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# Tag Info

Accepted

### What does $M_m |\psi_i\rangle$ mean in the equation $p(m|i)=\langle\psi_i|M_m^\dagger M_m|\psi_i\rangle$?

Measurement postulate The statement you are asking about is a postulate of quantum mechanics, so it cannot be mathematically derived from other facts in the theory. Instead, it is justified by its ...
• 23.2k
Accepted

### Confusion about the output distribution of Haar random quantum states

The two facts are connected in that they both arise as a result of rotational invariance of the Haar measure. We will derive them in the case of large $n$ since this is when the Porter-Thomas ...
• 23.2k
Accepted

• 969
Accepted

### Computing expectation value of $|\langle z|C|0^n\rangle|^2$ over Haar random circuit

The issue that easily leads to confusion is the dual role played by output bitstring probability. It enters the computation of the average in two ways. On one hand, it determines how often one sees ...
• 23.2k
Accepted

### Nielsen & Chuang Exercise 6.13: Standard deviation of classical counting algorithm

Since the classical algorithm samples "uniformly and independently $𝑘$ times from the search space", equation $(5)$ should be, $P(X_i=1, X_j=1)= P(X_i=1)P(X_j=1)=\frac{M^2}{N^2}$ instead. ...
• 321
Accepted

### Compute the large $n$ distribution of $|\langle z_i|\psi\rangle|^2$ over Haar random quantum states

In the following, I'll show the evaluation of the probability densities of the transition probabilities: $|\langle \psi | z\rangle^2$ and their pairwise independence. I didn't work out the full mutual ...
• 2,575
Accepted

### How to interpret complex probability of superposition state?

You forgot to take the absolute value. The Born rule for computing measurement outcome probability from the state vector amplitudes says that the probability is the square of the magnitude of the ...
• 23.2k
Accepted

• 2,915

### How do I get correct measurement probabilities in ZX calculus?

OK, I made two mistakes. Both were corrected by a closer reading of the paper "Simulating quantum circuits with ZX-calculus reduced stabiliser decompositions". First, as was pointed out by ...
• 221
Accepted

• 326