All Questions
130
questions
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49
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Seperable Quantum States
Some similar questions have been ask before, but I still don't really get the definition of seperable states in quantum mechanics.
Consider a bell state of a two qubit system.
\begin{align}
\left|\Psi\...
4
votes
3
answers
294
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Is maximal entanglement basis independent?
Is there a basis such that if we measure the bell state $\dfrac{|00\rangle+|11\rangle}{\sqrt2}$ the results might not be correlated at all (or at least not maximally)?
For example $\dfrac{|00\rangle+|...
2
votes
0
answers
92
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Computing Fubini-Study expectation values over $\mathbb{C}P^n$
In finite-dimensional textbook quantum mechanics, we postulate that states of our system are rays in a Hilbert space $\mathcal{H}$ with dimension $\dim{\mathcal{H}} = n+1$ where $n \in \mathbb{N}$, ...
-2
votes
1
answer
52
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What does doubly-entangled $W$-like state do with three-particle setup?
First, is entanglement of three particles in $W$-like state deliberately possible (and not by chance)? Second, is the following statement correct?
In the doubly entangled $W$ state, represented as
$$ |...
2
votes
2
answers
102
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How to determine parameters such that the state $|\psi\rangle=\frac1{\sqrt2}|+\rangle|+\rangle+a|+\rangle|x+\rangle+b|-\rangle|-\rangle$ is separable?
Suppose that two spin-1/2 are in the state:
$$ |\psi \rangle = \frac{1}{\sqrt{2}} |+\rangle|+\rangle + a|+\rangle|x+\rangle + b|-\rangle|-\rangle $$
and we want to find values for a & b such that ...
0
votes
1
answer
105
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Path Integrals for entangled states
Is there a way of characterizing entanglement between states in a path integral formalism? If so, does this shed some light on the apparently non-local effects of quantum mechanics?
1
vote
3
answers
288
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How do I convert this separable state into a product state?
I know two particles in a Bell state cannot be written as a product state as they are entangled. But what if I had a classically correlated state$$\rho = \frac{1}{2}(|11\rangle\langle 11| + |00\rangle\...
3
votes
0
answers
85
views
Constructing wavefunction for a mixed state
This question is somehow the reverse of another question.
If a quantum system $S$ is in a pure state, then we can find a wavefunction that describes $S$. This wavefunction is unique up to a phase ...
2
votes
0
answers
39
views
A Hamiltonian acts simply on each state in some subspace. Can it be identified with a single simple operator on the subspace?
This is a simplified version of a recent question I asked. My hope is that this simplified version will be easier to tackle. The motivation behind both of these questions is roughly to ask "Given ...
0
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0
answers
51
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If my time evolution operator can't change my entanglement, can I find a simpler time evolution?
Consider a Hamiltonian $H$ on some spin chain of length $L$.
Suppose we have a subset of $n$ eigenstates $\{|\psi_i\rangle \}$ of $H$ obeying the following special condition. First, a couple quick ...
4
votes
1
answer
239
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Two states have the same Schmidt coefficients across every bipartition. Can they be mapped to each other by a product of single-site unitaries?
I have two states, $|\psi\rangle$ and $|\phi\rangle$. I have in mind that they live on a length $L$ spin chain with finite local Hilbert space dimension.
I know that for every Schmidt decomposition ...
1
vote
1
answer
248
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Reduced density matrices and relation to entanglement
I've read that if a state is a product state, the reduced density matrices are pure and if the state is entangled, the reduced density matrices are both mixed.
What would it mean if you had a system ...
6
votes
3
answers
742
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Bell's inequality for angles 120°
In 1964, John Bell first derived the original Bell inequality, $|E(a,b)-E(a,c)|\leq1+E(b,c)$. Here $a,b,c$ are three different possible spin measurement directions, and $E$ is the measured ...
-4
votes
1
answer
117
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How to know which states are entangled from a state vector? [closed]
consider the following state vector of three qubits
$$(1/2)|000⟩+(1/2)|011⟩+(1/2)|101⟩+(1/2)|110⟩.$$
how to know which qubits are entangled with respect to their basis states, in other words, how do ...
-2
votes
1
answer
117
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How can we figure out what fraction of pure states in a Hilbert space are entangled? [duplicate]
The full Hilbert space of a quantum system will generally contain entangled states, and thus when entanglement is lost through decoherence, parts of Hilbert space become inaccessible. Is there a ...