All Questions
Tagged with textbook-and-exercises bell-basis
22
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Hong Ou Mandel interference and bell basis measurment
It is well known that using Hong Ou Mandel interference in polarization one can only detect 2 out of the 4 bell states($|\psi^+\rangle$ and $|\psi^-\rangle$ can be detected but $|\phi^+\rangle$ and $|\...
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Quantum teleportation of unknown qubit when the entangled state is not a Bell state
Assume Bob and Alice have two particles with a prior entanglement: $A$ and $B$. The entangled state $|Ψ⟩$ is maximally entangled, and $$|Ψ⟩ = \frac{1}{\sqrt{2}}(|00⟩ + j|11⟩)\,,$$ where $j$ is 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 ...
- 518
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1
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How does a "measurement of $\vec v\cdot\vec \sigma$" on two-qubit states work?
Michael A. Nielsen & Isaac L. Chuang, Quantum Computation and Quantum Information, 10th Anniversary Edition p.113, Box 2.7 states that "if a measurement of $\vec v\cdot\vec\sigma$ is ...
- 217
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2
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How to determine with local measurements which Bell state we have?
We have 2-qubit state which we know is 1 of 4 Bell states. Can we determine, using unitary transformations and single-qubit measurements, which Bell state do we have, and if we can, how?
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Two-qubit Bell measurement matrix where the two qubits are not contiguouis
In the answer here, it is explained that where the measurement operates on only a subset of the qubits of the system (for example qubits 2 and 3 out of five), the matrix can be constructed using the ...
- 701
2
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1
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398
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What happens if a Pauli $X$ gate is applied to part of a Bell state?
I have started to learn about the mathematics behind ebits and I have a question. Assume $\color{red}{\text{Alice}}$ and $\color{blue}{\text{Bob}}$ share the following ebit:
$\begin{align}\vert\Phi^+ \...
- 822
1
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0
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Calculating probability that two entangled qubits are the same when measured in different bases
Given the entangled state
\begin{equation}
|\Phi^+\rangle = \frac{1}{\sqrt 2} |00\rangle + \frac{1}{\sqrt 2} |11\rangle
\end{equation}
I am trying to calculate the probability that the two qubits end ...
- 359
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votes
2
answers
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Show that the Bell states form a basis
I can't seem to understand how to show that the Bell states for a basis. Should I explain that through the circuit and what gates are used or by the basic proof behind proving a set as a basis?
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1
answer
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Bell's experiment: checking the probabilities
I have some doubts on the calculations behind Bell's experiment, which goes as follows: a pair of entangled photons is shared between two scientists, Alice and Bob, who possess a bunch of polarizers ...
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2
votes
1
answer
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Show algebraically that $U|0\rangle\otimes |0\rangle+U|1\rangle\otimes|1\rangle=|0\rangle\otimes U^T|0\rangle+|1\rangle\otimes U^T|1\rangle$
Suppose that Alice applies a unitary operator $U$ with real entries to her qubit in an EPR pair $|\beta\rangle=\frac{1}{\sqrt 2}(|00\rangle+|11\rangle)$. Is this the same as having Bob apply $U^T$ to ...
- 133
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1
answer
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Probability on measuring bell state in x-basis with pauli operator sigma x [duplicate]
I am confused about how to calculate the probabilities of getting a certain result when measuring a Pauli observable on a Bell state. When you measure an observable the state is projected onto an ...
4
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3
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How to show that Bell states are orthonormal
I was reading some material on QC online and I found some material that explains how to show that Bell states are orthonormal but without details.
I understand that we need to check $\langle state1|...
- 309
2
votes
1
answer
166
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EPR Experiment: What does it mean for Alice to measure $\vec{v} \cdot \vec{\sigma}$ on her qubit?
I am trying to understand Box 2.7 on page 113 of Quantum Computation and Quantum Information book by Nielsen and Chuang. They start out with following wave function:
\begin{equation}
\psi = \frac{|01\...
- 359
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1
answer
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How do get from $|0\rangle=\alpha|a\rangle+\beta|b\rangle$, $|1\rangle=\gamma|a\rangle+\delta|b\rangle$ to an expression for $|01\rangle-|10\rangle$?
My question is linked to the Nielsen Chuang book. Particularly equation 2.216 on basis change from $|0\rangle$, $|1\rangle$ to orthonormal $|a\rangle$ and $|b\rangle$. How do we get the equation from ...
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