# Tag Info

### Why is the coefficient-squared the probability, and not just the coefficient itself?

Scott Aaronson describes quantum mechanics as "statistics but with the L2-norm". States are L2-norm unit vectors (sum of squared amplitudes is 1) instead of L1-norm unit vectors (sum of ...
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### Is there a comprehensive list of counterexamples in quantum information?

A few weeks ago I launched a little side project of mine: a google document on Counterexamples in Quantum Information The idea was to have a centralized document acting as a reference work for ...

• 461
1 vote

### Equivalence of quantum circuits

The circuits are not equivalent in general. As an example, take $A = B = X$. The unitary matrices representing the circuits are different: ...
• 643
1 vote

### Efficient computation of probabilities for an N-particle state

For $\phi_p=0$, the normalization equals the permanent, which is hard to compute. This suggests that even the probability of one string $x_1,\dots,x_N$ is hard to compute. I'm not entirely sure what ...
• 6,561
1 vote

### Prove the fidelity can be written in terms of Pauli expectation values as ${\rm tr}(\rho\sigma)=\sum_k \chi_\rho(k)\chi_\sigma(\rho)$

A more general perspective on this is offered thinking in terms of operator frames. Suppose we're working in a $\mathbb{C}^d$. Let $(\mathcal O_i)_{i=1}^n$ be a set of Hermitian operators that spans ...
• 24.8k
1 vote

### Show that quantum channels act as affine transformations in the Bloch sphere

There is already mistake in the very first line of your computation: When you write $\mathcal{E}(\rho)=[\ldots]=\frac12(I+\sum_l E_l(\vec{r}.\vec{\sigma})E_l^\dagger)$ you forgot to apply the channel ...

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