Questions tagged [entanglement]
For questions about the principle and application of quantum entanglement. It is a physical phenomenon which occurs when pairs or groups of particles are generated, interact, or share spatial proximity in ways such that the quantum state of each particle cannot be described independently of the state of the other(s), even when the particles are separated by a large distance—instead, a quantum state must be described for the system as a whole. (Wikipedia)
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How does a measurement in a certain basis disentangle a qubit from the cluster state? [closed]
How does a measurement on a certain basis disentangle a qubit from the cluster state?
4
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1answer
70 views
Distinguishing $\frac{| 0 \rangle + e^{i\theta} |1 \rangle}{\sqrt{2}} $ from $| 0 \rangle/|1 \rangle$ with probability $1/2 + \epsilon$
I am given one copy of one of two quantum states -
$\frac{| 0 \rangle + e^{i\theta} | 1 \rangle}{\sqrt{2}} $, for some unknown fixed $\theta$.
One of $| 0 \rangle/|1 \rangle$ - don't know which one, ...
1
vote
1answer
74 views
How is this expression for a GHZ state obtained in the nature paper by Pan et al. (2000)?
Can someone tell me how the authors of the paper "Experimental test of quantum nonlocality" (Nature link to abstract) have rewritten their equation 1 in terms of equation 2 and 3?
2
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1answer
55 views
The expectation of a measurement of qubit 2 after qubit 1 has been measured
In section 1.2.4 (page 13) of these lecture notes http://users.cms.caltech.edu/~vidick/teaching/fsmp/fsmp.pdf, it says
\begin{aligned}\left\langle\psi\left|X_{1}^{0} Z_{2} X_{1}^{0}\right| \psi\right\...
2
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2answers
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How do we change the basis of a given qubit state?
I'm reading this paper (Link to pdf) about a test of entanglement with three particles.
I wanted to ask if there is any mathematical shortcut to express one quantum state on another basis like the ...
4
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1answer
61 views
Why is entanglement creation difficult?
No matter from the true physical realization to date or from some papers, it seems that multipartite entanglement creation is difficult. However, the circuit showing below can easily create ...
3
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0answers
60 views
Why does the entanglement entropy give the number of singlets required to create a given state?
I've read that, given a bipartite pure state $|\Phi\rangle$, its entanglement (equivalently here, von Neumann) entropy $E(\Phi)$ gives the asymptotic number of singlets required to create $n$ copies ...
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1answer
40 views
How do I represent a Werner state in ket notation?
I want to represent Werner state in the form of ket vector notation. Is there a way in which I can represent it in vector form?
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2answers
217 views
How do local quantum gates affect an entangled state?
(1)
Assume we have the Bell State $$ \frac{\lvert 0_{A}0_{B}\rangle + \lvert 1_{A}1_{B}\rangle}{\sqrt{2}} $$
where A and B stand for Alice and Bob.
Now say Bob applies the X gate to his qubit.
I think ...
5
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1answer
60 views
Entanglement properties of $SU(8)$ quantum circuits vs nearest-neighbor $SU(4)$ quantum circuits
For this question, fix three qubits $q_1, q_2, q_3$. I'll use the notation $U_{123} \in SU(8)$ to denote an arbitrary quantum circuit/unitary on the three qubits, and $U_{12}, U_{23} \in SU(4)$ to ...
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2answers
50 views
Does the entangibility of density operators rely on what component spaces are being specified?
Is the entangibility of density operators relied on what component spaces are being specified?
More precisely, let $H$ be a Hilbert space, $\rho$ be a density operator on $H$. Suppose we were not ...
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0answers
25 views
Quantum based lottery using W-State and spatial separation
I'm thinking of a use case of building a quantum based lottery. Using a W-state with spatial separation (see this question) the circuit is build at one location and afterwards the n qubits are ...
3
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2answers
55 views
Entanglement distribution of W-State over different locations
I would like to create a quantum system with the gates for a W state where each qubit is at a different location. Entanglement distribution has been proven in several research articles. I'm new to ...
3
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2answers
102 views
How to describe the transformation induced by the CNOT on arbitrary input states?
Introductions to Quantum Computing treat the Control qubit of a CNOT as unchanged, and this is true for some Control values, eg |0⟩, |1⟩, and (at least when used with a Hadamard-transformed |1⟩ Target)...
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2answers
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Does the definition of separability of pure states require the components of the summands to be pure?
Does the definition of separability of pure states require the components of the summands to be pure? More precisely, let $\rho$ be a pure state (i.e., $\rho=|\phi\rangle\langle\phi|$) on the space $...
5
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1answer
108 views
What is the notation for factoring a state when non-adjacent qubits are entangled?
Suppose I have the entangled state
$$|\psi\rangle = \frac{1}{\sqrt{2}}(|000\rangle + |110\rangle).$$
If i want to factor the non-entangled parts of this state out, I can easily write that down as
$$|\...
3
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1answer
51 views
How is measurement performed on a stream of polarized photons?
Is it possible to use a simple laser to measure qubits in optical quantum computers, or is a single-photon emitter absolutely necessary? If you can do it with a simple laser, how would you go about ...
5
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2answers
151 views
Is it true that for a quantum algorithm to be efficient it must feature a highly entangled state at some point?
I'm wrapping my head around how and why quantum computers can provide advantage over classical. A basic and naive argument is that the dimension of the Hilbert space of $n$ qubits grows as $2^n$. ...
4
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1answer
41 views
Biggest variance of $h=\sum_i H_i$?
What's the biggest variance of $h=\sum_i H_i$ where $H_i$ is the hamiltonian act on the ith qubit?
If the n qubits state is separable, i.e., the state is $\mid\psi_1\rangle\otimes\mid\psi_2\rangle\...
1
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1answer
57 views
Why does entanglement complicate quantum simulation?
To model a single qubit one would need enough memory for $2$ complex numbers. If we have an $N$ qubit system, we would have to store $2N$ complex numbers.
The general statement is that to store an $N$-...
4
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2answers
114 views
Role of entanglement in a VQE ansatz for combinatorial problems
Variational Quantum Eigensolver is used in quantum chemistry and combinatorial optimization (CO). I'm interested in the latter. In the CO setting a Hamiltonian is a diagonal matrix with real entries ...
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2answers
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How to calculate the amount of entanglement for each qubit in a quantum computer
I am an electrical engineer and am learning about quantum computing. I am writing a simulator in Python to help with the learning process.
The code that I have can simulate up to 10 qubits. I have (so ...
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1answer
75 views
Given $|\psi\left(t\right)\rangle=\sum_{n=0}^{N}c_{n}\left(t\right)|N_{1}\rangle_{a}|N_{2}\rangle_{b}$, what is the expression for $c_n(t)$?
We have:
$$|\psi\left(t\right)\rangle=e^{-iH_{NL}t}|N\rangle_{a}|0\rangle_{b}$$
Also
$$|\psi\left(t\right)\rangle=\sum_{n=0}^{N}c_{n}\left(t\right)|N_{1}\rangle_{a}|N_{2}\rangle_{b}$$
I would like to ...
3
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1answer
86 views
Do entangled states always result in some form of correlation?
Consider a bipartite state $\rho$, and denote with $\Pi^A\equiv \{\Pi^A_a\}_a$ and $\Pi^A\equiv\{\Pi^B_b\}_b$ local projective measurements.
Let the associated joint probability distribution be $p_\Pi$...
5
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1answer
131 views
How can one cheat in Mahadev's classical verification protocol if one can find a "claw''?
I was going through the seminal paper of Urmila Mahadev on Classical Verification of Quantum Computations(for an overview see this excellent talk by her). As a physicist by training, I am not very ...
3
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1answer
60 views
What do states that are uncorrelated with respect to a given local measurement look like?
Consider a bipartite state $\rho$, and let $\Pi^A\equiv \{\Pi^A_a\}_a$ and $\Pi^A\equiv\{\Pi^B_b\}_b$ be local projective measurements.
Suppose that measuring $\rho$ in these bases gives uncorrelated ...
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1answer
85 views
Argue positivity of mean value of an entanglement witness matrix for all separable state [closed]
Given $\
\hat{W}=\mathbf{1}_{A B}+\sigma_{x}^{A} \otimes \sigma_{x}^{B}-\sigma_{y}^{A} \otimes \sigma_{y}^{B}-\sigma_{z}^{A} \otimes \sigma_{z}^{B}
$
how can i show that for every separable state $\...
4
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1answer
53 views
Where is entanglement present and absent in the one clean qubit model of computation?
Based on my limited and poor understanding, a quantum circuit in the "one clean qubit" model of quantum computation generally acts on a single pure (clean) qubit tensored with $n-1$ qubits ...
3
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0answers
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What is the relationship between entanglement and quantum correlation?
What is the relationship between entanglement and quantum correlation? Are they synonym?
Sometimes, these two words look like synonym; people use one word to explain another,
These states are not a ...
4
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1answer
144 views
How do you build a circuit to make an equal superposition of $n$ outcomes?
Suppose we start with $|00...0\rangle$.
We want to build an equal superposition over $|0\rangle + ... + |n-1\rangle$.
When $n=2^m$ for some $m$, I know I can do this using $H^{\otimes m}$.
What is the ...
3
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0answers
48 views
Modeling building blocks for quantum computation
If I would design library for quantum computation I would naively consider a sequences of entangled qudits with unit length as a building blocks. I.e., unit length elements from $$\mathbb{C}^{d_{1}}\...
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0answers
49 views
Is there a simple quantum gate that shows off the power of Quantum interference?
I'm trying to build a deep understanding of where the power of quantum computing comes from when compared to probabilistic computing. A naive observation might be that probabilistic computing would be ...
2
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4answers
135 views
Can a qubit be entangled with an arbitrary quantum state, without altering it?
For example, if an adversary were to get hold of one half of an entangled 2-qubit quantum state, $|\psi \rangle$, travelling along a channel, would they be able to entangle one of their own qubits ...
2
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1answer
59 views
How to calculate the evolution of ket states through a simple quantum circuit?
I am having difficulties with the calculations of qubits.
I think I can do them, but it feels so massivly inefficient!
In this tutorial grover's algorithm for example, there's a simple oracle given ...
3
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2answers
215 views
Is it possible to retrieve $|\psi_1\rangle,|\psi_2\rangle$ from their tensor product $|\psi_1\rangle\otimes|\psi_2\rangle$?
Consider two quantum states$$\left| \psi_1 \right> = \alpha \left|0\right> + \beta\left|1\right>$$ and $$\left| \psi_2 \right> = \gamma \left|0\right> + \delta\left|1\right>$$
Now ...
2
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1answer
30 views
Unitary interaction term of two-qubit graph state
Consider the controlled phase gate $$U_{ab}(\varphi_{ab}) := e^{-i \varphi_{ab}H_{ab}}~~~~\text{where}~~~~H_{ab} := |1 \rangle^{a} \langle 1 | \otimes |1 \rangle^{b} \langle 1 |$$ is the two-qubit ...
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2answers
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Is the tensor product of 2 Hadamard gates entangled?
Assume that you have a system of two qubits in the state $|11 \rangle$. Apply $H \otimes H$, where $H$ is the Hadamard matrix. Is the state $(H \otimes H)|11\rangle$ entangled?
I know if we take the ...
2
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1answer
45 views
Can we convert two single qubit states into single mixed state?
Consider two qubits
$$\left| \psi_1 \right> = \alpha \left|0\right> + \beta \left|1\right>$$ and $$\left| \psi_2 \right> = \alpha_1 \left|0\right> + \beta_1 \left|1\right>$$
Is it ...
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1answer
150 views
Error in the Toth's 2012 paper: “Multipartite entanglement and high-precision metrology”?
This paper is a paper in 2012 and cited by a lot of papers. And there does not exist comment in arxiv or error statement in PRA. But when I reading this paper, I think the right part of the eq(23) ...
2
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1answer
74 views
Given $|\psi\rangle=(U_A\otimes U_B)|0,0\rangle$, is $|\psi\rangle\!\langle\psi|$ always a product state?
say I have some state in the combined space $\psi$ ∈ $H_A\otimes H_B$, where $\psi=U_A \otimes U_B|0,0\rangle$ (operators from respective spaces), and $\rho_A, \rho_B$ the respective density matrices.
...
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1answer
46 views
What is an example of an entangled state whose correlations are describable with a local hidden variable model?
When talks about CHSH inequality, we always say that the states that violate the inequality are entangled, while some states that do not violate the inequality can also be entangled.
For the latter ...
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1answer
101 views
Does $\mathrm{Tr}(\rho\sigma) > 0$ prove that a state $\sigma$ is separable?
As an example I have the density matrix:
$\rho = \frac{1}{3}(| \phi^+ \rangle\langle\phi^+| + | 00 \rangle\langle 00|+| 11 \rangle\langle11| )$
And the two-qubit state is:
$\frac{1}{3}(| \phi^- \...
2
votes
2answers
58 views
How to prove that EPR outcomes have equal probability no matter the basis?
Recently in class, we learned about the EPR state. I know that no matter what basis the first qubit is measured in, the two outcomes have an equal probability. However, how does one prove this? I ...
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0answers
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Can the CCNR entanglement criterion be seen as a “natural” statement about entanglement breaking channels?
(The CCNR criterion) The computable cross-norm or realignment (CCNR) entanglement criterion, as discussed in (Gühne and Toth 2008), is based on the observation that any bipartite state $\rho$ can be ...
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1answer
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Reduced density matrix of the ensemble of two-qubit state that is possessed by Alice and Bob
Consider the entanglement-based protocol that in each round Alice prepares a Bell state $\Phi_+= \frac{1}{\sqrt{2}}(|00\rangle+|11\rangle)=\frac{1}{\sqrt{2}}(|++\rangle+|--\rangle)$ and sends one ...
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1answer
31 views
Does Toffoli AND conjugate affect superposition if used in Shor's algorithm?
I have come across several papers that use Toffoli AND conjugate to minimize the T-depth. But since it contains a measurement, does it affect Shor's algorithm (in terms of interference, entanglement, ...
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1answer
88 views
How to get_statevector() with defined gates in Qiskit?
I'm learning Qiskit for my QC lectures and I'm not able to run the following code:
...
2
votes
2answers
51 views
How do you transmit a single qubit of an entangled qubit over?
When we talk about superdense coding, we say that Alice and Bob share an entangled qubit and then after this, Alice transmits her qubit over to Bob after performing the necessary manipulation.
What ...
5
votes
2answers
110 views
What is the physical intuition behind taking the partial trace of a state?
I want to confirm my understanding of a partial trace.
Essentially, we have a system that $H_a \otimes H_b$. When we trace out system $b$, what we are doing is basically reducing the system down to as ...
6
votes
3answers
594 views
Are entangled and Bell states the same thing?
I am a little confused whether the entangled state and Bell state are the same thing? If they have a bit of contrast, what is the difference between them?
