of Consistency of Local Density Matrices with Applications to Quantum ...
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### Initialize circuit by density matrix (i.e. mixed state) by Cirq, Qiskit, QuTip

I want to do a simulation involving: mid-circuit measurement (i.e. based on the measurement result of some qubits to append further gates on other qubits; e.g., Pauli error correction in entanglement ...
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### Finding the eigenvalues of a qutrit state

I am interested in the state: $\frac{1}{\sqrt{2}} (\left|11\right> + \left|22\right>)$ If I find the density matrix of this, I find the $9 \times 9$ matrix $\rho$. If I want to find the reduced ...
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Given a state in bra-ket notation as $|\psi\rangle=\frac{1}{\sqrt{3}}(|001\rangle+|010\rangle+|100\rangle)$. What is the density matrix of this state written using Pauli's spin operator?
Let us consider the tensor product of two finite Hilbert spaces $\mathcal{H}_1\otimes \mathcal{H}_1$. According to Watrous book, the set of separable states is the convex hull of the set of product ...