# Questions tagged [quantum-state]

Questions about or related to quantum states. Consider using the density-matrix tag when relevant.

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### Qiskit, Statevector.from_label

I apply Grover's on an eigh qubits circuit I just want to amplify the states whose qubits 6 and 7 are |1> The following test works (the state 11011001 is correctly amplified) ...
5 votes
2 answers
306 views

### What is the expectation value of $|\langle \psi|U|\psi \rangle|$ over Haar random states $|\psi\rangle$?

We know the average unitary fidelity, $\int |\langle \psi|U|\psi \rangle|^2 d\psi$, has a nice closed-form solution: $\frac{1+\frac{1}{d}|Tr (U)|^2}{1+d}$, thanks to Horodecki and Nielsen. However, I ...
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2 votes
1 answer
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### Global vs local: global density matrix and all the reduced density matrix

I prepare a $n$-qubit quantum state $\sigma$ whose ideal state is $\rho$, then perform state tomography on all the $m$- qubit reduced states. Ideally, I find that all the $m$- qubit reduced states are ...
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2 votes
1 answer
48 views

### Change of basis on a per vector component level

Suppose we have an $n$-qubit quantum state in the computational basis encoded in a classical blackbox function $f(x)$. That is, with $x \in \{0,1\}^n$ we can query $f$ and get the respective ...
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1 vote
1 answer
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### Can we use purity for separable states?

Purity is a measure of how much a state is pure. Suppose $\rho$ is a density matrix. Then purity $p$ is defined as $$p = \mathrm{tr}(\rho^2).$$ I wonder if we can use purity for separable states? Or ...
• 469
2 votes
2 answers
89 views

### Does the inequality $\mathrm{tr}(L^\dagger L \rho^2)-\mathrm{tr}(L^\dagger \rho L\rho )\geq 0$ hold generally?

Does the inequality $$\mathrm{tr}(L^\dagger L \rho^2)-\mathrm{tr}(L^\dagger \rho L\rho )\geq 0$$ hold for any density matrix $\rho$ and any non-Hermitian Lindblad operator $L$?
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9 votes
2 answers
360 views

### Does post selection of a qubit introduce non-linearity?

Problem I have a multi-qubit state $\lvert \psi \rangle$ and an ancilla qubit $\lvert 0 \rangle$ that I use to extend my state, getting the new state $\lvert 0\rangle \otimes \lvert \psi \rangle$. ...
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2 votes
1 answer
72 views

### Is the global phase of qubits important if qubits interact with each other?

I know that if we have two qubits in states differing by a global phase it does not matter that they are in the same state. But if we have a qubit in state_1 and another in state_2 does the global ...
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1 vote
1 answer
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### SX operator and superposition

I am running some tests using the probabilities we get from statevector to assert values in qiskit. For instance, with two qubits and a hadamard gate on the first one we have: ...
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1 vote
2 answers
112 views

### How to get a state vector from bloch sphere coordinates for 1 qubit?

I need to get a state vector for one qubit from bloch coordinates no matter if there could be many states that describes the same bloch coordinates, and it does not have to be normalized, because the ...
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2 votes
1 answer
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### Rotation of qubit - Pauli Gates XYZ

I don't understand how to apply a Pauli Gate on a qubit. Lets say 8 got a qubit with in state: $$|\psi\rangle = 0.891 |0\rangle+ 0.454i |1\rangle$$ How would I compute e.g. rotating it 90 degrees ...
1 vote
1 answer
38 views

### What is the Eigen Value corresponding to a Coin Toss when we make a measurement?

I am asking this question to all the Quantum Computing or Quantum Mechanics practitioners. I have studied that when you measure a state, then you will get an eigenvalue for sure corresponding to ...
2 votes
1 answer
72 views

### Upper bounding the trace distance between a noisy and noiseless quantum state

Consider a quantum state $$\rho = \begin{pmatrix} \rho_{00} & \rho_{01} \\ \rho_{10} & \rho_{11} \\ \end{pmatrix}.$$ Now, consider the effect of the amplitude damping noise $\mathcal{N}$ of ...
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4 votes
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### Holevo bound and indistinguishability of non-orthogonal quantum states

I was trying to understand the fact that non-orthogonal quantum states cannot be reliably distinguished and I came across this link. The explanation finishes with the result that the probability of ...
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0 votes
2 answers
112 views

### circuit for quantum simulation?

What would be the circuit for operation exp(iθZ⊗Z⊗Z⊗X) by only using CNOTs and single-qubit gates. And How we can improve the circuit to implement the operation exp(iφZ⊗Z⊗X⊗Z ).exp(iθZ⊗Z⊗Z⊗X).Are ...
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3 votes
3 answers
491 views

### When does CNOT entangle?

Let $|\psi_1\rangle$ and $|\psi_2\rangle$ be qubit states such that $\text{CNOT}|\psi_1\rangle \otimes |\psi_2\rangle$ is entangled. I'm interested in if there is a simple condition that this imposes ...
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1 vote
1 answer
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### Expressibility and Entanglement Capability of the Parameterized Quantum Circuits

I am trying to calculate the expressibility and entangling capability of a quantum state resulting from a circuit as defined in reference I. One of my attempts was to follow reference II which gives ...
4 votes
0 answers
52 views

### Is circuit cutting equivalent in anyway to quantum teleportation?

I've been introduced recently to circuit cutting, and after seeing the 4 orthogonal measurements with their 8 corresponding initializations but no initial transfer of classical info, the first thing ...
0 votes
0 answers
42 views

### Initialize data qubits in the first step of syndrome measurement

I saw many papers that say that in syndrome measurement of the stabilizer codes, such as surface codes and color codes, firstly, all data qubits are initialized to $|0\rangle$. What is the reason? I ...
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