# Questions tagged [density-matrix]

A density matrix is a matrix that can be used to describe a quantum system in a mixed state, a statistical ensemble of several quantum states. This should be contrasted with a single state vector that describes a quantum system in a pure state.

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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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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 $$\mathbb{C}^{d_{1}}\... 0answers 78 views ### Analyzing the composition of a channel with its adjoint in relation with an identical composition obtained for the channel's complement Let us consider two quantum channels \Phi:M_d\rightarrow M_{d_1} and \Phi_c:M_d\rightarrow M_{d_2} that are complementary to each other, i.e., there exists an isometry V:\mathbb{C}^d\rightarrow \... 0answers 44 views ### Pure state ensembles achieving the Holevo \chi-quantity with at most d^2 states Theorem 8.10 in Chapter 8 of Theory of Quantum Information asserts that the Holevo capacity of a quantum channel (between density operators on \mathbb{C}^d) can be achieved by an ensemble consisting ... 0answers 69 views ### Reduced Density Matrix Equation of Motion to describe an Ellipse Given a pure two qubit state |\psi_{AB}\rangle. If we trace out system B, the remaining density matrix \rho_A = Tr_B|\psi_{AB}\rangle\langle\psi_{AB}|, can be represented as a point lying ... 0answers 58 views ### What does "decoherence attenuates the density matrix" mean? I'm reading the paper Implementation of the Quantum Fourier Transform. On page 4, they write To a first approximation, decoherence during the course of the QFT attenuates the entire density matrix. ... 0answers 44 views ### Find the qutrit analogue of certain qubit and ququart formulas of Li and Qiao for testing separability In eqs. (33), (43)-(46), (56) of their paper, "Separable Decompositions of Bipartite Mixed States" https://arxiv.org/abs/1708.05336, Li and Qiao present a number of formulas pertinent to testing the ... 0answers 57 views ### Reduced density matrix of a Haar random state and its Schmidt decomposition Consider a Haar random quantum state |\psi\rangle. Note that$$\rho =\mathbb{E}[|\psi\rangle\langle \psi|] = \frac{\mathbb{I}_{n}}{2^{n}}.$$\mathbb{I}_n is the identity operator on n qubits. ... 0answers 98 views ### 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 ... 0answers 98 views ### 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 ... 0answers 42 views ### 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 ... 0answers 21 views ### 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 ... 0answers 120 views ### 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 ... 0answers 40 views ### 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} ... 0answers 51 views ### 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&... 0answers 27 views ### 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.\... 0answers 97 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 ...
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 ...