From 8d937b3c066e856edf121a41a4577bfbff14b2a1 Mon Sep 17 00:00:00 2001 From: JingYu Ning Date: Thu, 22 Jul 2021 22:09:21 +0800 Subject: [PATCH] update get started --- docs/src/get_started.md | 11 ++++++++--- 1 file changed, 8 insertions(+), 3 deletions(-) diff --git a/docs/src/get_started.md b/docs/src/get_started.md index 23a7046..8969e0f 100644 --- a/docs/src/get_started.md +++ b/docs/src/get_started.md @@ -189,7 +189,13 @@ W(x, p) = \sum_{m, n} \rho_{m, n} W_{m, n}(x, p) Here, ``\rho`` is the density matrix of the quantum state, defined as: ```math -\rho = \sum_{m, n} p_{m, n} | m \rangle \langle n | +\rho = \sum_{m, n, i} \, p_i \, | n \rangle \langle n | \hat{\rho}_i | m \rangle \langle m | +``` +```math +\hat{\rho}_i = | \psi_i \rangle \langle \psi_i | +``` +```math +\hat{\rho}_i \, \text{is a density operator of pure state.} ``` And, ``W_{m, n}(x, p)`` is the generalized Wigner function @@ -220,7 +226,7 @@ julia> heatmap(w.x_range, w.p_range, w.𝐰_surface') Usually, we describe a quantum state using two non-commuting observables `X`(position) and `P`(momentum) in phase space. The joint distribution is also known as Wigner function. -In experiments, we measure the E field of the light using the homodyne detector. +In homodyne experiments, we measure the E field of the light using the homodyne detector. The phase of the wave are the eigenvalues of the quadrature operator ``X_{\theta}`` where ``X_{\theta = 0} = X`` and ``X_{\theta = \pi/2} = P`` @@ -235,7 +241,6 @@ julia> heatmap(θs, xs, ps') ``` ```@raw html - ```