All Questions
Tagged with quantum-entanglement linear-algebra
14
questions
4
votes
2
answers
228
views
If two quantum states have the same Schmidt bases at all times, are they equal?
In brief:
if two quantum states can be Schmidt decomposed using the same sets of joint basis at all times, no matter the evolution they go through, are the quantum states equal?
In detail:
Consider ...
- 151
3
votes
1
answer
139
views
Is there a relation between some kind of distance and the Schmidt basis?
Consider two bipartite quantum states $|\phi\rangle^{AB}$ and $|\psi\rangle^{AB}$ (in a finite dimensional Hilbert space $\mathcal H_A\otimes \mathcal H_B$), such that
$$\| |\phi\rangle\langle\phi|^{...
- 33
0
votes
2
answers
72
views
The eigenstates of a single EPR particle
I am curious whether there is a sense in which each of the EPR particles is in an eigenstate of some observable.
Consider a pair of EPR particles 1 and 2, of which combined state is given by
$|\Psi\...
- 1,073
0
votes
1
answer
60
views
Can a nonlinear evolution be linear at the level of reduced states?
Consider a (possibly unphysical) non-linear transformations of bi-partite quantum states,
$$\mathcal{N} (a A + b B) \neq a \mathcal{N}(A) + b \mathcal{N} (B)$$
for some density matrices $A,B \in \...
- 25
1
vote
5
answers
1k
views
Mathematical explanation of bra-ket notation in quantum mechanics
$\newcommand{\hp}[1]{\hphantom{#1}}$
We have the entangled state of two pairs of qubits:
$$
|\psi \rangle =\frac{1}{2}|0011\rangle-\frac{1}{2}|0110\rangle-\frac{1}{2}|1001\rangle+\frac{1}{2}|1100\...
- 253
2
votes
0
answers
71
views
Measurement operator in a Bell experiment
I'm trying to figure out why a Bell experiment gives rise to the payoff (measurement) operator used in this paper on quantum game theory.
Two players are each in control of one half of an entangled ...
- 21
1
vote
2
answers
196
views
What's the physical meaning of a reduced density matrix in EPR?
Consider an EPR situation in which there are two particles, a and b, of which state is given by
$\Psi = \frac{1}{\sqrt2}(|1\rangle|0\rangle + |0\rangle|1\rangle)$,
where $|0\rangle$ and $|1\rangle$ ...
- 1,073
31
votes
7
answers
7k
views
What is the actual use of Hilbert spaces in quantum mechanics?
I'm slowly learning the quirks of quantum mechanics. One thing tripping me up is... while (I think) I grasp the concept, most texts and sources speak of how Hilbert spaces/linear algebra are so useful ...
- 531
0
votes
1
answer
164
views
A counter example for proving Schmidt Decompostion doesn't hold in general for tri-partite systems
I have been trying hard at this. Schmidt decomposition in bi-partite systems itself is pretty unintuitive for me.
I have tried to understand two different proofs and I followed one well, but just wasn'...
3
votes
2
answers
119
views
Why does entanglement negativity not satisfy the triangle inequality in the usual sense?
I am a bit puzzled, I’ve read in some places, like the original paper by Vidal, that
$$
\mathcal{N}(\sum_n a_n \rho_n)\leq \sum_n a_n \mathcal{N}(\rho_n)
$$
whenever $a_n \geq 0$ and $\sum_n a_n =1$. ...
- 1,544
1
vote
1
answer
2k
views
Schmidt decomposition of entangled state [closed]
I have a problem with some homework our teacher assigned. I have to find the Schmidt decomposition of the entangled state
$$\lvert\psi\rangle_{A,B}=\frac{1}{2}\lvert0\rangle_{A}\lvert0\rangle_{B}-\...
2
votes
1
answer
426
views
How can eigenvectors of a Hermitian matrix be entangled?
You have a tensor product space $H_1 \otimes H_2$. Any vector $w$ in this space has a Schmidt decomposition:
$$
\mathbf{w} = \sum_{i} \alpha_i \mathbf{u_i}\otimes\mathbf{v_i}
$$
Vector $w$ is not ...
- 1,619
1
vote
1
answer
296
views
Finding all decompositions of mixed states
Some quantities, such as the entanglement of formation, are defined using a quantity that is minimized over all possible decompositions of a mixed state. A closed form can be found for this in some ...
- 695
6
votes
2
answers
674
views
Why is the dimension of the set separable states $\dim\mathcal H_1+\dim\mathcal H_2$?
Please can you help me to understand how the dimension of the set of separable states is $\dim \cal H_1 + \dim \cal H_2$?
This is the relevant passage:
So far, we have assumed implicitly that the ...
- 233