New answers tagged density-matrix
6
votes
Accepted
Finding the eigenvalues of a qutrit state
Maybe you forgot about the coefficient $\frac{1}{\sqrt{2}}$. The correct reduced density matrix is $$\frac12 (\left|1\right>\left<1\right| + \left|2\right>\left<2\right|)$$
2
votes
How to find density matrix of 3 qubit W state?
We can get the density matrix $\rho$ for a pure state $|\psi\rangle$ using
$$\rho=|\psi\rangle\langle\psi|$$
And to write $\rho$ using the Pauli basis $\left\{ P_i \right\}$,
$$\rho = \sum_{i=0}^N \...
4
votes
Accepted
Is possible to write a separable state as a finite or countable infinite sum of product states?
Yes, you can always write an integral of separable states as a (finite) convex combination of product states, owing to the fact that the set of separable states is compact.
A quick way to see this is ...
1
vote
QISKIT: ValueError: too many subscripts in einsum DensityMatrix()
Try to transpile your circuit into 1- and 2-qubit gates:
qc = transpile(qc, basis_gates=['cx', 'u'])
rho = DensityMatrix(qc)
This issue happens because Numpy ...
2
votes
Accepted
Derivation of Choi-Jamiolkowski isomorphism
It's easier to work with matrix units $E_{ij} = |i\rangle \langle j|$. In particular, we have
$$
|\Omega\rangle \langle \Omega| = \sum_{i,j}c_i\overline{c_j} E_{ij} \otimes E_{ij}\tag{1}\,.
$$
The ...
1
vote
Accepted
How to get the Kraus operator $M_0=\sqrt{1-p}\, I$ for the depolarizing channel, from its isometric representation?
The unitary representation specifies how the isometry $U$ acts on pure states. The channel $\Phi$ is related to $U$ by $\Phi(\rho)=\operatorname{tr}_E[U\rho U^\dagger]$. Notice that on pure states ...

glS♦
- 23.4k
Top 50 recent answers are included
Related Tags
density-matrix × 354quantum-state × 129
linear-algebra × 65
textbook-and-exercises × 60
entanglement × 58
mathematics × 36
measurement × 26
quantum-operation × 25
qiskit × 24
nielsen-and-chuang × 22
information-theory × 18
entropy × 15
programming × 13
bloch-sphere × 12
trace-distance × 12
quantum-gate × 11
probability × 10
matrix-representation × 9
decoherence × 9
partial-transpose × 9
haar-distribution × 8
fidelity × 7
kraus-representation × 7
projection-operator × 7
noise × 6