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.
40
questions with no upvoted or accepted answers
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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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82
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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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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 ...
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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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4
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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( \...
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4
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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-...
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3
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214
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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. ...
- 1,119
3
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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}}\...
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3
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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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3
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64
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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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3
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74
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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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3
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137
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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 ...
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3
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62
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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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3
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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} ...
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3
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answers
51
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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 ...
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43
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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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81
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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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answers
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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 \...
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2
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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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170
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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 $\rho$ ...
- 21
2
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269
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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 ...
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45
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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 ...
- 945
2
votes
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answers
21
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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 ...
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1
vote
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answers
18
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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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1
vote
0
answers
44
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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 ...
- 1,124
1
vote
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answers
37
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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, ...
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1
vote
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answers
110
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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-...
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1
vote
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answers
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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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0
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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 ...
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1
vote
0
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154
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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&...
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1
vote
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103
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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.\...
1
vote
0
answers
217
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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 ...
- 11
1
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74
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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 ...
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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- \...
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17
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How can i get the superposition of 8 bits from 26 bits outputs in qiskit
the only idea i see is get state vector from density_matrix
for example, i have the circult:
...
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36
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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}...
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57
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Question regarding the trace-preserving quantum operator trace distance
In Michael A. Nielsen & Isaac L. Chuang, Quantum Computation and Quantum Information, 10th Anniversary Edition, the proof of Theorem 9.2 (Trace-preserving quantum operations are contractive) on ...
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52
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Simon Algorithm without measurement
I want to use the reduced density matrix to compute the measurement probability: $prob(y)=\langle y|\rho|y\rangle$ for a 3-qubit simon algorithm, instead of measuring the ancilla qubits. Here $\rho=...
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Figuring out which experiment is being performed from the results of the experiment
Consider two different experiments involving qubits. In Experiment 1, a qubit is prepared in the mixed state $I/2$, where $I$ is the $2 × 2$ identity matrix. Alice then chooses an
orthonormal basis $B$...
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