4
votes
Accepted
What is the operator-sum representation of the two-qubit depolarizing channel?
As pointed out in the comments, you cannot use the one-qubit formula because something like $X\rho X$ does not make sense if $\rho$ is a 2-qubit state. In fact, for this reason the answer you based ...
- 2,823
3
votes
Accepted
Invalid coefficients in Quantum Process Tomography of the Hadamard gate
The formula $(3)$ is only true when the basis $\rho_j$ is orthonormal. Indeed, to derive $(3)$, we hit both sides of $(2)$ with $\mathrm{tr}(.\rho_k)$ and use $\mathrm{tr}(\rho_j^\dagger\rho_k)=\...
- 24.1k
3
votes
Do POVM and generalized measurements really describe all possible measurements we can do on a quantum system (open dynamics)?
I would argue that your procedure does not correspond to a "measurement of system A" in an operational sense. For me, a measurement device should be able to take in a state $\rho_A$ (free to ...
- 6,216
2
votes
Can this minus operation be implemented via a quantum channel?
Of course you can assume $\rho_1>\rho_2$ to ensure a positive output for your particular problem, but that does not change the fact that there cannot be a positive linear map $\Phi:\mathbb C^{3\...
- 2,823
2
votes
Do POVM and generalized measurements really describe all possible measurements we can do on a quantum system (open dynamics)?
There's a few different things here, so let me try to break down a few different arguments:
Why are POVMs the most general possible measurement? — I'd say POVMs are simply what you get when applying ...
glS♦
- 26.3k
2
votes
Do POVM and generalized measurements really describe all possible measurements we can do on a quantum system (open dynamics)?
POVMs are the most general measurement as long as you insist that the probability $p_i(\rho)$ for any outcome $i$ is a linear function of $\rho$ (that is, any such linear $p_i(\rho)$ can be written as ...
- 7,653
2
votes
When performing a projective measurement on a subsystem X entangled with another system Y, can the evolution of Y be unitary?
Non existence for "forgetful" measurements
Suppose after the entangling operation the state is some $\rho_{XY}$. Given a POVM $\{M_a\}_a$ we can describe the final state of system $Y$ and ...
- 6,216
1
vote
Accepted
Mathematical properties used to derive Kraus operators
You have
$$\rho_{\rm in}\otimes|e_0\rangle\!\langle e_0|
= (\rho_{\rm in}\otimes I)(I\otimes |e_0\rangle\!\langle e_0|)
= (I\otimes |e_0\rangle\!\langle e_0|)(\rho_{\rm in}\otimes I).
$$
The main &...
glS♦
- 26.3k
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