# 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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### 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?
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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 ...
1 vote
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### Calculating probability that two entangled qubits are the same when measured in different bases

Given the entangled state $$|\Phi^+\rangle = \frac{1}{\sqrt 2} |00\rangle + \frac{1}{\sqrt 2} |11\rangle$$ I am trying to calculate the probability that the two qubits end ...
• 349
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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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1 vote
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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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1 vote
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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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1 vote
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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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1 vote
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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 ...
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### Show that Quantum Fourier Transform maps Bell states to Bell states

Given Bell states $\mathcal{B} = \{\left\vert \phi^{\pm} \right\rangle, \left\vert \psi^{\pm} \right\rangle\}$, show that Quantum Fourier Transform(QFT) maps $\mathcal{B}\rightarrow \mathcal{B}$ by ...
• 133
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### Trouble understanding the EPR Experiment

I fail to understand the EPR experiment. From Wikipedia: Alice now measures the spin along the z-axis. She can obtain one of two possible outcomes: +z or −z. Suppose she gets +z. Informally speaking, ...
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### Output of Bell State Measurement

I was trying to see the output of Bell State Measurement in IBM Quantum Experience but in the simulation down the circuit in the histogram, it showed me that the possible qubit will be $|00\rangle$ ...
1 vote
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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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### 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. ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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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 ...
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