$ \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}} $
FullPage
Overview
Notations
Concepts
The expectation value is the average measurement value that is expected to be gotten if the experiment is prefermed a large amount of times.

Notations

The expectation value is denoted with $\langle A\rangle$ and defined in general for a mixed state as $$\begin{align*} \langle A\rangle =\sum_{i=1}^mP_i\langle\psi_i|A|\psi_i\rangle, \end{align*}$$ where $m$ is the number of states.
For a pure state, this can be simplified to $$\begin{align*} \langle A \rangle =\langle \psi|A|\psi\rangle \end{align*}$$.

Concepts

Expectation value can be calculated in multiple methods. $$\begin{align*} \braket{A}= \sum_{i=1}^m P_i\braket{\psi_i|A|\psi_i} \\ &=\text{Trace}(\rho A),\end{align*}$$ where $P_i$ is the probability of the system being in the state $\ket{\psi_i}$ (?) and $\rho$ is the density matrix.
The expectation value is the average measurement value that is expected to be gotten if the experiment is prefermed a large amount of times.

Notations

The expectation value is denoted with $\langle A\rangle$ and defined in general for a mixed state as $$\begin{align*} \langle A\rangle =\sum_{i=1}^mP_i\langle\psi_i|A|\psi_i\rangle, \end{align*}$$ where $m$ is the number of states.
For a pure state, this can be simplified to $$\begin{align*} \langle A \rangle =\langle \psi|A|\psi\rangle \end{align*}$$.

Concepts

Expectation value can be calculated in multiple methods. $$\begin{align*} \braket{A}= \sum_{i=1}^m P_i\braket{\psi_i|A|\psi_i} \\ &=\text{Trace}(\rho A),\end{align*}$$ where $P_i$ is the probability of the system being in the state $\ket{\psi_i}$ (?) and $\rho$ is the density matrix.
FullPage
Overview
Notations
Concepts
FullPage
Overview
Notations
Concepts
The expectation value is the average measurement value that is expected to be gotten if the experiment is prefermed a large amount of times.

Notations

The expectation value is denoted with $\langle A\rangle$ and defined in general for a mixed state as $$\begin{align*} \langle A\rangle =\sum_{i=1}^mP_i\langle\psi_i|A|\psi_i\rangle, \end{align*}$$ where $m$ is the number of states.
For a pure state, this can be simplified to $$\begin{align*} \langle A \rangle =\langle \psi|A|\psi\rangle \end{align*}$$.

Concepts

Expectation value can be calculated in multiple methods. $$\begin{align*} \braket{A}= \sum_{i=1}^m P_i\braket{\psi_i|A|\psi_i} \\ &=\text{Trace}(\rho A),\end{align*}$$ where $P_i$ is the probability of the system being in the state $\ket{\psi_i}$ (?) and $\rho$ is the density matrix.
The expectation value is the average measurement value that is expected to be gotten if the experiment is prefermed a large amount of times.

Notations

The expectation value is denoted with $\langle A\rangle$ and defined in general for a mixed state as $$\begin{align*} \langle A\rangle =\sum_{i=1}^mP_i\langle\psi_i|A|\psi_i\rangle, \end{align*}$$ where $m$ is the number of states.
For a pure state, this can be simplified to $$\begin{align*} \langle A \rangle =\langle \psi|A|\psi\rangle \end{align*}$$.

Concepts

Expectation value can be calculated in multiple methods. $$\begin{align*} \braket{A}= \sum_{i=1}^m P_i\braket{\psi_i|A|\psi_i} \\ &=\text{Trace}(\rho A),\end{align*}$$ where $P_i$ is the probability of the system being in the state $\ket{\psi_i}$ (?) and $\rho$ is the density matrix.
FullPage
Overview
Notations
Concepts