$ \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\abs}[2][]{\left\lvert#2\right\rvert_{\text{#1}}} \newcommand{\ket}[1]{\left\lvert#1 \right.\rangle} \newcommand{\bra}[1]{\langle\left. #1\right\rvert} \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\dd}{\text{d}} \newcommand{\dv}[2]{\frac{\dd #1}{\dd #2}} \newcommand{\pdv}[2]{\frac{\partial}{\partial #1}} $
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Overview
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A mixed state is a classical mixture of several quantum states.

Notations

Mixed states are often represented with density matrices, as they cannot be represented by a state vector.

Concepts

We can differetiate a classical mixture of pure states from solely pure states by putting them through matrices.
Suppose we have a collection of particles in the state $\ket{\psi}=\ket{+}_{x}$, and a classical mixture of $\ket{+}_z$ and $\ket{-}_z$. We can differentiate the two states by measuring their spin in their $x$ axis, as all of the pure state would be observed to be $+\frac{\hbar}{2}$. The classical mixture would be both $\ket{+}_z$ and $\ket{-}_z$ randomly being measured $+\frac{\hbar}{2}$ or $-\frac{\hbar}{2}$, in contrast to the pure state which only gives measurements of $+\frac{\hbar}{2}$.
A mixed state is a classical mixture of several quantum states.

Notations

Mixed states are often represented with density matrices, as they cannot be represented by a state vector.

Concepts

We can differetiate a classical mixture of pure states from solely pure states by putting them through matrices.
Suppose we have a collection of particles in the state $\ket{\psi}=\ket{+}_{x}$, and a classical mixture of $\ket{+}_z$ and $\ket{-}_z$. We can differentiate the two states by measuring their spin in their $x$ axis, as all of the pure state would be observed to be $+\frac{\hbar}{2}$. The classical mixture would be both $\ket{+}_z$ and $\ket{-}_z$ randomly being measured $+\frac{\hbar}{2}$ or $-\frac{\hbar}{2}$, in contrast to the pure state which only gives measurements of $+\frac{\hbar}{2}$.
FullPage
Overview
Notations
Concepts
FullPage
Overview
Notations
Concepts
A mixed state is a classical mixture of several quantum states.

Notations

Mixed states are often represented with density matrices, as they cannot be represented by a state vector.

Concepts

We can differetiate a classical mixture of pure states from solely pure states by putting them through matrices.
Suppose we have a collection of particles in the state $\ket{\psi}=\ket{+}_{x}$, and a classical mixture of $\ket{+}_z$ and $\ket{-}_z$. We can differentiate the two states by measuring their spin in their $x$ axis, as all of the pure state would be observed to be $+\frac{\hbar}{2}$. The classical mixture would be both $\ket{+}_z$ and $\ket{-}_z$ randomly being measured $+\frac{\hbar}{2}$ or $-\frac{\hbar}{2}$, in contrast to the pure state which only gives measurements of $+\frac{\hbar}{2}$.
A mixed state is a classical mixture of several quantum states.

Notations

Mixed states are often represented with density matrices, as they cannot be represented by a state vector.

Concepts

We can differetiate a classical mixture of pure states from solely pure states by putting them through matrices.
Suppose we have a collection of particles in the state $\ket{\psi}=\ket{+}_{x}$, and a classical mixture of $\ket{+}_z$ and $\ket{-}_z$. We can differentiate the two states by measuring their spin in their $x$ axis, as all of the pure state would be observed to be $+\frac{\hbar}{2}$. The classical mixture would be both $\ket{+}_z$ and $\ket{-}_z$ randomly being measured $+\frac{\hbar}{2}$ or $-\frac{\hbar}{2}$, in contrast to the pure state which only gives measurements of $+\frac{\hbar}{2}$.
FullPage
Overview
Notations
Concepts