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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Mutual information of shared state is larger than expectation values
Im trying to prove the following identity for a special case:
Alice and Bob share the Bell state
\begin{align*}
|\psi\rangle = \frac{1}{\sqrt{2}}(|00\rangle+|11\rangle).
\end{align*}
Consider the ...
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Are there quantum algorithms to estimate the partial transpose?
The entanglement negativity and the positive partial-transpose criteria play important roles in quantifying the amount of entanglement for mixed states. Yet, because these measures generally involve ...
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Can you apply a CNOT gate on qubits in MBQC that aren´t next to each other?
Is it possible to apply a CNOT gate in MBQC to qubits that aren´t next to each other?
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How to show that the GHZ state is absolutely maximally entangled?
A multipartite state is called absolutely maximally entangled if for its any bipartition the reduced density matrix of smaller part is maximally mixed. Show that GHZ state has this property.
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How to convert a partially entangled state into maximally entangled using SLOCC
Let's say I have a generic partially entangled two-qubit state with Schmidt decomposition
$$|\psi\rangle_{AB} = \sqrt{\alpha} |00\rangle_{AB} + \sqrt{\beta}|11\rangle_{AB}.$$
I know from Lo and ...
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Adding measurement circuits to the singlet state circuit and want to create single circuit
I am trying to add the measurement of Alice and bob's circuit to the singlet circuit. Actually, I am trying to build the e91 protocol. But it is giving me an error like this.
...
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Is possible to write a separable state as a finite or countable infinite sum of product states?
Let us consider the tensor product of two finite Hilbert spaces $\mathcal{H}_1\otimes \mathcal{H}_1$.
According to Watrous book, the set of separable states is the convex hull of the set of product ...
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Recent references establishing connections between stabilizer error correction and entanglement distillation procedures
I know some concrete entanglement distillation protocols (from this review).
I also know there are connections between error-correction codes and entanglement distillation (again this review but also ...
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What is the difference between quantum teleportation and quantum entanglement with dense coding?
What is the actual difference between quantum teleportation and quantum entanglement with dense coding.
Wikipedia says:
Quantum teleportation is a technique for transferring quantum information from ...
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Creating entangled states via Rydberg blockade
I was watching a talk by Prof. Mikhail Lukin and I have a silly question.
In the talk, he discussed that a typical procedure for generating a Bell pair consists of using the Rydberg blockade on two ...
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What is the relation between maximally entangled and maximally mixed?
In Wikipedia I read the following:
"A multipartite state ${\displaystyle |\psi \rangle }$ of a system is called absolutely maximally entangled if for any bipartition ${\displaystyle A|B} $ of ${...
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Is there some theorem that proves that entanglement is necessary for quantum advantage? [duplicate]
Gottesman-Knill theorem kind of implies that entanglement is not sufficient to produce quantum advantage because it can be simulated in many cases (for Clifford gates combinations). Also it is kind of ...
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When does a Hamiltonian result in the construction of an IC-POVM?
Consider a generic $d_A$-dimensional quantum system $A$, for example made of $n$ qubits. Now consider a second higher-dimensional system $B$, with $d_B=d_A^2$, and the quantum map
$$
\rho_A \...
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Possible post - measurement states for Bell state $\frac{1}{\sqrt{2}}[|00\rangle + |11\rangle]$
This is in reference to page 241 of Introduction to classical and quantum computing by Thomas.G Wong.
The author starts off with a Bell state $\frac{1}{\sqrt{2}}[|00\rangle + |11\rangle]$.
In trying ...
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General Bell state expression: What condition for mixture of Bell states to be entangled?
Convention: $|qubit_{A}, qubit_{B}\rangle$
The general Bell state equation: $|\beta(a,b)\rangle = \frac{1}{\sqrt{2}}\sum_{k=0}^{1}(-1)^{ka}|k, k\oplus b\rangle = \frac{1}{\sqrt{2}}[|0,0 \oplus b\...
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How to create a maximally entangled state of two 4-level quantum mechanical systems?
Let's say that I have a 4-level quantum state, which is described by a linear combination of the following four eigenbases:
$$|\text{red}⟩ = \begin{bmatrix}
1 \\
0 \\
0 \\
0
\end{bmatrix} , |\text{...
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Finding entanglement in matrix that is a sum of 4 Bell states
A general Bell state:
$|\beta(a,b)\rangle = \frac{1}{\sqrt{2}}[|0,0 \oplus b\rangle + (-1)^{a}|1,1 \oplus b \rangle]$
$|\beta(0,0)\rangle = \frac{1}{2}[|00\rangle \langle 00| + |00\rangle \langle 11| +...
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a three partite quantum state with maximum entanglement
I thought the only three-partite states with maximum entanglement are GHZ and W states. but i found out the below state has maximum entanglement too
$\frac{1}{2}(\left| 111 \right>+\left| 100 \...
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Does Bob know the state of the qubit Alice teleported after the completion of the teleportation protocol?
Notation: $|\text{Alice}_{1\,\,}\text{Alice}_{2\,\,}\text{Bob}_{1}\rangle$
Alice and Bob shared an entangled state, say a Bell state $| \Phi_{+}\rangle = \frac{1}{\sqrt{2}}\bigg[|00\rangle + |11\...
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Why is a Bell state involved in quantum teleportation?
Notation: $|\text{qubit}_{1}, ..., \text{qubit}_{N}\rangle$.
The goal of quantum teleportation is to send quantum information using classical bits.
A source transmits a state $|\psi\rangle_{A_{0}} = \...
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Magic square operator's measurement product
In the talk by Andrea Coladangelo (link) at 29:30, he claims that if $X_1X_2X_3 = I$, such that the operators commute. Then, the product of the measurement results on an EPR pair of the same dimension ...
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gate actions in classical (not in the physics sense) superdense coding narrative
I am currently reading through superdense coding and the setup is as follows:
Both Alice and Bob shares a fixed entangled state $|\psi\rangle = \frac{1}{\sqrt{2}}[|00\rangle + |11\rangle]$ with the ...
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Why does Schmidt decomposition (2 qubits) requires density matrix of each system?
This is in reference to Nielson & Chang (page 109).
Schmidt decomposition: suppose $|\psi\rangle$ is a pure state of a composite syste, AB. Then there exists orthonormal state $|i_{A}\rangle$ for ...
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How to correctly describe state preparation?
I came across a rather basic state-preperation description that I didn't fully understand. So far, I thought I got the basics of density matrices, but now I am confused. I hope you can help me finding ...
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Open neighborhood of an entangled state with non-decreasing Schmidt rank
Let $\psi\in H_A \otimes H_B$ be an entangled state, which means that it has Schmidt rank $r \geq 2$. Does there exist some $\epsilon>0$ for which all states $\varphi$ with $\|\psi - \varphi\|< \...
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Can qubits be entangled without being classically corelated?
I have read before that classical correlations between qubits does not guarantee entanglement, but is the opposite also true?
Consider a 3 qubit system, prepared as follows:
$1-$ A Hadamard gate is ...
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Can we use entanglement for cascaded measurements
My question is as follows:
Suppose we have two entangled states, for example, a GHZ state where
$|000\rangle$ and $|111\rangle$ are entangled
Now, suppose the $|111\rangle$ state is entangled with ...
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Is it possible to produce an entangled state by measuring an unentangled state?
Wondering if it's possible to produce an entangled state by measuring an unentangled state. I tried a few examples, but it seems it's not possible.
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Using bell state shared between two nodes to perform a CNOT gate between different qubits across the nodes
Consider a distributed quantum computer, where two qubit gates can be performed between qubits in the same individual quantum information processor (QIP), but not in separate ones. Suppose each QIP ...
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Use of maximally entangled states in dense coding and quantum teleportation
In studying about the procedures of superdense coding and quantum teleportation, I have seen that maximally entangled states are used in both cases to show that how entanglement can be used as ...
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Why can't we use a two-qubit entangled state to send information faster than light? [duplicate]
I think this question is more suitable for physics, but I am using a quantum computing example to understand why this should not work. Note that I am not a physicist and I know only the basics of ...
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Superluminal communication via entanglement transceivers
I know that this has been disregarded but I could not follow up since I'm new and it's an old post anyway.
I understand the reason that superluminal communication via entanglement won't work. Is that ...
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Upper bound on entanglement entropy of a Product State for any possible partition of the Joint System
Let $|\psi\rangle$ be an $n$ qubit quantum state on a line with Von Neumann entanglement entropy at most $r$ with respect to any bipartition of the qubits (does not have to be a contiguous bipartition)...
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Conditions for entangling $A$ with $C$ via an interaction on $AB$
I have three qubits in subsystems $A$, $B$, $C$. System $A$ initially contains some state $\rho_A$, and $BC$ contains a bipartite pure state $|\psi\rangle_{BC}$. I apply a unitary operation $U$ acting ...
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What is a general entangled bipartite system?
Is there a general pure entangled bipartite system that all other entangled bipartite systems are a special case of it?
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CNOT and quantum entanglement
I have the following problem:
"Consider two parties: Alice in possession of the one-qubit state |ψ⟩ = α|0⟩ + β|1⟩, and Bob who starts with a qubit in the state |0⟩
Show that Alice can teleport ...
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Is quantum mutual information an entanglement measure?
For a bipartite system, the quantum mutual information is defined via the Von Neumann entropy as follows:
$$I(A:B)=S(A)+S(B)-S(AB).$$
It's always positive. Is it an entanglement measurement?
Also how ...
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Quantum Computer Basics [closed]
I am a newbie to Quantum Computing world. My collage professor asked me to do presentation on quantum computing. I have read many articles online but still I think I am not satisfied with what I found....
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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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Understanding entanglement distillation via stabilizer codes?
I am having some trouble understanding the distillation of EPR pairs using a stabilizer code. This idea goes back to the paper by Bennet, DiVincenzo, Smolin, and Wooters.
The idea (I think) is that $k$...
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Why are all Rényi entropies equal for Clifford dynamics?
In this paper, by Adam Nahum et al., the authors trivially states that "For Clifford dynamics all Rényi entropies are equal ... " which is not trivial to me.
Is there a paper or lecture ...
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How to compute a partial trace of the form ${\rm Tr}_S [s^\dagger b- s b^\dagger, \vert \psi \rangle \langle \psi \vert \otimes \rho_B]$?
Let us consider a entangled state for the signal-idler system in its Schmidt decomposition form
\begin{align}
\vert \psi \rangle_{SI} = \sum_{\alpha} \sqrt{p_{\alpha}} \vert w_{\alpha} \rangle_S \vert ...
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How to get the counts of measurement in QSIM simualtor
I had generate Bell State, $\frac{1}{\sqrt{2}}(|01\rangle - |10\rangle)$ now when I measured that in $Z$ basis how can I get the state of individual qubit separately and not the probability of the ...
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Understanding quantum computing power of entanglement
I read here that the power of quantum computing lies in the fact that the Hilbert space size of a $n$ qubits register grows exponentially with $n$, but only when entangled.
I would like to understand ...
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Distributing entanglement using entanglement swapping
I've read papers that consider the problem of sharing entanglement between A and C with an intermediate B. A and B share an entangled state and so do B and C. Then, entanglement swapping is used to ...
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Entanglement entropy of a projector
In this paper the author goes from the equation (13): $\rho_A = \frac{|G_A|}{2^{N_A}}\mathcal{P}^{(\overrightarrow k_A)}$, where $\mathcal{P}^{(\overrightarrow k_A)}$ is a projector acting on a ...
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DumpRegister sometimes blank?
I'm just getting into the baffling world of Quantum Computing so forgive me if this is straightforward...
I'm using Microsoft's Q# simulator so I know I'm allowed to peek into the internals of a Qubit ...
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Any evidence it won't be exponentially harder to add more qubits?
I appreciate quantum circuits can solve certain problems exponentially faster than classical circuits.
Q. Are there reasons to believe it won't be double as hard to build a quantum computer with i+1 ...
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General structure of the state with $I(A:B|C)_{\rho}{=}2 \log_2 \{\min (d_A, d_B)\}$
The conditional quantum mutual information (CQMI) of a state $\rho^{ABC}$ respects the dimension bound $I(A:B|C)_{\rho}{\leq}2 \log_2 \{\min (d_A, d_B)\}$ (Mark Wilde's book, exercise 11.7.9). One ...
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Can we use superdense coding with unentangled pair of qubits?
In transferring information through the means of superdense coding, entangled pair of two qubits is used. Can we use superdense coding with unentangled pair of qubits too?
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