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)
457
questions
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What is the difference between having a single-qubit state and knowing a result of a measurement you want to perform on it?
In the quantum teleportation protocol Alice can send Bob an unknown quantum state $|\psi\rangle$. If the only thing Bob does with $|\psi\rangle$ is to measure it in some basis, I guess it would be ...
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1answer
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How to make sense of phases of individual qubits in the context of multiple entangled qubits?
I hear that phase information of qubits is important and you can clearly see the phase of a qubit when represented on the Bloch sphere.
But, I am not sure what to think of the phase of individual ...
6
votes
1answer
371 views
Are nearly all pure two-qubit state entangled?
I am using the code below, utilizing QETLAB's RandomStateVector(4) and IsPPT, to generate a random state and to judge whether the state is entangled or separable:
...
0
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1answer
66 views
Is there any possibility to draw graphs for a maximally entangled state?
I am working on quantum entanglement swapping and I have derived that:
$|\psi\rangle=\frac{1}{2}(|0001\rangle+|0010\rangle+|0100\rangle+|1000\rangle)$
Is there any possibility that I can make a ...
0
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0answers
36 views
Can any separable state be written as a convex combination of separable states? [closed]
A state $\rho_{AB}$ on some space $\mathcal H_A\otimes \mathcal H_B$ is separable if there are two states $\rho_A,\rho_B$ on $\mathcal H_A$ and $\mathcal H_B$ respectively such that $\rho_{AB}=\rho_A\...
2
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1answer
98 views
How to deal with entanglement relativistically?
When discussing relativistic quantum mechanics, Dirac notation is dropped completely which makes the description of entangled particles difficult. However when discussing quantum entanglement and ...
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2answers
223 views
Why are Bell states the maximally entangled ones?
I just want to know why actually Bell states are examples of maximally entangled states and significance of that "maximal" term. Is there anything for proving that?
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How to efficiently construct quantum circuits of oracles in multi-target quantum search?
In standard Grover's quantum search with only one target or its extension of multi-target quantum search, one of the two key parts is to quantize the boolean function
$$f(x):\{0,1,\cdots,N-1\}\...
1
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1answer
72 views
Can we do error correction for entangled particles?
There are several quantum error correction techniques, such as 3-qubit bit-flip code, and Shor’s 9-qubit code. 3-qubit bit-flip code is a straightforward technique for correcting a single error (...
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1answer
327 views
What are min and max overlaps of a maximally entangled state with a separable state?
Let $A,B$ be Hilbert spaces of dimension $d$. Let $\rho$ be some separable quantum state of the composite system $AB$. Given a maximally entangled state:
$$\vert\phi\rangle = \frac{1}{\sqrt{d}}\sum_{i=...
5
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3answers
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Intuition for why $\frac{|00\rangle+|11\rangle}{\sqrt{2}}$ can be written as $\frac{|++\rangle+|--\rangle}{\sqrt{2}}$
In analyzing measurement of $\frac{|00\rangle+|11\rangle}{\sqrt{2}}$ in the local $|+\rangle$, $|−\rangle$ basis, through algebra manipulation, the initial state is first written as $\frac{|++\rangle+|...
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2answers
316 views
What does "measurement destroys information" mean?
I am reading a paper on quantum cryptography. The author used two facts:
quantum-
information cannot be copied
and
Furthermore, measurements destroy information...
For the first statement, I came ...
0
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0answers
28 views
Quantum check sample implementation
I've been trying to figure out how to create a simple circuit in Qiskit to create a check (cheque ) generation and verification as described in this paper.
I started with 3 qubits, first one with the ...
4
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2answers
161 views
What is the role of entanglement in quantum-computational speed-up?
The way I see it, there are three main quantum properties utilized in quantum computing - superposition, quantum interference, and quantum entanglement. I'm looking to understand which one is ...
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0answers
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Unitary Transformations for States with Same Entanglement [duplicate]
$\newcommand{\Ket}[1]{\left|#1\right>}$
I know this has been asked before in another context (How to construct local unitary transformations mapping a pure state to another with the same ...
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votes
2answers
180 views
How to construct local unitary transformations mapping a pure state to another with the same entanglement?
$\newcommand{\Ket}[1]{\left|#1\right>}$In Nielsen's seminal paper on entanglement transformations (https://arxiv.org/abs/quant-ph/9811053), he gives a converse proof for the entanglement ...
0
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1answer
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This is a question about IBM quantum circuit used to generate the quantum cheque state
I'm learning about quantum cheque. And I read "Experimental realization of quantum cheque using a five-qubit quantum computer" which is written by Bikash K. Behera ,Anindita Banerjee and ...
2
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2answers
306 views
Qiskit CNOT-gate matrix mixup?
In the qiskit textbook chapter 1.3.1 "The CNOT-Gate" it says that the matrix representation on the right is the own corresponding to the circuit shown above, with q_0 being the control and ...
2
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0answers
87 views
A way to check if entanglement is increased or decreased
I was wondering if there is a way to check if the amount of entanglement is increased or decreased after a quantum operation without calculating the actual value.
That is, it does not concern with the ...
2
votes
1answer
67 views
Prove the subadditivity for the von Neumann entropy of a bipartite state
I want to prove the subadditivity relation $S(\rho_{AB})\le S(\rho_A)+S(\rho_B)$ for the Von Neumann entropy. The tip is to use the Klein inequality $S(\rho_{AB}\Vert \rho_A\otimes \rho_B)\ge 0$: $$S(\...
2
votes
2answers
69 views
Classical versus quantum correlations and partial traces
Given a bipartite state $\rho_{AB}$ living in the Hilbert space $\mathcal H(A\otimes B)$ we can always define two local states on $A$ and $B$ respectively by taking the appropriate partial traces: $$\...
6
votes
2answers
157 views
Can one always find purifications which preserve equality of statistical mixtures?
When pure states $|\psi_1⟩$, $|\psi_2⟩$ and $|\phi_1⟩$, $|\phi_2⟩$ in $\mathcal{H}_A \otimes \mathcal{H}_B$ have identical statistical mixtures
$$\frac{1}{2}(|\psi_1⟩⟨\psi_1| + |\psi_2⟩⟨\psi_2|) = \...
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2answers
487 views
What happens to the Bell state qubits after the Quantum Teleporation?
I'm reading on the Quantum Teleporation and I couldn't find anywhere what happens to the bell state qubits after the Quantum Teleporation.
2
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2answers
177 views
How to understand combination states vs pure/mixed states?
I've learned that representing a combination of two states, I simply need to take the tensor product of the states. For example:
$$\left|\Psi\right>=\alpha_0\left|0\right>+\beta_0\left|1\right&...
0
votes
3answers
87 views
How does one interpret intuitively the CNOT gate?
How does one interpret the CNOT gate? The CNOT gate takes a separable state and turns into an entangled state. The oracle in the Deutsch algorithm does the same thing. But how does one understand this ...
0
votes
1answer
46 views
Test for Entanglement of Unitary
Define a quantum gate(or unitary) $U$ as entangling if there is a product state that $U$ produce entangling state when applied on.
I've referred previous answer that notion of 'entangling power' can ...
1
vote
2answers
72 views
On existence of orthonormal basis for each subsystem in Separable state [closed]
A separable state in $\mathcal{H}_{a}\otimes\mathcal{H}_{b}$ is given by
$$\rho_{s}=\sum_{\alpha,\beta}p(\alpha,\beta)|\alpha\rangle\!\langle\alpha|\otimes|\beta\rangle\!\langle\beta|.$$
Now, my ...
1
vote
1answer
59 views
How can I observe the effects of the entanglement?
A possibly to ignorant question. Here I read:
For example, if she measures a $|0\rangle$,Bob must measure the same, as $|00\rangle$
is the only state where Alice's qubit is a $|0\rangle$
In the ...
0
votes
1answer
47 views
Restrictions on Quantum Gates and Pure Partially Traced Output States
Suppose we have a quantum circuit that contains an arbitrary number of quantum gates and takes as an input more than a single qubit, say three. What are the restrictions on the quantum gates and the ...
2
votes
0answers
58 views
Spreading of entanglement with depth for Haar random states
Consider a Haar random quantum state of depth $d$. Consider any bipartition of this state. According to this paper (page $2$):
Haar-random states on $n$ qudits are nearly maximally entangled across
...
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1answer
108 views
Find the conditions under which the state $|\phi\rangle = \sum_{y=0}^{2^n -1} e^{\frac{2 \pi i a y}{2^n}} |y\rangle$ is unentangled
Show that the state $ |\phi\rangle = \sum_{y=0}^{2^n -1} e^{\frac{2 \pi i a y}{2^n}} |y\rangle $ is unentangled if $a \in \{ 0,1,...,2^n - 1\} $ and $|\phi\rangle$ can be expressed in the form $ \...
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vote
2answers
105 views
How can the state $\frac{1}{\sqrt{2}}(|00\rangle+|11\rangle)$ be entangled if both spins are the same?
I'm reading Qiskit's documentation. https://qiskit.org/textbook/ch-gates/multiple-qubits-entangled-states.html#3.2-Entangled-States- and they show qubits entangled as $|00\rangle$ (both qubits spin ...
1
vote
0answers
48 views
Calculating probability that two entangled qubits are the same when measured in different bases
Given the entangled state
\begin{equation}
|\Phi^+\rangle = \frac{1}{\sqrt 2} |00\rangle + \frac{1}{\sqrt 2} |11\rangle
\end{equation}
I am trying to calculate the probability that the two qubits end ...
5
votes
1answer
104 views
Does a basis of maximally entangled states exist for two-qubit or two-qutrit system so that the density matrices of the basis states don't commute?
I want to find a basis of maximally entangled states $|\Psi_i\rangle$, for $\mathcal{H}^{2} \otimes \mathcal{H}^{2}$ and, $\mathcal{H}^{3} \otimes \mathcal{H}^{3}$ such that the density matrices of ...
2
votes
3answers
80 views
Do sequences of operations (including measurements) applied to different halves of an entangled pair always commute?
Let us say $A$ has one half of an entangled qubit pair, and $B$ has the other half. $A$ may be able to perform any type of operation on their half of the pair, such as unitary operations, entangling ...
7
votes
1answer
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Can one quantify entanglement between different parts of a system?
Consider some state $|\psi\rangle$ of $n$ qubits. One can take any subsystem $A$ and compute its density matrix $\rho_A =Tr_{B} |\psi\rangle \langle\psi|$. The entanglement between subsystem $A$ and ...
5
votes
1answer
98 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
87 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
56 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
votes
2answers
119 views
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 ...
5
votes
1answer
80 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
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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 ...
1
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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?
5
votes
2answers
227 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
votes
1answer
77 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 ...
3
votes
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 ...
1
vote
0answers
29 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
votes
2answers
101 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
votes
2answers
105 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)...
4
votes
2answers
52 views
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 $...