# Tag Info

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### How to perform quantum state tomography on two qubits?

Preliminary I would like to rewrite the equation that you have in a slightly different manner. Since a density matrix can be written as a matrix, we can also write it down as a linear combination of ...

### What is the relationship between Choi and Chi matrix in Qiskit?

( I copied some text from a previous answer of mine) Defining the Choi and $\chi$ matrix The Choi matrix is a direct result of the Choi-Jamiolkowski isomorphism. Some intuition on what this is can be ...
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### Is there a circuit to compare two quantum states?

The task that you describe in your question — a circuit which flips a single qubit, if and only if the two input states are different — is not possible. We can show this as follows. First, there is no ...
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### In shadow tomography, how is the state reconstructed from its shadows?

Under the assumption that the ensemble $\mathcal{U}$ faithfully produces the Haar expectations at least to the second moment, the inversion can be performed as suggested in the last paragraph of the ...
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### Can quantum state tomography break bb84?

No, weak measurement and quantum tomography don't break BB84. I recommend that you create an explicit quantum circuit that implements the weak measurement or the quantum tomography, and check for ...
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### Why can any density operator be written this way? (quantum tomography)

From linear algebra, if $v_1, \dots, v_n$ is a basis of the vector space $V$ then every vector $v\in V$ can be written as a linear combination $$v = a_1 v_1 + \dots + a_n v_n\tag1$$ where the ...
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### Why is the complexity of $n$-qubit state tomography not upper bounded as $O(3^n)$?

Let's say you have a magical machine that gives you $\langle P_{p} \rangle$ (which are expectation values and therefor, well, numbers) and only the $\langle P_{p} \rangle$. It does this for all the $3$...
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### Unknown quantum circuit symbol

The picture has two parts: The first goes until the dots. It is simply three $|0\rangle$ states. (The ground state.) You will recognize that the same picture -- but only until the dot -- is used in ...

### How to measure the sign of quantum amplitudes

An empirical solution could be to use the Grover's Diffusion Operator $D$. Lets say the qubits are in an initial state $|\psi\rangle = \sum_{0}^{2^n-1}\alpha_i|i\rangle$. Since global phase/sign is ...
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### Does computing the quantum mutual information $I(\rho^{AB})$ require full tomographic information of $\rho^{AB}$?

The mutual information can be written in terms of the relative entropy, please see Nielsen and Chuang (the entropy Venn diagram figure 11.2). I am writing the equation in the question's notation: I(...

### How to distinguish two states with same density matrix using a quantum state tomography?

The question presupposes a misconception that the vector form of a state $|\psi\rangle$ exists independently of its density operator form $|\psi\rangle\langle\psi|$, which is often described as ...
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### How to perform Quantum Process Tomography for three qubit gates?

I am sure that since you are asking this question you probably already understand this, but for future & other's reference let me give a quick recap of what we are trying to achieve. Quantum ...
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### Lower bounds on the number of measurements outcomes required for quantum state tomography

I apologise in advance. This is a rough and hand-waivy answer. You can give "information-theoretic" lower bounds by noting that the measurements can be seen as a linear map $M$ from quantum ...
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### Using Classical Shadow to predict quantum state's fidelity has nothing to do with the dimension of the density matrix?

Without really checking your arguments, there is a fundamental reason why the scaling could be fine, but it is still not strange at all. The point is that you estimate with additive precision, but ...
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### Are SIC-POVMs optimal for quantum state reconstruction?

First of all, here's a short disclaimer: I'm not an in-depth expert in this field, I'm just currently getting in contact with tomography more and more often :) So take the following with a grain of ...
The lack of positive semidefiniteness is very easy to see. Suppose your quantum state is $|0\rangle\langle 0|$, and you do tomography by measuring in the $X, Y,$ and $Z$ bases. Furthermore, assume ...