# 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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### Stabilizer witness for entanglement detection

I am studying on entanglement detection applying stabilizer operators. In page 4 of this paper https://arxiv.org/abs/quant-ph/0501020 ,"for the detection of $N$-qubit entanglement we have to make ...
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### Prove that maximally entangled states $|\Phi\rangle$ satisfy the identity $(U\otimes I)|\Phi\rangle=(I\otimes U^T)|\Phi\rangle$

The definition of maximally entangled state is \begin{equation} \vert \Phi \rangle = \frac{1}{\sqrt{d}} \sum_i \vert i \rangle \vert i \rangle, \tag{1} \end{equation} where $d$ is the dimension of the ...
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### why entanglement of an Antiferromagnetism case decreases in presence of a nonuniform magnetic field?

supposing a two qubit xxx Heisenberg chain in presence of a non-uniform external magnetic field (in z direction), the Hamiltonian of the system is as follow: H = J (σx ⊗ σx + σy ⊗ σy + σz ⊗ σz ) + (B-...
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### Is it ever beneficial to communicate qubits that aren't EPR pairs?

When Alice wants to send a qubit $q$ to Bob, she doesn't have to send $q$ itself. She can instead generate an EPR pair $(a, b)$, send $b$ to Bob, and teleport $q$ to Bob by consuming $(a,b)$ and ...
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### Computation for threshold of CNOT gate

I'm trying to reproduce some threshold results using 7-qubit Steane code in those legacy papers. I managed to obtain the graph for circuit noise and single qubit gate e.g. the pseudocode for computing ...
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### Why not just use Bell state entanglement in the CHSH game?

In the CHSH game, both Alice and Bob receive random bits $x$ and $y$ from a referee Charlie. Based on the bit values and a strategy discussed between Alice and Bob beforehand they will respond with ...
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### Is it advantageous for a state to have higher Bell CHSH violation?

For a density matrix $\hat \rho$, one can construct a "Bell operator" $\hat B$, such that the violation of the inequality $\langle \hat B \rangle \le 2$ is a clear indication of quantum ...
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### With $\vert\Psi^+\rangle$ the Bell state, can $\sqrt{\rho}\vert\Psi^+\rangle\langle\Psi^+\vert\sqrt{\rho}$ be simplified?

Let $\vert\Psi^+\rangle_{AB} = \frac{1}{\sqrt n}\sum_{i=1}^n\vert i\rangle_A\vert i\rangle_B$ be the maximally entangled state in Hilbert space $\mathcal{H}(AB)$ and $\rho_A$ be some state in Hilbert ...
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### Proof of Nielsen's theorem (Theorem 12.15) given in Nielsen-Chuang (assumption of invertibility)

Theorem 12.15 of Nielsen and Chuang's 10th anniversary edition is Nielsen's Theorem (1999). In particular, it says, Theorem 12.15: A bipartite pure state $\mid \psi \rangle$ may be transformed to ...
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### Entangling two non-physically adjacent qubits

Entanglement can be performed just between two ** adjacent qubits** (e.g. 1 and 2) or even non-physically adjacent qubits on the processor architecture can be entangled (e.g. 2 and 6). How entangled ...
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### Can separable, but non-valid "states", be used as a resource to generate entanglement?

Suppose two parties, Alice and Bob, who are separated share the "state" $\sigma_{AB}=|0\rangle\langle1|_A\otimes |0\rangle\langle1|_B$. Of course, this not a valid quantum state as it does ...
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### Matrix representation for biproduct mixed states

Nielsen and Chuang [10e, p. 74] introduce the Kronecker product $A\otimes_K B$ as a matrix representation of the tensor product $A\otimes B$ of the operators $A$ and $B$ (for clarity I use a subscript ...
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### Is there a way to know whether entanglement will happen before doing an operation?

I applied a controlled phase gate (the phase is $\pi/4$) to qubits in the states $|+\rangle$ and $|-\rangle$ and I got interesting states - both qubits have shown phase shift as given below. I came to ...
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### When do qubits get entangled?

I was just curious; when do the qubits get entangled? Do the qubits get entangled right after initialization or do they get entangled when we apply Hadamard Gates to the qubits?
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### Can't understand how $D_{A,B} + D_{A,C} \ge E_{A,B}+E_{A,C}$ is proved used the subadditivity of entropy

I am reading Monogamy properties of quantum and classical correlations. Eq.10 states that $$D_{A,B} + D_{A,C} \ge E_{A,B}+E_{A,C},$$ where $D_{i,j}$ is the quantum discord, and $E_{A,B}$ is the ...
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### Can you construct a quantum circuit where all qubits are initially in a superposition, but there is still entanglement?

The most basic example of entanglement is when we have 2 qubits, where q0 is in the |+> state and connects to q1 (which is in the |0> state) with a cnot gate: The state is entangled, as the ...
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I am reading through some notes and am stuck on a bit of math that shows the max possible coherence. Our wave function is $|\psi\rangle =\frac{|01\rangle+|10\rangle}{2}$ and doing $|\psi\rangle \... 3 votes 2 answers 224 views ### Qualitative meaning of the bond dimension of a matrix product state Consider a matrix product state (MPS) with a bond dimension$D$. What is the physical intuition behind the bond dimension? Is it, in any way, related to the spatial geometry? In this note, it is ... • 1,011 3 votes 1 answer 84 views ### How to check entanglement for multipartite states? While that question is only asking two-qubit, I'm asking with any size qubit in general about how to check if qubit with any size in entangled state? For example is this 3-qubit in entangled state?$\...
I understand the von Neumann entropy of a $2$-composite system is that of the reduced density matrix? What is the von Neumann entropy of an entanglement of a more than $3$ composite system?