All Questions
Tagged with quantum-entanglement hilbert-space
163
questions
6
votes
2
answers
639
views
When is a state entangled?
I have read from What's the difference between an entangled state, a superposed state and a cat state? that an entangled state is one that cannot be expressed as product state. Suppose we have the ...
0
votes
2
answers
58
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How can I construct a trivial product state in the continuum?
When working on the lattice it is easy to define a trivial product state. A state $|\psi\rangle$ is a trivial product state if it admits the following tensor decomposition,
\begin{equation}
|\psi\...
0
votes
1
answer
49
views
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\...
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4
votes
3
answers
294
views
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+|...
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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 $n \in \mathbb{N}$, ...
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-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
$$ |...
- 3
2
votes
2
answers
102
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How to determine parameters such that the state $|\psi\rangle=\frac1{\sqrt2}|+\rangle|+\rangle+a|+\rangle|x+\rangle+b|-\rangle|-\rangle$ is separable?
Suppose that two spin-1/2 are in the state:
$$ |\psi \rangle = \frac{1}{\sqrt{2}} |+\rangle|+\rangle + a|+\rangle|x+\rangle + b|-\rangle|-\rangle $$
and we want to find values for a & b such that ...
- 189
0
votes
1
answer
105
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Path Integrals for entangled states
Is there a way of characterizing entanglement between states in a path integral formalism? If so, does this shed some light on the apparently non-local effects of quantum mechanics?
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1
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3
answers
288
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How do I convert this separable state into a product state?
I know two particles in a Bell state cannot be written as a product state as they are entangled. But what if I had a classically correlated state$$\rho = \frac{1}{2}(|11\rangle\langle 11| + |00\rangle\...
- 411
3
votes
0
answers
85
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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 ...
- 1,440
2
votes
0
answers
39
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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 ...
- 2,292
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 ...
- 2,292
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 ...
- 2,292
1
vote
1
answer
81
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Preserving the entanglement of a 2 qubit bellstate when including a third qubit: a general case?
So suppose we have two 2-qubit bell states $|\Psi_{AB}\rangle$ and $|\Psi_{BC}\rangle$ defined the usual way. I want to create a three qubit pure state from qubits A,B, and C such that the ...
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votes
0
answers
71
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What do we mean by causality when we say that entanglement measurements are uncaused? [duplicate]
I’m having a hard time wrapping my head around how the measurement of particle A does not affect the state of an entangled particle B even if no superluminal speeds exist.
Suppose Alice makes a ...
user385269
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 ...
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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 ...
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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
1
vote
1
answer
56
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Relative "volume" of entangled vs product states [duplicate]
A system containing $n$ qubits is described by a $2^n-$dimensional Hilbert space. Some of these states can be decomposed as product states, but not all of them. The remaining ones are called entangled ...
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0
votes
1
answer
63
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Are there non-trivial two-party stabilizers in bipartite entanglement for product states?
In this recent paper where the authors discuss finite classification of entanglement types, on pg. 29 in appendix A, it is claimed that in bipartite entanglement for product state $|00\rangle$ there ...
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votes
0
answers
212
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Confusion about the tensor product structure of a multi-fermion Hilbert space
I often see people study entanglement in fermionic systems. The setup is often like this. Suppose we have a 1d lattice of $2L $ sites, which is divided into a left part and a right part, each with $L ...
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0
votes
2
answers
61
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Are multimode states a product state of single mode states?
Books such as 'Quantum Theory of Light by Rodney Loudon (page 140)' and 'Quantum Optics for Beginners by Ficek and Rizda (page 43)' claim that the multimode state is nothing but a tensor product of ...
-2
votes
1
answer
144
views
What is meant by " a basis is diagonal"?
I am trying to understand Schmidt decomposition. I am stuck in one sentence here. See the example picture.
Here, I can understand everything except the line "For both
HA and HB the Schmidt basis ...
3
votes
1
answer
88
views
Why is the entanglement of formation upper bounded by the Schmidt number?
I have read many times in several articles (such as https://arxiv.org/abs/1609.05033) that the entanglement of formation EoF puts a lower bound on entanglement dimensionality $d$ (i.e., the Schmidt ...
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1
vote
0
answers
46
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What happens when a maximally entangled state passes through a $k$-extendible channel?
In the context of Phys. Rev. A 104, 022401 (arXiv:1803.10710), Figure 3
What happens when a maximally entangled state( not $k$ extendible even for $k=2$) passes through a $k$-extendible channel? We ...
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1
answer
57
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Can an entangled state in general be created by destructive interference in some subspace?
For instance, if we have a general two-qubit state $$|\psi\rangle=\frac{1}{2}(|0\rangle+e^{i\varphi_a}|1\rangle)\otimes(|0\rangle+e^{i\varphi_b}|1\rangle)=\frac{1}{2}(|00\rangle+e^{i\varphi_b}|01\...
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votes
1
answer
137
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Does spin entanglement imply position entanglement?
My question is whether two electrons can be entangled only with respect to their spins but not with respect to some other observable, such as position.
I initially believed that spin-entanglement ...
- 1,073
2
votes
2
answers
94
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Why does the fact that all quantum systems are open mean that no quantum state can be pure
I am teaching myself about open quantum systems and I am confused by the following statement on the wikipedia page about open quantum systems:
"The fact that every quantum system has some degree ...
- 941
3
votes
3
answers
2k
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Entanglement and density matrices [closed]
Suppose I have a system composed of two subsystems (each is a 2-state system).
Let $$|\psi\rangle = \frac{1}{\sqrt{2}}(|0\rangle_A \otimes |1\rangle_B - |0\rangle_B \otimes |1\rangle_A)$$ be an ...
0
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1
answer
185
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On an intuitive way of characterizing "the amount of entanglement" in a bipartite system
Context of the question:
Schlosshauer (978-3-540-35773-4, p. 33) states:
"A useful intuitive way of quantifying the entanglement present in
this state [(1)] is to consider the following question:...
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4
votes
1
answer
244
views
Is a state being unentangled equivalent to statistical independence for all pairs of subsystem observables?
I imagine the answer is yes since, if so, the definition of unentangled is rather non-obvious and yet it gives an operational way to check for statistical independence.
I am working with the standard (...
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0
answers
55
views
Is the set of $k$-extendible states compact?
Let 𝑘 ∈ ℕ
. A state 𝜌_𝐴𝐵 on a bipartite Hilbert space A ⊗ B
is 𝑘-extendible with respect to B if there exists a state 𝜌_(𝐴𝐵_𝑘)
on A ⊗ B^(⊗𝑘), which is invariant under any permutation of the ...
- 11
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vote
0
answers
72
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Could Dark Matter be comprised of gravitational waves entrained in the bulk?
The evidence is strong that more massive galaxies have more massive Dark Matter (DM) halos (for example, Qi Guo et al, Monthly Notices of the Royal Astronomical Society, Vol 404 (2010)). Might this ...
- 11
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1
answer
156
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Is entanglement the only way to get mixed state that is consistent with the Schrödinger equation?
If we treat our entire system (say an electron and a bunch of atoms) quantum mechanically then all possible interactions will be unitary transformations. Thus any state that I describe will always be ...
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1
vote
0
answers
44
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Representation of $d$-dim maximally mixed state in different bases
Consider the maximally entangled state in $d$ dimensions, $|\Psi\rangle:= \frac{1}{\sqrt{d}} \sum_{i=0}^{d-1} |i,i\rangle^{AB}$, where $|i\rangle^{AB} := |i\rangle^{A}\otimes|i\rangle^{B}$ and $\{|i\...
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vote
1
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463
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Entanglement Entropy and Entanglement Negativity for pure/mixed separable/entangled state
My question is how is Entanglement Entropy (EE) and Entanglement Negativity (N) related to the combinations of pure/mixed and separable/entangled states? That is for pure separable (PS), pure ...
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1
vote
3
answers
322
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If you change the state of one entangled particle will it change the other? [duplicate]
I have seen a bunch of duplicates of this question and I’m sorry if this is a true duplicate, but all the other duplicates have super long and complicated answers that I don’t understand.
I just want ...
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5
answers
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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\...
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1
answer
73
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Arbitrary entangled matter-photon emitter
I am recently approaching to photonics and integration between matter qubits together with photons. I have an interest in understanding the assumption I can do when abstracting such technologies.
I ...
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6
answers
2k
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Why do we need mixed states in quantum mechanics?
I am trying to understand the necessity of density matrices and the notion of "mixed states" in quantum mechanics (I read all the other posts about this, I promise).
As far as I understand, ...
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votes
2
answers
126
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How is quantum entanglement understood? [duplicate]
I need enlightening on quantum entanglement. If the entangled pair of particles are, for simplicity's sake, a red and blue ball and I look at one ball and find it to be red then obviously the other ...
- 1
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votes
1
answer
111
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Quantum Fisher Information for finding distance between two states [closed]
If we have two points at $x$ and $x'$ at distance d that have entanglement bond. At each point we consider some state let say coherent states $\psi(\mu,x)$ and $\psi(\mu,x')$. Can we measure the ...
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0
answers
127
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Is the NOON state entangled even if $N=1$?
Let $\mathcal{H}\cong\mathbb{C}^2$ be the Hilbert space of states of a single particle. Let $\{|\psi_A\rangle, \psi_B\rangle\}$ be a basis for $\mathcal{H}$. I now want to describe an ensemble of ...
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1
answer
260
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Maximally entangled states of a qutrit system [closed]
How do I construct a qutrit system and then a maximally entangled state for a qutrit system?
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2
votes
2
answers
125
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Is my simplistic understanding of a Qubit, Superposition and Entanglement correct? [closed]
I've gone through a number of Lenny Susskind's lectures on entanglement (both just for the joy of it and to better understand quantum mechanics) where he delves into the idea of a qubit.
For the sake ...
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2
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85
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Can you create a pair of entangled particles with asymmetric probabilities of quantum states?
Is it possible to create two entangled particles emitted such that the "left" particle has a different liklihood of being measured in a certain state than the "right" particle?
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vote
2
answers
259
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Intuition/Motivation behind mixed states
I have some confusion regarding pure, mixed and entangled states and I'm trying to gain some clarity on this.
Set up, and my current understanding:
One fundamental distinction I seem to have (please ...
- 593
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votes
0
answers
52
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Understanding another Inequality on Entanglement Entropy Found in Hastings Paper on the Area Law
I am currently reading and trying to reproduce the proof found in the following paper by Hastings, in which he proves that the ground state of 1D gapped systems follow an area law. I am trying to ...
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