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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Understanding the Hadamard gate and what is meant by qubits [duplicate]

I'm trying to understand the Qiskit documentation in order to see if there are differences in notation from my quantum mechanics lecture notes. The Hadamard Gate transforms $ |0 \rangle$ into $|+ \...
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Quantum entanglement as topological entanglement

According with Aravind: the Hopf link, L2a1, corresponds to the Bell state $\frac{1}{\sqrt 2}\big (|00\rangle+|11\rangle\big )$, the Borromean link (L6a4) can be considered as GHZ state $\frac{1}{\...
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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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1 answer
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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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Proof that Bell state can be transformed into any 2-qubit state $\vert\psi\rangle$ under LU

In the Dür, 2000 paper, he gave a statement that (...) Any state $\vert\psi\rangle$ can be obtained from Bell State with certainty From his paper too, it's known that we can transform $\vert\psi\...
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Does any quantum channel satisfy ${\rm Tr}(\mathcal E^\dagger \mathcal E) \in[0, d^2]$?

I am reading the paper "Direct Fidelity Estimation from Few Pauli Measurements". According to the paper, the entanglement fidelity between the a unitary channel $\mathcal U$ and a quantum ...
2 votes
1 answer
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Prove that there are infinitely many entanglement classes under LU

Dur, 2000 states that (...)But even in the simplest systems, $|\psi\rangle$ and $|\phi\rangle$ are typically not related by LU, and continuous parameters are needed to label all equivalence classes. ...
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Is LOCC equivalence the same as LU equivalence?

I'm currently learning on LOCC transformations. In the Dur, 2000 paper, there is a statement that (...) two pure states $|\psi\rangle$ and $|\phi\rangle$ can be obtained with certainty from each ...
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2 answers
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Why only one of the qubits is rotated in the CHSH circuit?

When reading various tutorials on how to calculate CHSH, there is only a single qubit which is rotated inside of the quantum circuit, it is also only ever rotated around a single axis. I would like to ...
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Is it necessary to apply CNOT for the sole purpose of "establishing a correlation" between two qubits

Disclaimer: I recently started learning quantum information. I've been exploring creating the $|\Phi^+\rangle = \frac{1}{\sqrt{2}} (|00\rangle + |11\rangle)$ Bell state (starting with the state $|00\...
3 votes
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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 ...
3 votes
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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 ...
2 votes
1 answer
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How are two-qubit states like $|00\rangle+|01\rangle+|10\rangle-|11\rangle$ related to entanglement?

I've been going through different rotations of two-qubit states and noticed the states $$ |00\rangle+|01\rangle+|10\rangle-|11\rangle\\ |00\rangle+|01\rangle-|10\rangle+|11\rangle\\ |00\rangle-|01\...
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Circuit construction for Destructive Swap and DIP test from the VQSD paper

The paper VQSD The Destructive Swap Test computes Tr(στ ). The Diagonalized Inner Product (DIP) Test computes Tr(Z(σ)Z(τ )) via a depth-one circuit. Can you demonstrate how this work?
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Entanglement purification implementation with Qiskit

I'm quite new to qiskit, does anyone have any idea how to use the reset mechanism in qiskit to perform EPP? As in the protocol one EPR pair needs to be measured and the results are checked to accept/...
1 vote
1 answer
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Why $|0\rangle \langle 0|=\frac {1}{n} \sum_{j=1}^{n}|0_j\rangle \langle 0_j|\bigotimes \mathbb {I}_{\overline j}$ in VQLS

I am having some trouble to derive equation In paper Variational Quantum Linear Solver $|0\rangle \langle 0|=\frac {1}{n} \sum_{j=1}^{n}|0_j\rangle \langle 0_j|\bigotimes \mathbb {I}_{\overline j}$ $|...
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Why uncomputing removes entanglement in general?

I met a subroutine to change the phase for a subset of basis vectors, and I can't understand why uncomputing in this case removes the entanglement. I want to generalize it a little. Specifically, I ...
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Entanglement of the $i$-th qubit with the $j$-th qubit for this specific quantum circuit

Suppose that I have a Quantum Circuit with $N$ qubits initialized to $|0\rangle$. The Quantum circuit is described by the followin Figure: The angles of the rotations $R_y$ are random. At which point ...
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How to implement this circuit either using Jupiter notbook or qiskit

I am new to quantum-computaions and learning qiskit. I am trying to construct a two qubits circuit that performs a bell measurement using $\{|\beta_{01}\rangle \langle \beta_{01}| \} $ projectors. ...
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3 answers
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Realizing a swap gate using a commutator sequence and an auxiliary qudit

Say I have two qudits $1$ and $2$, each of which has Hilbert space of dimension $m$. Is it possible to introduce an auxiliary qudit $a$ (of any dimension $d_a\in \mathbb{Z}_{\geq 2}$) and find quantum ...
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Who first introduced the mathematical definition of entanglement?

I know the definition of entangled state and separable state from Wikipedia, but I can't find the references that brought up the mathematical description of the entangled state and separable state. Is ...
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What are the outcome probability in entanglement distillation?

In the paper "C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher. Concentrating partial entanglement by local operations. Physical Review A, 53:2046–2052, 1996, quant-ph/9511030" ...
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2 answers
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Why does entanglement of 3 qubits break this?

Another user asked about the Ekert Quantum Key Distribution protocol: Alice and Bob each randomly choose one of three bases separated by $120^{\circ} $ in which to measure, and then later compare the ...
2 votes
1 answer
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The Ekert Protocol (E91) for Quantum Key Distribution

My question is specifically from the book Quantum Computing for Everyone by Chris Bernhardt. In the last section (The Ekert Protocol for Quantum Key Distribution) from Chapter 5 (Bell's Inequality). I ...
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What is the cost of measurement?

I am exploring a quantum algorithm to solve a partial derivative equation with time derivative. It performs the same entangling unitary to advance the solution by one time step. Is it more efficient ...
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6 votes
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How does quantum teleportation work with mixed shared states?

I am given the scenario that instead of the two parties (A & B) sharing the bell state $|\phi_+\rangle$ they share the mixture $\rho_\lambda = \lambda|\phi_+\rangle\langle\phi_+|+(1-\lambda)\frac{\...
3 votes
1 answer
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types of states that can be created with a given number of entangling gates

I want to know if it is possible to say something in general about the "richness" or "complexity" of quantum states that can be created using a given number of entangling 2-qubit ...
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2 votes
1 answer
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How to factorize a multi-qubit quantum state?

Let's say I have an arbitrary n-qubit quantum state $|\psi\rangle$. Is there a simple way to compute the states of individual qubits (or sets of qubits if they are entangled) that compose $|\psi\...
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1 vote
1 answer
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How can I conceptualize virtual indices used in the time evolving block decimation (TEBD) algorithm?

I am trying to work with the Heisenberg $XX$ model which the Hamiltonien is given by $\hat{H} = -J \sum_i \left(\hat{X}_i\hat{X}_{i+1} + \hat{Y}_i\hat{Y}_{i+1}\right), \quad J > 0.$ Using $s^+ = |{...
1 vote
1 answer
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How is phase kickback possible if qubits are unentangled?

If I have two independent (unentangled) qubits, let's say one in state |1> and the other one in some superposition state with equal amplitudes and arbitrary phases. If I measure the qubit that is ...
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1 vote
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Would QKD break down if you have the receiver box of Bob?

I want to understand QKD better and know about entangled photons. In this clip, they explain QKD: https://www.youtube.com/watch?v=cWpqlgF7uEA They explain that the ...
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2 answers
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How to create superposition of all bitstrings with exactly two ones on 4 qubits?

On a quantum circuit, how would I create an equal superposition of the states: $$|\psi\rangle=|0011\rangle + |0101\rangle + |0110\rangle + |1001\rangle + |1010\rangle + |1100\rangle.$$
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How to "separate" a separable density matrix?

If I have a bipartite system of two qubits $A$ and $B$, and the density matrix $\rho$ is separable, how do I decompose it into its separable parts? That is, give $\rho$, expand it as follows: $$\rho = ...
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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 ...
1 vote
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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 ...
2 votes
1 answer
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How to compute the maximum possible coherence of a two-particle Bell state?

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 ...
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1 answer
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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? $\...
2 votes
1 answer
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Does entanglement only exist between pairs of qubits?

I have read a bit in qiskit course so far. Why entanglement state always represent with 2-qubit? Why not 3-qubit or 1-qubit only? I do know that entanglement state happened when it can't represent ...
1 vote
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von Neumann entropy of an arbitrary composition system

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?
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