live! from Soda Hall!

[nibot]

Meh. I was all set to get an MRI brain-scan tomorrow morning in return for taking some quantum superposition of a sugar pill and this substance:

But it seems that "because of their cholinomimetic actions, cholinesterase inhibitors should be prescribed with care to patients with a history of asthma or obstructive pulmonary disease" I'm not eligible for the experiment. )-:

The other funny thing that happened today is that I called Diane and Christos Papadimitriou answered the phone!

Comments

Re: nitpicking....

[nibot.livejournal.com]

And I think (|00> + |11>)/sqrt(2) is the same as "with probability 1/2 |00>, with prob 1/2 |11>". i.e., Kenny describes a mixed state as a collection of superpositions in that form.

[anemone.livejournal.com]

So, I walked to my quantum buddy and asked.

Consider case A, a quantum bit in
|0> + |1> (I'm ignoring normalizing constants)

and the mixed state
with probability 1/2, |0>
with probability 1/2, |1>

If you measure in the standard 0,1 basis, they appear the same. But suppose you measure in a rotated basis, with your basis vectors |0> + |1> and |0> - |1> (again, normalized). To measure a quantum state in a basis, you take the dot product of state with each of the basis vectors, square them, and that gives you a probability distribution over the basis vectors.

In case A, you'll always get back the 1 on the first vector and zero on the second.

In case B, half the time you'll get 1 on the first vector and zero on the second.

Then, in case A, you always get back the first vector.

In case B, you get back the first vector half the time, and the second vector the other half the time.