Linked Questions

39 votes
8 answers

If all quantum gates must be unitary, what about measurement?

All quantum operations must be unitary to allow reversibility, but what about measurement? Measurement can be represented as a matrix, and that matrix is applied to qubits, so that seems equivalent to ...
auden's user avatar
  • 3,399
8 votes
3 answers

How does the spectral decomposition of the Choi operator relate to Kraus operators?

In Nielsen and Chuang's QCQI, there is a proof states that Theorem 8.1: The map $\mathcal{E}$ satisfies axioms A1, A2 and A3 if and only if $$ \mathcal{E}(\rho)=\sum_{i} E_{i} \rho E_{i}^{\dagger} $$...
Sherlock's user avatar
  • 613
7 votes
2 answers

Deduce the Kraus operators of the dephasing channel using the Choi

I'm trying to deduce the Kraus representation of the dephasing channel using the Choi operator (I know the Kraus operators can be guessed in this case, I want to understand the general case). The ...
user2723984's user avatar
  • 1,056
3 votes
4 answers

Can a Kraus representation act as the identity on any operator?

In the textbook “Quantum Computation and Quantum Information” by Nielsen and Chuang, it is stated that there exists a set of unitaries $U_i$ and a probability distribution $p_i$ for any matrix A, $$\...
Amplituhedron's user avatar
3 votes
1 answer

How does the Kraus decomposition imply the Stinespring representation?

To show that the Kraus decomposition $\Phi(\rho)=\sum_{k=1}^D M_k\rho_S M_k^\dagger$ implies the Stinespring form $$\Phi(\rho)=\text{tr}_E[U_{SE}(\rho_S\otimes|0\rangle\langle 0|_E)U_{SE}^\dagger]$$ ...
user15135's user avatar
  • 165
1 vote
1 answer

Prove that different Kraus decompositions are related through a unitary, using the Choi isomorphism

I consider a process $\mathcal{E}$ that is at least CP and hermitian preserving. I know that the Choi matrix then has the form: $$ M = \sum_k |M_k \rangle \rangle \langle \langle M_k | $$ Where $|M_k \...
Marco Fellous-Asiani's user avatar
1 vote
0 answers

Matrix Representation of Quantum Channels

I am working on a project and I expect to have expressions of a bunch of quantum channels of interest. The quantum channels will be in matrix form. For example for a 2 qubit system, the quantum ...
user22511's user avatar
2 votes
2 answers

Find an operator-sum representation for a depolarizing channel acting on 2qubit

In Nielsen and Chuang (page:379), it shows how to represent a 1 qubit depolarizing channel in operator-sum representation. $$ \mathcal{E}_1(\rho)=pI/2+(1-p)\rho =(1-3p/4)\rho+p/4(X\rho X+Y\...
LX.CC's user avatar
  • 29
0 votes
0 answers

Stinespring Representation

I need to conduct a numerical analysis of a quantum channel using SDP and therefore, I need the Stinespring representation of this quantum channel: $$\Phi=\mathrm{Tr}_{\mathrm{DE}}\Big((\mathrm{Id}^{\...
milenteor's user avatar
1 vote
1 answer

Can one define a Choi state for a a classical channel?

Suppose one has a classical channel $W(y|x)$ that is a conditional probability distribution. Can one define a Choi state for this channel? My guess is that one should think of it as a special case of ...
EVMaverick's user avatar