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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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How to generate the Bell state $\frac{1}{\sqrt{2}}(|01\rangle+|10\rangle)$ from the state $|00\rangle$ using Qiskit?

I want to generate the Bell state $(|01\rangle+|10\rangle)/\sqrt{2}$ from the state $|00\rangle$ in qiskit, applying the Hadamard gate followed by the $\text{CNOT}$ gate. But it generates $(|11\rangle-...
Xilot Xilot's user avatar
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What operations are allowed in LOCC?

I have a question regarding a wording from an exercise book: “Two states psi and phi of a composite system are said to be 'LOCC equivalent' if each can be converted to the other using only local ...
Alex1111's user avatar
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Why divide $\theta$ by 2 when doing the Bell's Inequality Experiment?

I understood the CHSH game correlations by watching Prof. Vazirani's video. I also understood that the correlation between two measures taken from different basis are related by the cosine of the ...
Gustavo Mirapalheta's user avatar
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1 answer
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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 ...
Dogukan's user avatar
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Measuring one qubit in an entangled pair in another basis?

Qubits are usually measured in the computational basis, but we can change the basis by a unitary $U$ to measure in the basis formed by the columns of $U$. For example, if $| \psi \rangle = | 0 \rangle$...
Andrew Baker's user avatar
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2 answers
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creating a generalised Bell state with gates

The Bell state is $$|\beta(a,b)\rangle = \frac{1}{\sqrt{2}}\sum_{k=0}^{1}(-1)^{ka}|k,k \oplus b\rangle\,.$$ How do I get to a general Bell state given an initial state $|ab\rangle$ here $a,b = 0, 1$? ...
Physkid's user avatar
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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 ...
Physkid's user avatar
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General Bell state expression: What condition for mixture of Bell states to be entangled?

Convention: $|qubit_{A}, qubit_{B}\rangle$ The general Bell state equation: $|\beta(a,b)\rangle = \frac{1}{\sqrt{2}}\sum_{k=0}^{1}(-1)^{ka}|k, k\oplus b\rangle = \frac{1}{\sqrt{2}}[|0,0 \oplus b\...
Physkid's user avatar
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How can I simplify tensor product expressions quickly?

Suppose I have a 2-qubit system in the first Bell state, $\left| \beta_{00} \right>$. I want to make the measurement in the computational/$Z$-basis on the first qubit, say qubit $A$. That means I ...
requiemman's user avatar
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Does Bob know the state of the qubit Alice teleported after the completion of the teleportation protocol?

Notation: $|\text{Alice}_{1\,\,}\text{Alice}_{2\,\,}\text{Bob}_{1}\rangle$ Alice and Bob shared an entangled state, say a Bell state $| \Phi_{+}\rangle = \frac{1}{\sqrt{2}}\bigg[|00\rangle + |11\...
Physkid's user avatar
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Why is a Bell state involved in quantum teleportation?

Notation: $|\text{qubit}_{1}, ..., \text{qubit}_{N}\rangle$. The goal of quantum teleportation is to send quantum information using classical bits. A source transmits a state $|\psi\rangle_{A_{0}} = \...
Physkid's user avatar
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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 ...
Samuel Jaramillo's user avatar
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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 ...
Khilesh Chauhan's user avatar
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3 answers
451 views

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 ...
Stéphane's user avatar
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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 ...
Tawfik's user avatar
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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 ...
Michael.Andy's user avatar
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2 answers
221 views

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 $\rho$. ...
user8183310's user avatar
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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 ...
Lalit Vinde's user avatar
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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\...
Steve J.'s user avatar
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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\...
razor_chk's user avatar
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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 ...
Jammy's user avatar
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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\...
Sutasu's user avatar
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2 answers
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State tomography on a subsystem of the GHZ state

Premise: I am not sure whether I am missing something theoretically. Given a circuit creating a GHZ state over 3 qubits, say q1, q2 and q3. If I do not consider q3 and perform a state tomography over ...
Daniele Cuomo's user avatar
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1 answer
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Transforming an unkown phase into unkown bit values on bell states

Consider the state $|\Psi^\pm\rangle = \frac{1}{\sqrt{2}}(|01\rangle \pm |10\rangle)$. The $|\Psi^\pm\rangle$ state is a bell state up to an unkown phase. I am looking for a sequence of single-qubit ...
Daniele Cuomo's user avatar
7 votes
2 answers
639 views

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{\...
Luca Ion's user avatar
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1 answer
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Transpile cu1 to basis gates

I am trying to transpile cu1 to basis gates. How would a circuit transpiled for cu1 gate end up being in basis states (u3 and cx) ?
Joydeep Bhattacharjee's user avatar
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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 ...
Hans's user avatar
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2 votes
1 answer
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How to generate CNOT-gates via Bell pairs

In this paper from Christophe Piveteau and David Sutter, the authors use Bell pairs to generate CNOT-gates. The procedure is shown in Fig.2 and Fig.3 of the paper. By doing the calculations about that ...
stopper's user avatar
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2 answers
302 views

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?
kludg's user avatar
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141 views

Basis for permutation invariant states

It is known that the maximally entangled qubit states form a basis (the Bell basis). Let $\Phi$ be the canonical maximally entangled state i.e. $$\Phi = \left(\frac{\vert 00\rangle + \vert 11\rangle}{\...
user1936752's user avatar
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How to initialize a state of the form$\frac{1}{\sqrt{2}}(|\texttt{++}\rangle + |\texttt{--}\rangle$) in the circuit model?

I wonder how to initialise a Bell-like state, in the circuit model, where instead of standard $|\Phi^{\texttt{+}}\rangle$, the entanglement is in the x-basis. Hence a state $\frac{1}{\sqrt{2}}(|\...
Daniele Cuomo's user avatar
3 votes
2 answers
273 views

Is a "Bell measurement" equivalent to a projective measurement in a different basis?

Let \begin{align} H = \frac{1}{\sqrt{2}}\begin{bmatrix} 1 & 1 \\ 1 & -1\end{bmatrix}\in M_2(\mathbb C), \quad \mathrm{CNOT} = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 &...
QuantumHumanLearner's user avatar
2 votes
0 answers
267 views

Measurement Base of Fusion Gate

I am reading this article on "Fusion-based quantum computation" and they claim there about Fusion Gate type-2 that it collapses the state to 2 types of eigenstates, and returns 2 results - $...
Ron Cohen's user avatar
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5 votes
3 answers
480 views

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:...
Adam Warlock's user avatar
4 votes
1 answer
397 views

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 ...
cbakos's user avatar
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1 answer
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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 ...
Arthur Shawcross's user avatar
2 votes
1 answer
145 views

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 ...
Anna Naden's user avatar
1 vote
1 answer
156 views

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 ...
Anna Naden's user avatar
10 votes
2 answers
309 views

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 ...
user97154's user avatar
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2 votes
1 answer
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Decompose bell measurement gate into combination of controlled-not gates and one-qubit gates

OPENQASM2.0 has only one two-qubit gate: controlled not. For a teleportation experiment, I need to perform a measurement in the Bell basis. That is, I need a two-qubit gate with matrix representation $...
Anna Naden's user avatar
3 votes
1 answer
236 views

How to create a Bell state with asymmetric amplitudes using single-qubit and CNOT gates?

Is there a systematic way - in terms of a quantum circuit with single qubit and CNOT gates - to create a bell state with asymmetric amplitudes, e.g., $$ \alpha |00\rangle + \beta|11\rangle $$ where $\...
NaturalLog's user avatar
3 votes
1 answer
154 views

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 ...
Kittu A's user avatar
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1 answer
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Are mixtures of pairs of Bell states perfectly distinguishable by local operations?

Consider the four Bell states $$ |\psi^{00}\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle), \hspace{2mm} |\psi^{01}\rangle = \frac{1}{\sqrt{2}}(|00\rangle - |11\rangle),\hspace{2mm} |\psi^{10}\...
user16106's user avatar
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2 answers
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Why are Bell states the maximally entangled ones?

I just want to know why actually Bell states are examples of maximally entangled states and significance of that "maximal" term. Is there anything for proving that?
user avatar
5 votes
3 answers
224 views

Intuition for why $\frac{|00\rangle+|11\rangle}{\sqrt{2}}$ can be written as $\frac{|++\rangle+|--\rangle}{\sqrt{2}}$

In analyzing measurement of $\frac{|00\rangle+|11\rangle}{\sqrt{2}}$ in the local $|+\rangle$, $|−\rangle$ basis, through algebra manipulation, the initial state is first written as $\frac{|++\rangle+|...
Claire's user avatar
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1 answer
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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^+ \...
M. Al Jumaily's user avatar
2 votes
2 answers
625 views

What happens to the Bell state qubits after the Quantum Teleportation?

I'm reading on the Quantum Teleportation and I couldn't find anywhere what happens to the bell state qubits after the Quantum Teleportation.
Malik Naik's user avatar
1 vote
1 answer
157 views

How to do error correction after encoded Bell measurement?

Need some help with the concepts of encoded/logical bell measurement. Please visualize the picture in your mind. Suppose I have a node with 7+7 qubits side by side, left 7 is $|0_{L}\rangle$ and right ...
Pritam Sinha's user avatar
1 vote
0 answers
176 views

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 ...
morpheus's user avatar
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1 answer
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Does a basis of maximally entangled states exist for two-qubit or two-qutrit system so that the density matrices of the basis states don't commute?

I want to find a basis of maximally entangled states $|\Psi_i\rangle$, for $\mathcal{H}^{2} \otimes \mathcal{H}^{2}$ and, $\mathcal{H}^{3} \otimes \mathcal{H}^{3}$ such that the density matrices of ...
junfan02's user avatar
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