# Questions tagged [density-operator]

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

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### What is a completely positive map *physically*?

I am sure this question is really stupid, but I could not refrain from asking it in this forum. This can be considered as a continuation of this question. ...
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### What does the sum of two qubits tell about their correlations?

How much can I learn about correlations between two quits by measuring the sum of their values? What is the best way to formalize such a question? Below is my original, longer formulation of the ...
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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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### Why can't every quantum state be expressed as a density matrix/operator?

It was my previous impression that all quantum states in a Hilbert space can be represented using density matrices† and that's already the most general formulation of a quantum state. Then I came ...
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### Does a physical interpretation of density matrix cross-terms exist?

Say we have some state $$|\psi\rangle=\frac{1}{\sqrt{2}}(|0\rangle+i|1\rangle)$$ it is in a quantum superposition of $|0\rangle$ and $|1\rangle$. Its density matrix is \rho=\begin{pmatrix}\frac 1 2 &...
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### Green functions and density matrix

tl;dr The single particle density matrix is directly related to NEGF as shown here, I wish to find a way to relate NEGF also to density matrices which describe probability distribution of many body ...
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### Entanglement of Mixed Quantum State

As per Wikipedia: Quantum entanglement is a physical phenomenon that occurs when pairs or groups of particles are generated or interact in ways such that the quantum state of each particle cannot ...
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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 in a statistical ensemble of ...
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### What's the physical meaning of the kernel of density matrix?

The kernel of this linear map is the set of solutions to the equation A x = 0, where 0 is understood as the zero vector. But what's the physical meaning of the kernel of density matrix?
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### If an isolated quantum system consists of only one particle, is it possible for it to be in a mixed state?

Mixed states are defined as the statistical ensemble of pure states. Classically, I understand the word, "statistical" referring to a system with a large number of microscopic particles. So if I go ...
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### What is a Gibbs state?

What is a Gibbs state and what does it differ from a pure state? Say I have a two-level atom and it is described by a Gibbs state $\rho_G = \dfrac{e^{- \frac{H}{kT}}}{Z}$. I know $Z$ is a partition ...
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### States versus ensembles in quantum mechanics

In quantum mechanics, we talk about (1) vectors, (2) states, and (3) ensembles (e.g., a beam in a particle accelerator). Suppose we want to translate this into mathematical definitions. If I'd never ...
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### Hilbert space for Density Operators (instead of Banach spaces)

Is it possible to construct a well defined inner-product (and therefore orthonormality) within the set of self-adjoint trace-class linear operators? In the affirmative case, dynamics could be analyzed ...
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### Coherences in the density matrix

It is said that the off-diagonal elements of density matrix are "coherence". When a system interacts with its environment the off-diagonal elements decay and the final density matrix is the diagonal ...
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### Trying to understand mixed states

I took a basic quantum chemistry course (McQuarrie's "Quantum Chemistry"), but it never dealt with mixed states -- only pure states (or if it did, we never got to it in class). So I'm trying to ...