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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1
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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 ...
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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 ...
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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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2
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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 $\rho$. ...
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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 ...
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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\...
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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\...
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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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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\...
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2
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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 ...
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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 ...
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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{\...
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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) ?
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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 ...
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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 ...
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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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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}{\...
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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}}(|\...
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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 &...
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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 - $...
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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 ...
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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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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
$...
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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 $\...
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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 ...
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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}\...
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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?
user18115
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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+|...
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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^+ \...
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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.
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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 ...
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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 ...
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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 ...
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Inconsistent result trying to simulate measurement of a 2 qubit system
Consider a 2 qubit system in the initial state:
$$
\begin{pmatrix}
0 \\ \frac{\sqrt{2}}{2} \\ -\frac{\sqrt{2}}{2} \\ 0
\end{pmatrix}
$$
the so-called Bell-pair. Now let's measure the spin of the first ...
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Why does $(XZ\otimes I)|\Phi^+\rangle$ equal the Bell state $|\Psi^-\rangle$?
I'm slightly confused by the solution provided below by a suggested solution online to convert |$\phi^+$⟩ to |$\psi^-$⟩.
I tried doing the operation XZ but I got $\frac{1}{\sqrt2}$(|10⟩-|01⟩) instead ...
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Measure a state in Hadamard basis [closed]
I can't understand how a state measure on the Hadmard basis collapses to $$ |+\rangle =\dfrac{|0\rangle+|1\rangle}{\sqrt{2}} $$ or $$ |-\rangle =\dfrac{|0\rangle-|1\rangle}{\sqrt{2}} $$
as they dont ...
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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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Are entangled and Bell states the same thing?
I am a little confused whether the entangled state and Bell state are the same thing? If they have a bit of contrast, what is the difference between them?
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What gate combinations create entangled two-qubit states?
I know that in order to make a two quit entangled state, this quantum circuit is used:
But I was wondering if there are any other gate combinations which also create entangled two quit states.
If ...
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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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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 ...
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EPR pair and individual operations [closed]
I have created an EPR pair. Let's suppose it's $(|00\rangle + |11\rangle)/\sqrt{2}$. We both of our halves and then we move into our places.
If I ask you how does your half look like (mathematical ...
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Q-Sphere representation of Bell States
I'm currently going through Lab1 of the Qiskit Quantum Computing Course, where one task is to create the Bell State
$$\frac{1}{\sqrt{2}}\left(\vert01\rangle + \vert10\rangle\right)$$
Technically it ...
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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 ...
