Trail Tripping: Back to the Forest

I'm returning to the Haliburton Forest 50 Miler next weekend, and am a bit apprehensive. Deep breaths. Try to keep it simple. Here's the basic, back-of-the-envelope plan.

First, my taper needs to be

$|\Psi \rangle \in H_A \otimes H_B.$

and

$\rho_T = |\Psi\rangle \; \langle\Psi|$ .

To start the race, my effort should be something like

$\rho_A \ \stackrel{\mathrm{def}}{=}\ \sum_j \langle j|_B \left( |\Psi\rangle \langle\Psi| \right) |j\rangle_B = \hbox{Tr}_B \; \rho_T$ .

Oh, and for the uphills

$\rho_A = (1/2) \bigg( |0\rangle_A \langle 0|_A + |1\rangle_A \langle 1|_A \bigg)$

And then the downhills (duh)

$\rho_A = |\psi\rangle_A \langle\psi|_A .$

Naturally, for the second half we'll be looking at

$|\Phi^\pm\rangle = \frac{1}{\sqrt{2}} (|0\rangle_A \otimes |0\rangle_B \pm |1\rangle_A \otimes |1\rangle_B)$

Or, alternatively

$H_n(x)=(-1)^n e^{x^2}\frac{d^n}{dx^n}\left(e^{-x^2}\right)$ .

(But if I see a bear, I need to run like

$\langle\hat{T}\rangle = \bigg\langle\psi \bigg\vert \sum_{i=1}^N \frac{-\hbar^2}{2 m_\text{e}} \nabla^2_i \bigg\vert \psi \bigg\rangle = -\frac{\hbar^2}{2 m_\text{e}} \sum_{i=1}^N \bigg\langle\psi \bigg\vert \nabla^2_i \bigg\vert \psi \bigg\rangle$ )

Happily, my fueling and hydration intake is fool-proof:

$|\mathrm{GHZ}\rangle = \frac{|0\rangle^{\otimes M} + |1\rangle^{\otimes M}}{\sqrt{2}},$

And finally, though it's out of my control I can't help but hope for ideal weather conditions throughout the day:

$|\psi_\text{NOON} \rangle = \frac{|N \rangle_a |0\rangle_b + |{0}\rangle_a |{N}\rangle_b}{\sqrt{2}}, \,$

So really, what could go wrong?

4 comments:

GZ said...: Haha! That is AWESOME. Perfect!; August 27, 2013 at 3:54 PM
Sara Montgomery said...: Did you like the GHZ one, GZ? Not sure what H could stand for but you can decide.; August 27, 2013 at 6:21 PM
Eliza Ralph-Murphy said...: Heard it through the grapevine that you had a good run:-) Congratulations!! Now if I can only decipher your above formula(s) for success before October 5th!; September 9, 2013 at 10:31 AM
Sara Montgomery said...: Thanks, EJ. The beauty of the formulas is that can mean whatever the heck you want them to. (Unless you're a quantum physicist.); September 9, 2013 at 12:15 PM

Trail Tripping

Tuesday, August 27, 2013

Back to the Forest

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