I'm trying to create a quantum circuit which does the following very simple thing:
Alice has two qubits, and she wants to measure the observables: X⊗Z, Z⊗X, and Y⊗Y, each taking values in {-1,1}.
Note that this is a commuting set of observables, so it should be possible to measure all three...
Ok...following what you guys have explained - I did some reading and the whole thing is much clearer now in my mind. I don't want to spend too much time studying RHS in detail... I will instead jump into the theory of distributions, as it is what seems to be lacking in my background. (After all...
but what about ##F(x)=\frac{1}{x}##, then F(x) is square integrable, and so is in the Hilbert space L2, whereas ##xF(x)=1## is not square integrable. So the operator x takes us outside the Hilbert space - and is therefore not defined on that F(x)
Now I know what I should read about next: rigged Hilbert spaces...any suggestions for a good reference? (preferably something written for quantum mechanists as opposed to mathematicians). Thank you!
I hope it's ok for me to step in with my own question. Which are the (dense) subsets of the Hilbert space on which the position and momentum operators are defined?
How would an operator like x fail to be defined on a subset? Is it by failing to be bounded on that subset?
I would very much...
I'm reading a book - and I've been stuck for a while on the same page. This is only a calculus question. We have the action:
S=\int d^4x \;\mathcal{L}
with the Lagrangian (density):
\mathcal{L}=\mathcal{L}(\phi,\dot{\phi},\nabla\phi)
We then vary S:
\delta S = \int d^4x...
One more thing: it is not clear to me how the adhesive bonding picture explains the fact that no static friction is encountered if an object is lifted upward.
Also, all mechanical forces are of course electromagnetic in nature, and are typically very complicated to describe from first principles. For example, hitting a wall with a hammer is an extremely complicated electromagnetic interaction.
Friction in my mind has a part which cannot be accounted...
Hmmm... I have not read Feynman's book, but I really should. As a general rule, everything Feynman writes is correct, unless corrected by Feynman himself!
It is the "SAME surface", and not the "SAME bonds" :)
What I meant is: say we have two rough surfaces, each with a certain...
I was touring the forums and came across this. I hope I am not derailing this interesting conversation with my following (long, hopefully not too irrelevant) comment essay:
Before I became the physics graduate that I now am, I used to enjoy thinking philosophically about QM. Having a...
Hi. I'm sure there are much more qualified people here who can give better answers, but I would like to comment:
I think that thinking about some weak chemical bonds between particles of the two solids in contact is not accurate. The picture I have in my mind is of two rough surfaces, each...
So what is this item ##\hat{x}\otimes \hat{y}##?
More importantly, what is the vector space spanned by it? I know it is ##V_1\otimes V_2##, but what is the geometric picture of this space?
Some physicists use tensor product and direct product synonymously. The definition given above is the direct product according to Gilmore - he defines the tensor product on groups only - see page 28 of the above mentioned reference.
In the sense that this space is spanned by...
The definition (taken from Robert Gilmore's: Lie groups, Lie algebras, and some of their applications):
We have two vector spaces V_1 and V_2 with bases \{e_i\} and \{f_i\}. A basis for the direct product space V_1\otimes V_2 can be taken as \{e_i\otimes f_j\}. So an element w of this space...