Skip to main content
OverflowAI is here! AI power for your Stack Overflow for Teams knowledge community. Learn more

New answers tagged

1 vote
Accepted

Can the spectral radius of a completely positive map exceed the spectral radius of its transition matrix?

While the inequality in quesiton does hold for all channels and all self-adjoint positive maps (as shown in the above question) perhaps surprisingly it fails for general completely positive maps. For ...
Frederik vom Ende's user avatar
0 votes

Efficient way to calculate trace of product of Pauli string and matrix?

We have $\text{Tr}(PM)=\sum_{ij}P_{ij}M_{ij}$ and $P$ is very sparse: it has sparsity $\frac{1}{2^N}$. So if you store $P$ in a sparse format, you can compute $\text{Tr}(PM)$ efficiently by summing ...
Nichola's user avatar
  • 391
2 votes
Accepted

Commutation of $XX$ and $ZZ$ operators

TL;DR: The cause of the apparent paradox is degeneracy: each of the two operators has (infinitely) many eigenbases. One of the eigenbases is shared, but it does not contain $|{++}\rangle$. The shared ...
Adam Zalcman's user avatar
  • 22.9k
2 votes

Commutation of $XX$ and $ZZ$ operators

Commuting operators share a set of eigenvectors that form a basis of the respective Hilbert space (in the finite dimensional case). Here are the 4 common eigenvectors of XX and ZZ that form a basis of ...
qubitzer's user avatar
  • 117
1 vote
Accepted

To what extent is the normal form of the Pauli transfer matrix unique?

It turns out that uniqueness can only be guaranteed if $\lambda_1>\lambda_2>|\lambda_3|$; otherwise one can construct counterexamples (as we will do below). In order to understand why ...
Frederik vom Ende's user avatar
2 votes
Accepted

In the QECC condition $\langle\psi|E_a^\dagger E_b|\phi\rangle=C_{ab}\langle\psi|\phi\rangle$, what is $C_{ab}$?

The concept of $C_{ab} $ in the context of the Quantum Error-Correcting Code (QECC) conditions as described in Theorem 2.7 can indeed be confusing due to the mathematical notation and the terminology ...
Bram's user avatar
  • 644
1 vote

In the QECC condition $\langle\psi|E_a^\dagger E_b|\phi\rangle=C_{ab}\langle\psi|\phi\rangle$, what is $C_{ab}$?

I imagine it's supposed to be a matrix $C$ with elements $C_{ab}$, i.e. $a$ indexes the row, and $b$ the column of $C$.
DaftWullie's user avatar
  • 58.7k
2 votes
Accepted

Is $\rho = \sum_{j} p_j|n_j\rangle\langle n_j|$ a valid construction for any mixed state?

The question is, how do you perform the diagonalisation routine? A typical way to achieve this is to have a set of unitaries $\{U_i\}$ for which the $|n_j\rangle$ are eigenstates with $\pm 1$ ...
DaftWullie's user avatar
  • 58.7k

Top 50 recent answers are included