The density operator describes a quantum system in an (in general mixed) state.

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How to connect these two formulations regarding the need for a density matrix in quantum mechanics?

I found these two formulations: The density matrix is: 1) "needed if we consider a system that is part of a larger closed system." 2) "needed for a system to be ...
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Shape of the state space under different tensor products

I am currently studying generalized probabilistic theories. Let me roughly recall how such a theory looks like (you can skip this and go to "My question" if you are familiar with this). Recall: In a ...
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Heisenberg XXX time evolution operator for three qubits

I've a problem to reproduce the result in equation (4) on page three of this paper: http://arxiv.org/abs/0802.2588. So far I've understood that they apply a Heisenberg XXX interaction between ...
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Thermal radiation in the Unruh Effect

The following formula has been given in 't Hooft's black holes notes ($|\Omega \rangle$ is the vacuum state of Minkowski space, O is a operator): $$\langle \Omega| O|\Omega \rangle = \sum_{n \ge 0} ...
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How can I write a Gaussian state as a squeezed, displaced thermal state

I would like to write a Gaussian state with density matrix $\rho$ (single mode) as a squeezed, displaced thermal state: \begin{gather} \rho = \hat{S}(\zeta) \hat{D}(\alpha) \rho_{\bar{n}} ...
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Can I usefully interpret a non-unital completely positive (CP) map as a cooling process?

Non-unital completely positive (CP) maps take a maximally mixed quantum state (aka a normalized identity matrix aka an infinite temperature state) and map it to something else. This necessarily ...
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Are the Wigner and Husimi transforms injective?

I am wondering if the Wigner function is injective. By injective I mean, that, for every density matrix $\rho$, there is a different Wigner distribution. The same question applies to the Husimi ...
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Sufficient criterion for su(2) invariant spin-1*spin_s bipartite density matrix

SU(2) invariant spin-1 and spin-S bipartite density matrix is given by $\rho ^{1,S}=\frac1{3*(2S+1)}[1+\alpha {S^A_i\times S^B_i}+\beta S^A_{ij}\times S^B_{ij}]$, i j varies from ...
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Superposition and density matrix. What are these states?

I just wanted to understand the following. Let's stay with the harmonic oscillator in QM, just to have an example at hand. First, there are all the different states for $n=1,2,...$. (Let's call them ...
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Density operator time evolution in the path integral approach

I want to know how the density operator of a system evovles when we use path integral approach.
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What is the link between the density matrix and Hestenes' spinors in geometric algebra?

The density matrix (or state matrix) is a generalization of a wave function that is able to describe incoherent superpositions of an N-state system. It is often written as a matrix and observables are ...
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Criterion of tangled state by using particular transposition of density matrix

Let's have (for simplicity) two-qubit density matrix $\rho $. If we make the particular transposition only by one qubit, we'll get some other matrix $\tilde \rho $. Then the criterion of the mixed ...
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Eigen value, matrix, Quantum game

In this paper, on the page 5 http://math.ucsd.edu/~dmeyer/research/publications/qstrat/qstrat.pdf in the second paragraph: his first action puts the penny into a simultaneous eigenvalue 1 eigenstate ...
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Non-unqiue basis sets of reduced density matrix in quantum mechanics/decoherence

In Why decoherence solves the measurement problem by Art Hobson: $|\psi \rangle _{SA} = c_1|s_1 \rangle |a_1 \rangle + c_2 |s_2\rangle |a_2 \rangle$ which is a wavefunction that describes non-local ...
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Reduced density matrix of coupled oscillators and entanglement entropy

This paper describes a way to find the entanglement entropy of $N$ entangled harmonic oscillators, after tracing out the first $n$. A few statement made within have royally confused me, and I haven't ...
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How to find density matrix?

The Beam-splitter matrix is $ B = \frac{1}{\sqrt{2}}\begin{pmatrix} 1 & 1\\ 1 & -1 \end{pmatrix} $. I want to apply $a^{\dagger}_{1}a^{\dagger}_{2} |00\rangle_{12}$ as the input state for ...
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Continous and Discrete basis, Multiplication of Density Matrix and Hamiltonian

Suppose I have a wave function $\psi(x)$ in position basis. I can make a density function by simply multiplying $\psi(x)$ and its conjugate $\psi^*(x)$. If I operate the density matrix ...
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How to measure the arbitrariness of a quantum state?

An arbitrary qubit is represented as $\alpha|0\rangle+\beta|1\rangle$ with $|\alpha|^2+|\beta|^2=1$. If we know either $\alpha$ or $\beta$, the state can be completely identified. The 'arbitrariness' ...