# 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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### CNOT and quantum entanglement

I have the following problem: "Consider two parties: Alice in possession of the one-qubit state |ψ⟩ = α|0⟩ + β|1⟩, and Bob who starts with a qubit in the state |0⟩ Show that Alice can teleport ...
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### Plotting the Bell state on a Bloch sphere

How can you plot the bell state on a Bloch sphere? bell = QuantumCircuit(2) bell.h(0) bell.x(1) bell.cx(0,1) Is there any good reference for understanding how ...
1 vote
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### Why does my quantum circuit run so slow on a real IBM quantum hardware?

I have created a very simple circuit on qiskit to produce a Bell state: bell = QuantumCircuit(2) bell.h(0) bell.cx(0, 1) bell.measure_all() And I then run it on a ...
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### How are the Bell states entangled

I've been trying to follow Qiskit Global Summer School 2020 and understood that if a pure state $S$ on systems $A$ and $B$ cannot be written as a tensor product of some state from $A$ and some state ...
1 vote
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### Recover the noisy POVMs of Bell basis measurement

Considering Bell basis measurement, we have that the ideal POVMs are four Bell states, which can be obtained by reversing the following quantum circuits. Now, we add depolarizing errors to CX gate and ...
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### Simultaneous measurements and Bell basis measurements to estimate $\lvert\text{Tr}(\sigma \rho)\rvert^2$ in Huang et al. paper

Theorem 2 of this paper says if one is able to prepare $\rho^{\otimes k}$ then it is possible to predict expectation values of all $n$-qubit Pauli observables using $O(n)$ number of copies of $\rho$. ...
1 vote
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### Why we called a measurement as a Bell measurement?

So I am new to quantum computing, just come along the topic of Bell's measurement, until now we understood that we apply the Bell inverse (transpose conjugate) before taking measurement, so Bell's ...
1 vote
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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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### General representation for GHZ states in any orthonormal basis

We know that if we consider a Bell state for example $$|\Phi^+\rangle = \frac{|00\rangle + |11\rangle}{\sqrt{2}}$$ Then we can write this state in some other orthonormal basis in the same form. Like:...
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### How can the transformation between entangled states like two Bell states be derived?

As it is stated in this post: Transforming the first Bell state into the other Bell states, one can transform the $|\phi^{+}\rangle$ state to the $|\psi ^{-}\rangle$ by applying the tensor product of ...
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### Density matrix after measuring Bell state in CHSH game

In these notes, the author says the following about the CHSH game Does Alice and Bob’s ability to succeed more than 75% of the time mean that they are communicating? Well, we know it’s not possible ...
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### How to simulate the state of a system after partial measurement?

Based on the answers at here and here, I have a quantum simulator which implements the operations described in the classic Teleporting an Unknown Quantum State. Careful comparison of circuits with the ...
1 vote
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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 ...
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### What quantum gates admit a basis-independent interpretation of their action?

The SWAP gate swaps the state of the two qubits so that in the computational basis $|01\rangle \rightarrow |10 \rangle$ with a matrix representation given by: \begin{bmatrix} 1 & 0 & 0 & 0 ...
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### Are $(|00\rangle-|11\rangle)/\sqrt2$ and $(|11\rangle-|00\rangle)/\sqrt2$ the same quantum state?

The state $(|00\rangle-|11\rangle)/\sqrt2$ is an entangled state. If we think about the state $(|11\rangle-|00\rangle)/\sqrt2$, is this also entangled, but with maybe a phase change? The above two can ...