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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Query on Reduced Graph States

Reduced graph states are characterized as follows (from page 46 of this paper): Let $A \subseteq V$ be a subset of vertices of a graph $G = (V,E)$ and $B = V\setminus A$ the complement of $A$ in $V$. ...
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Tripartite quantum marginal problem

Consider a tripartite quantum system with the three subsystems labeled $A, B,$ and $C$. Now take two states $\rho_{AB}$ on the joint system $AB$ and $\rho_{BC}$ on the joint system $BC$. Under what ...
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Distribution of density operators under Stochastic Master Equation

Stochastic master equations (SME) are used in studies of open quantum systems. The general form of an SME is: \begin{align} \tag{1} d\tilde{\sigma}(t) = - i [H, \tilde{\sigma}(t) ]dt + \frac{1}{2}\...
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Reduced density matrix of a Haar random state and its Schmidt decomposition

Consider a Haar random quantum state $|\psi\rangle$. Note that $$\rho =\mathbb{E}[|\psi\rangle\langle \psi|] = \frac{\mathbb{I}_{n}}{2^{n}}.$$ $\mathbb{I}_n$ is the identity operator on $n$ qubits. ...
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Is there a way to write down the eigenstates of this two-qubit density matrix?

I am considering the density matrix which represents an arbitrary state for a pair of qubits. When written out in terms of the Pauli operators, this is as follows (certain terms vanish for another ...
Tom's user avatar
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Modeling building blocks for quantum computation

If I would design library for quantum computation I would naively consider a sequences of entangled qudits with unit length as a building blocks. I.e., unit length elements from $$\mathbb{C}^{d_{1}}\...
Fallen Apart's user avatar
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Analyzing the composition of a channel with its adjoint in relation with an identical composition obtained for the channel's complement

Let us consider two quantum channels $\Phi:M_d\rightarrow M_{d_1}$ and $\Phi_c:M_d\rightarrow M_{d_2}$ that are complementary to each other, i.e., there exists an isometry $V:\mathbb{C}^d\rightarrow \...
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Pure state ensembles achieving the Holevo $\chi$-quantity with at most $d^2$ states

Theorem 8.10 in Chapter 8 of Theory of Quantum Information asserts that the Holevo capacity of a quantum channel (between density operators on $\mathbb{C}^d$) can be achieved by an ensemble consisting ...
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Is the set of two-qubit absolutely separable states convex?

Companion question on MathOverflow Let us order the four nonnegative eigenvalues, summing to 1, of a two-qubit density matrix ($\rho$) as \begin{equation} 1 \geq x \geq y \geq z \geq (1-x-y-z) \geq 0. ...
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Reduced Density Matrix Equation of Motion to describe an Ellipse

Given a pure two qubit state $|\psi_{AB}\rangle$. If we trace out system $B$, the remaining density matrix $\rho_A = Tr_B|\psi_{AB}\rangle\langle\psi_{AB}|$, can be represented as a point lying ...
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Is there a two-qudit Choi entanglement witness $W^{(+)}$?

Example 2 in arXiv:1811.09896 states that the "Choi EW (entanglement witness) $W^{(+)}$ obtained from the Choi map in $d=3$ $\ldots$ is given by \begin{equation} W^{(+)} = \frac{1}{6} \left( \...
Paul B. Slater's user avatar
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What proportions of certain sets of PPT-two-retrit states are bound entangled or separable?

For two particular (twelve-and thirteen-dimensional) sets of two-retrit states (corresponding to 9 x 9 density matrices with real off-diagonal entries), I have been able to calculate the Hilbert-...
Paul B. Slater's user avatar
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Finding Wigner function of four maximal entangled Bell state

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 ...
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Increasing the von Neumann entropy despite the measurement?

Background Assume we have a density matrix $\rho$ of a sub-ensemble. However, we have an imperfect measuring instrument. While it does perform a measurement, we do not know exactly when it performs ...
More Anonymous's user avatar
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What does "decoherence attenuates the density matrix" mean?

I'm reading the paper Implementation of the Quantum Fourier Transform. On page 4, they write To a first approximation, decoherence during the course of the QFT attenuates the entire density matrix. ...
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Are there different orderings of the fifteen SU(4) generators in common use?

I've recently performed certain analyses (Archipelagos of Total Bound and Free Entanglement) pertaining to eq. (50) in Separable Decompositions of Bipartite Mixed States , that is \begin{equation} ...
Paul B. Slater's user avatar
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Find the qutrit analogue of certain qubit and ququart formulas of Li and Qiao for testing separability

In eqs. (33), (43)-(46), (56) of their paper, "Separable Decompositions of Bipartite Mixed States" https://arxiv.org/abs/1708.05336, Li and Qiao present a number of formulas pertinent to testing the ...
Paul B. Slater's user avatar
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Density matrix and State vector give different result in mesolve in QuTiP

qutip mesolve gives me different population evolve depending on that initial state is state vector or density matrix. And, in some situation, it gives me negative population. It doesn't make sense... ...
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Liouvillian, Lindbladian, and Davies generator

I have a rather basic question. I'm starting to read papers such as Chen–Brandao, Chen–Kastoryano–Brandao–Gilyen and I'm having trouble parsing even what kind objects a Liouvillian, Lindbladian, and ...
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How to "separate" a separable density matrix?

If I have a bipartite system of two qubits $A$ and $B$, and the density matrix $\rho$ is separable, how do I decompose it into its separable parts? That is, give $\rho$, expand it as follows: $$\rho = ...
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Simulating density matrices in quantum simulators

I would like to load random quantum states sampled from a given density matrix based on its classical probabilities ie based on the definition of the given density matrix: $\rho = \sum_i p_i |\psi _i \...
quics-ilver's user avatar
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How can a density matrix be prepared on a quantum register?

I am currently trying to implement the VQSE algorithm. There the biggest eigenvalues and their corresponding eigenvectors of a density matrix $\rho$ are computed. In contrast to VQE, the matrix $\rho$ ...
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What is the relation between density matrices and phase-space probability distributions?

According to its tag description, a density matrix is the quantum-mechanical analogue to a phase-space probability measure (probability distribution of position and momentum) in classical statistical ...
develarist's user avatar
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Quantum analogues of information theoretic measures: are log probabilities replaced with the density matrix?

Below is a question and an answer. How does quantum information relate to, diverge from or reduce to Shannon information, which used log probabilities? What people are more often interested in are ...
develarist's user avatar
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Density matrix of spatially (i.e., at the same time instant) vs. causally ( i.e., one evolves into the other) correlated quantum systems

In the classical case, if Y is the output of a classical channel whose input is X, it makes sense to speak of a joint distribution $P_{XY}$. In the quantum case, if a state $\rho_A$ is input to a ...
Dina Abdelhadi's user avatar
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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 ...
Dudu Ponar's user avatar
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How is Pauli twirling so powerful?

So the Pauli twirling approximation gives us a quantum channel $\Phi$ that transforms a density matrix $\rho$ to: $\Phi(\rho)\mapsto\sum_{i=0}^3 \sigma^i \rho \sigma^i,$ where $\sigma^0 = \mathbb{I}, \...
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General Bell state expression: What condition for mixture of Bell states to be entangled?

Convention: $|qubit_{A}, qubit_{B}\rangle$ The general Bell state equation: $|\beta(a,b)\rangle = \frac{1}{\sqrt{2}}\sum_{k=0}^{1}(-1)^{ka}|k, k\oplus b\rangle = \frac{1}{\sqrt{2}}[|0,0 \oplus b\...
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How do I show that a reduced density matrix of $1$ is $\rho_{12}^{1} = Tr_{2}[\rho_{12}] = \sum_{i}\langle i_{2} | \rho | i_{2} \rangle$?

Let the system be a 2 - qubit system and let $\rho_{12}$ be a density matrix of some state for this 2 - qubit system. How do I show that a reduced density matrix of $1$ is $\rho_{12}^{1} = Tr_{2}[\...
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What does the product of two density matrices represent physically?

A quantum state, pure or mixed, can be described by a density matrix that encodes the Bloch vector $\hat{m}$ analog of a quantum state like $\rho = \frac{1}{2}[\mathbb{I} + \hat{m}.\vec{\sigma}]$. Let ...
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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?. ...
Luis ALberto's user avatar
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List of inequalities for purity of a traced out bipartite system

I would like to know if there are inequalities related to the purity of the partial trace of a bipartite system. The purity $P$ of a density matrix $\rho$ is given by $$P(\rho) = Tr(\rho^2).$$ The ...
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Reduced density matrix accuracy in amplitude estimation

I am implementing QAE (Quantum Amplitude Estimation), which is very similar to QPE (Quantum Phase Estimation) with a Grover Operator as the U matrix of QPE. I want to check my results, in the outputs ...
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Density matrix derivation of an entangled state in amplitude dampling channel

The density matrix for an entangled state when both the qubits decohere with probability D1 and D2 in amplitude damping channel is given as $\rho_d$ in \href{https://www.nature.com/articles/nphys2178}...
chetan waghmare's user avatar
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How are $\theta, \phi$ and $\lambda$ for the U3 gate derived in Abhijith et al. 2018?

I am looking to implement Quantum PCA from this paper (page 62). They have their code on Github. I have gone through the paper multiple times but failing to understand how they got numbers (for theta, ...
Nihir's user avatar
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Qutip: Mesolve gives different and weird results with different fock state numbers

I have been trying to simulate the average number of particles at 3 sites of coupled harmonic oscillators. I have used the code from the below tutorial: https://notebook.community/ajgpitch/qutip-...
anand_quanta's user avatar
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Show that while calculating partial traces the probability is independent of the basis of one of the measurements

Consider calculating the probability of the outcome m alone of some composite system $AB$. $p_A(m) = \sum_{n=0}^{d_B-1} p_{AB}(m,n) $ $= \sum_{n=0}^{d_B-1}(⟨α_m|⊗⟨β_n|)\rho_{AB}(|α_m⟩⊗|β_n⟩)$ I'm ...
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Is $\rho | \psi \rangle$ invariant in the Wigners friend thought experiment?

Background Let's say I have a gas of $N$ particles where I cannot distinguish between the particles at a temperature $T$. Its density matrix is given by $\rho$. Note, if my friend happens to measure ...
More Anonymous's user avatar
1 vote
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QuTiP VS RK45: Which one gives the correct results for time-dependent systems?

I am writing a code for a quantum thermal machine which includes both coherent and dissipative time evolutions in its different stages of operation. However, evolving the system with "mesolve&...
Ali Pedram's user avatar
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Evaluation of Wigner function representation of a Bloch Sphere

Consider Wigner function representation of a qubit in the basis labeled by $\sigma_z$ and $\sigma_x$ eigenvalues. A general single qubit mixed state has the Bloch representation,$\rho = 1/2 (I + r.\...
Sudhir Kumar Sahoo's user avatar
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285 views

Numerical methods for finding an eigen basis of a degenerate Liouvillian

I'm trying to find the steady-state of a master equation, $$\dot{\rho}(t) = \mathcal{L}\rho(t),\tag{1}\label{1}$$ In the form where we vectorise the density matrix and matrixify (??) the Liouvillian ...
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Which state describes carrier transport through channel? A mixed state or a pure state?

A pure quantum state is a state which can be described by a single ket vector. A mixed quantum state is a statistical ensemble of pure states. When carriers transport from source to drain in a Field ...
邱信淵's user avatar
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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 ...
Showhands's user avatar
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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 ?...
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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 ...
Luis ALberto's user avatar
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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 ...
Dimitri's user avatar
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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: ...
Luis ALberto's user avatar
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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 &...
joy Jaganath's user avatar
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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 ...
Zee's user avatar
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Relation between the output density matrix and the annihilation operators?

The annihilation opertors $\{\hat{a_R}^{(m)}\}_{m=1}^{M}$ of the modes obey the relation \begin{align} \label{annihilation} \hat{a_R}_R^{m} &= \sqrt{\eta_h} e^{i \phi} \hat{a_S}^{(m)} + \sqrt{1- \...
Michael.Andy's user avatar