10
votes
3answers
534 views

Entangled or unentangled?

I got a little puzzled when thinking about two entangled fermions. Say that we have a Hilbert space in which we have two fermionic orbitals $a$ and $b$. Then the Hilbert space $H$'s dimension is just ...
0
votes
0answers
134 views

Can experiment distinguish the basis in which a singlet state is represented?

Let $\left(|\uparrow\rangle,|\downarrow\rangle\right)$ and $\left(|\nearrow\rangle,|\swarrow\rangle\right)$ be two bases of the $2$-dimensional Hilbert space $H$. Can an experiment distinguish ...
7
votes
2answers
192 views

Under what assumptions can we split a Hilbert space into subspaces?

I was thinking about an apparently simple question about quantum mechanics, if I am looking at a quantum system described by a Hilbert space $\cal{H}$ under what hypothesis can I define A and B as ...
17
votes
2answers
149 views

What Shannon channel capacity bound is associated to two coupled spins?

The question asked is: What is the Shannon channel capacity $C$ that is naturally associated to the two-spin quantum Hamiltonian $H = \boldsymbol{L\cdot S}$? This question arises with a view ...