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.
26
questions
2
votes
1answer
33 views
Two qubit state + Depolarizing channel = Bell diagonal state?
In multiple sources, e.g. RGK, KGR, it is stated (without proof) that if you take any two qubit state and send it through a depolarizing channel, the resulting state would be a Bell-diagonal state. ...
0
votes
1answer
69 views
What are the possible results of measuring $X$ and $Z$ on the state $|01\rangle+|10\rangle$?
When calculating the probability of getting +1 on X-basis on the first qubit of Bell's state $|01\rangle+|10\rangle$, the result is 1/2 with the state after measurement |++⟩ while the probability of ...
3
votes
2answers
43 views
Can the following Bell states have probability amplitudes other than 1/2 and still be entangled?
From my understanding, a qubit is entangled when the state of one qubit depends on the other, and vice versa. Can the following bell states have probability amplitudes other than 1/2 and still be ...
4
votes
3answers
58 views
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 ...
2
votes
2answers
53 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 ...
1
vote
1answer
39 views
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 ...
3
votes
1answer
56 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 ...
4
votes
1answer
149 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\...
2
votes
2answers
94 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 ...
2
votes
3answers
209 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 ...
1
vote
0answers
87 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\...
2
votes
1answer
65 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 ...
0
votes
1answer
43 views
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 ...
1
vote
0answers
44 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> +...
3
votes
2answers
159 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 ...
0
votes
0answers
40 views
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 ...
3
votes
3answers
229 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
$$| \psi \rangle = \sum_i \lambda_i | i_A \rangle | ...
1
vote
1answer
155 views
Is back in time (classical) information transfer possible (based on delayed choice entanglement swapping)?
Delayed choice entanglement swapping.
Two pairs of entangled photons are produced, and one photon from each pair is sent to a party called Victor. Of the two remaining photons, one photon is sent to ...
2
votes
2answers
147 views
What is the property of any entangled pair of qubits?
We know that any of the Bell states has the special property that the second qubit will be found in a state which is predictable based on measuring one of the qubits. But assuming any other pair of ...
4
votes
1answer
132 views
Problem with quantum tomography on two qubits
With reference to question on how to do quantum tomography on two qubits, I would like to ask you for help again. I tried to do the tomography on state
\begin{equation}\psi=\frac{1}{2}\begin{pmatrix}...
2
votes
1answer
337 views
Transforming the first Bell state into the other Bell states
As I understand it, you can transform the different Bell states into one another by applying various gates. Wikipedia has the Bell states written out as follows:
And says that you can generate bell ...
-1
votes
1answer
49 views
Find the Bell States of A and B in the following scenario
Let A has quantum memories $M_1$ and $M_2$ and B has quantum memories $M_3$ and $M_4$ capable of holding one qubit.
2 Bell states are shared among A & B in the following way:
First Bell state $|...
1
vote
0answers
44 views
Determining the quantum secret
I earlier posted I question Representing a Bell measurement on non adjacent qubits for which I got an excellent answer. Now I want to build upon that and do further analysis which is where I am stuck. ...
1
vote
1answer
72 views
Representing a Bell measurement on non adjacent qubits
I have a state
$${|\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\...
2
votes
1answer
97 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 = \...
2
votes
2answers
66 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 +...
