Questions tagged [bell-basis]

For questions related to Bell basis - i.e. converting a state to the Bell basis, working with such states and measuring in the basis.

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Bell state preparation

I was watching some lectures on qubits. They were talking about how to generate a Bell state. They described it as follows: Prepare state 00: $$\left |0 \right> \otimes \left |0 \right>$$ Apply ...
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50 views

How does Bell measurement work in the teleportation?

I'm a complete beginner and one of the first things I was taught was the teleportation protocol. In the protocol, the party sending its state (which we call say $|\phi\rangle$) makes a Bell ...
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What is the representative matrix for a measurement in the Bell-state basis?

I have a few questions about measurement in Bell-state basis. In particular, if $Z = \begin{bmatrix} 1 & 0\\ 0 & -1 \end{bmatrix}$ is for a measurement on the computational basis, then what ...
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53 views

Problem about entanglement swapping

I have been learning about the concept of entanglement swapping and found an equation mentioned in the textbook, Mathematics Of Quantum Computing: An Introduction written by Wolfgang Scherer. At ...
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1answer
98 views

How to apply the Schmidt Decomposition to a Bell state?

I am trying to understand the Schmidt Decomposition, currently in my QC class. We had a tutorial where we were told if $|\psi\rangle$ is a pure state of a composite system A then there exists $|i_A\...
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83 views

What happens when you send a Bell state through depolarizing channel?

For noise parameter $Q$ and a density matrix $\rho$, we know that the depolarization channel $\mathcal{E}$ would act like: $$ \mathcal{E}(\rho) = (1 - Q)\rho +Q\frac{I}{2}, $$ where $I$ is the ...
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3answers
180 views

What does the minus sign in the four bell states represent?

I am in grade 11, so answers as simple as possible. I understand that in quantum teleportation, the bell measurement must be made on the teleportee and the sender, and I understand that yields one of ...
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59 views

Creating Bell States with CNOT conditioned to the control qubit being set to zero

I was using qiskit to generate all of the Bell States. I created the following circuits for each state: $|\Phi^+\rangle :$ $|\Phi^-\rangle :$ $|\Psi^+\rangle :$ $|\Psi^-\rangle :$ The $|\Psi^\pm\...
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1answer
56 views

Fidelity With Bell State Calculation

Let's say I have the following state: $$ |\psi\rangle = \sqrt{\frac{2}{3}} |0000\rangle_{a_1b_1a_2b_2} + \sqrt{\frac{1}{6}} \big( |0011\rangle_{a_1b_1a_2b_2} + |1100\rangle_{a_1b_1a_2b_2} \big). $$ I ...
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1answer
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Creating Bell states (a question from tutorial) [closed]

I was going through a Quantum Computation lecture series on YouTube given by Umesh Vazirani. There in Lecture 6.3 he talks about creating a Bell state using a Hadamard and CNOT gate. He seems to be ...
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38 views

Constructing and Measuring in an Arbitrary 3-qubit basis

As part of a Quantum Theory project I have "constructed" an arbitrary 3-qubit basis: $\left|B_0\right> =\left|000\right>$ $\left|B_1\right> = \frac{1}{\sqrt{2}}\cos(x)(\left|100\right> +...
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116 views

How to measure in the bell basis?

The question is quite straightforward, I have some two qubit state and I want to measure it in the Bell basis. This question answers me partly, but I still have some doubts because, I thought that ...
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Do Bell state measurements satisfy the completeness condition from the no-signalling theorem?

Do Bell state measurements satisfy the completeness condition from the no-signalling theorem? In a quantum experiment involving unitary evolution and projective measurements,  do Bell state ...
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3answers
196 views

No Schmidt decomposition for tripartite states

Exercise 2.77 in Nielsen and Chuang asks to show by example that there exist tripartite states $| \psi \rangle_{ABC} $ which cannot be written as $$| \psi \rangle = \sum_i \lambda_i | i_A \rangle | ...
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146 views

Is back in time (classical) information transfer possible (based on delayed choice entanglement swapping)?

Delayed choice entanglement swapping. Two pairs of entangled photons are produced, and one photon from each pair is sent to a party called Victor. Of the two remaining photons, one photon is sent to ...
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2answers
131 views

What is the property of any entangled pair of qubits?

We know that any of the Bell states has the special property that the second qubit will be found in a state which is predictable based on measuring one of the qubits. But assuming any other pair of ...
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1answer
116 views

Problem with quantum tomography on two qubits

With reference to question on how to do quantum tomography on two qubits, I would like to ask you for help again. I tried to do the tomography on state \begin{equation}\psi=\frac{1}{2}\begin{pmatrix}...
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1answer
283 views

Transforming the first Bell state into the other Bell states

As I understand it, you can transform the different Bell states into one another by applying various gates. Wikipedia has the Bell states written out as follows: And says that you can generate bell ...
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1answer
49 views

Find the Bell States of A and B in the following scenario

Let A has quantum memories $M_1$ and $M_2$ and B has quantum memories $M_3$ and $M_4$ capable of holding one qubit. 2 Bell states are shared among A & B in the following way: First Bell state $|...
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Determining the quantum secret

I earlier posted I question Representing a Bell measurement on non adjacent qubits for which I got an excellent answer. Now I want to build upon that and do further analysis which is where I am stuck. ...
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1answer
68 views

Representing a Bell measurement on non adjacent qubits

I have a state $${|\psi\rangle} = s {\Bigl(|1\rangle_1|1\rangle_2-|0\rangle_1|0\rangle_2\Bigr)}\otimes{\Bigl(|0\rangle_3|1\rangle_4-|1\rangle_3|0\rangle_4\Bigr)}\otimes{\Bigl(|0\rangle_5|1\rangle_6-|1\...
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1answer
85 views

If Alice and Bob share a Bell state, can Alice send her individual qubit to a third party?

Suppose Alice wants to send Bob information. Each of them has been sent each of the qubits of the Bell state in advance. Suppose Alice has the first qubit and Bob has the second. $|\Phi^+\rangle = \...
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62 views

Projecting $\lvert ++ \rangle$ on Bell Basis

I understand that, projecting $\lvert 00\rangle$ on the Bell states would produce $\lvert\Phi^+\rangle$. Because, $$ CNOT(H\lvert0\rangle \otimes \lvert0\rangle) = \frac{1}{\sqrt{2}}(\lvert00\rangle +...