# 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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### 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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### How to find density matrix of 3 qubit W state?

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?
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### Is possible to write a separable state as a finite or countable infinite sum of product states?

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 ...
1 vote
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### QISKIT: ValueError: too many subscripts in einsum DensityMatrix()

I am trying to compute the entanglement entropy of a partition of a quantum system on qiskit. To do this, I call the function DensityMatrix(). If I go above 10 sites (e.g. 12), I get an error like: ...
1 vote
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### Derivation of Choi-Jamiolkowski isomorphism

I'm following the course Mathematical Methods of Quantum Information Theory by Reinhard Werner. In lecture 6, he gave a derivation of Choi-Jamiolkowski isomorphism, and I'm struggling to understand ...
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### Does separability of a matrix implies the matrix is a density matrix?

Suppose I have a matrix that is unknown whether it is a density matrix and assume that finding the eigenvalues of it is difficult because the matrix is expressed generally. However, suppose that this ...
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### Define a traceless part of $\rho$ [closed]

I saw in a paper: $|\bar{\rho}\rangle\rangle=|\rho\rangle\rangle-|\hat{I}\rangle\rangle / 2^{n / 2}$ for the $4^n$-dimensional vector representing the traceless part of $\rho$. https://arxiv.org/abs/...
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### calculate the reduced density matrix of a 2 qubit state and compare the eigenvalues

So I have the exercise to apply a Cz gate to the following 2 Qubit state $|a\rangle \otimes |b\rangle = (a_0 |0\rangle + a_1 |1\rangle) \otimes (b_0 |0\rangle + b_1 |1\rangle)\\\\$ Afterwards, I ...
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### Moments of Pauli coefficients of Haar-random states

I want to evaluate the quantity $\sum_{P\in \rm{P}^n}\text{Tr}^{\alpha}(\rho P)$, where $P$ is an element of n-qubit Pauli group $\rm{P}^n$ and $\rho$ is a density matrix of a Haar random state. It is ...
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### Can a density operator be written equivalently as $\rho=\sum_i p_i|\psi_i〉\!\langle\psi_i|$ and $\rho=\sum_i\lambda_i|\psi_i\rangle\!\langle\psi_i|$?

My doubt arises from page 99, 101 of the book Quantum Computation and Quantum Information by Michael A.Nielson and Issac L.Chung. Let {${p_{i}, | \psi_{i} \rangle }$} be an ensemble of pure states. ...
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### Induced measure on the set of density matrices defined through the Ginibre ensemble

I am defining a density matrix via $\rho = \frac{X^\dagger X}{\textrm{tr}(X^\dagger X)}$, where $X$ belongs to the Ginibre ensemble. This results in an induced distribution on the set of density ...
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I am trying to calculate the probability of a state (density matrix) being in a specific other state. Lets say I have a 2-dimensional state with the states given by the orthonormal basis states $|0\... 0 votes 1 answer 22 views ### Can density matrices of multipartite systems always be written as product states? suppose the density matrix$\rho_{ABC}$with the subsystems {A,B,C} can we write$\rho_{ABC}$as below?$\rho_{ABC}=\rho_A \otimes \rho_B \otimes \rho_C $if the answer is yes please share a ... 1 vote 2 answers 55 views ### How to perform a state density modification for a single targeted state only? I have a question about single target state modification... Suppose we have a 3 qubit state density distribution as follows (prenormalized): $$\begin{bmatrix} |000\rangle & 3 \\ |001\rangle & ... 2 votes 1 answer 103 views ### Is Klein's inequality due to Klein? You may be familiar with "Klein's inequality"; one form of it is$$ -\operatorname{tr}(\rho \log \sigma) + \operatorname{tr}(\rho \log \rho) \ge 0, $$stating that relative entropy is ... 0 votes 0 answers 30 views ### Lifting map and joint probability How to use lifting map approach to calculate the following joint probability after equation (12) of Quantum-like model of diauxie in Escherichia coli: Operational description of precultivation effect ?... 0 votes 0 answers 19 views ### how to find a quantum gate matrix from RHO before and RHO after evolve to evolve a 4x4 density matrix I use this method: rhoafter = np.dot(np.dot(gate,rhobefore),np.conjugate(gate.T)) And I want to find the gate from rhobefore and ... 3 votes 1 answer 127 views ### On the probability of agreeing with different density matrices? Let's say I have a density matrix and I (person 1) suspect it to be of the form:$$ \rho_1 = p_1 |\psi \rangle \langle \psi | + p_2 |\phi \rangle \langle \phi |$$|\psi \rangle and | \phi \rangle... 1 vote 1 answer 26 views ### Prove that Tr(\chi(\rho_A) \log(\chi(\rho_A)) = Tr(\rho_A \log(\chi(\rho_A)) I am trying to see how the following statement about trace Tr is true.$$ Tr(\chi(\rho_A) \log(\chi(\rho_A)) = Tr(\rho_A \log(\chi(\rho_A)), $$for some quantum state \rho_A, Where,$$ \chi(.) = \... 0 votes 0 answers 36 views ### Tf.einsum vs matmul for computing density matrix from a set of Cholesky decomposed matrices I am trying to construct a density matrix of shape 256x256 from a set of T matrices. These T matrices are all Cholesky-decomposed matrices. But I am not sure if the ... 0 votes 0 answers 51 views ### Is it possible to apply a quantum gate to a density marix from a partial trace? To apply a gate(matrix) to a 2 qubit partial trace(4x4 matrix) I have this function: ... 0 votes 1 answer 84 views ### Operator qubit ordering not matching circuit qubit ordering I tried constructing a cx gate manually using tensor products and one using QuantumCircuit in qiskit followed by converting it ... 0 votes 1 answer 60 views ### How to perform below operation in Qiskit? I want to implement the below equation in Qiskit.$(A \otimes B).\rho.(B^\dagger \otimes A^\dagger)$where$\rho$is a density matrix and$A$and$B$are CNOT gates. $$A=\begin{bmatrix} 1 & 0 &... 2 votes 2 answers 47 views ### Compatibility of partial_transpose in Qiskit I need to calculate the negativity of a density matrix; in doing so on Qiskit I stuck on the problem of computing the partial transpose for a problem of compatibility. Basically I extract my density ... 1 vote 0 answers 30 views ### How to Find a circuit that evolves from one density matrix to another(qiskit or cirq) given two density matrices, dmBefore and dmAfter, I want to generate(find) a circuit in Qiskit or Cirq that starting initaliazed with dmBefore ends with dmAfter after it's execution. Is it possible?. ... 0 votes 0 answers 20 views ### Observable for Absolute Overall Magnetization of an Ising Model I am currently following this tutorial for generating a phase transition plot that has been generated in the same tutorial. In this tutorial's magnetization ... 2 votes 2 answers 541 views ### What is the density matrix of a pure state? By definition of the density matrix for example the density matrix of |0\rangle state (pure state) is:$$\rho=|0\rangle \langle 0| = \begin{pmatrix} 1 & 0 \\ ... 3 votes 1 answer 46 views ### What trace properties are used in the identity${\rm tr}_A{\rm tr}_B(\rho\Pi)={\rm tr}_A(\rho_A{\rm tr}_B(\rho_B\Pi))$? To turn the probability of the projection over the Hilbert space$\mathcal H_A \otimes \mathcal H_B$into the POVM probabilty over$\mathcal H_A$we we use this equality:$$tr_Atr_B(ρΠ_i)=tr_A(ρ_Atr_B(... 1 vote 1 answer 54 views ### Non trace-preserving map in axiomatic approach to quantum operations In Nielsen and Chuang's Quantum Computation and Quantum information there is an axiomatic definition of the quantum operation (as one of the 3 approaches to quantum operations). A quantum operation is ... 2 votes 1 answer 184 views ### How does Qiskit/Qasm simulate the density matrix of up to 30 qubits? The full density matrix of 30 qubits contain$2^{30}$states. How does qiskit/qasm implement this without storing and computing the full$2^{30}$density matrix of possible state coefficients? 2 votes 1 answer 103 views ### Representation of maximally entangled states of$2n$qubits with Pauli matrices? I'm reading this paper while the author states in the eq(A1) that, for a$2n$qubits maximally entangled state$|\Psi ^+\rangle \langle \Psi ^+|$, we can write it with Pauli operators$P_u\in\left\{ I,...
I know that in algebra for a variable we have $\sqrt {x^2} = |x|$ What if $x$ is a density matrix? Please share resource for your answer.