New answers tagged density-matrix
6
votes
Prove that spectral decomposition is the minimal ensemble decomposition
Let's take your decomposition
$$
\rho=\sum_kp_k|\varphi_k\rangle\langle\varphi_k|
$$
and assume that the number of $k$ is smaller than the rank of $\rho$. Now, consider the space $S$ spanned by all ...
- 61.7k
1
vote
A proof that 4 ≥ ∞ when using the Quantum One-Time Pad
Let us define information-theoretically-secure encryption as follows: given any fixed plaintext, the distribution of ciphertext over uniform random keys is statistically indistinguishable from uniform....
- 11
2
votes
A proof that 4 ≥ ∞ when using the Quantum One-Time Pad
The Quantum One-Time Pad is information-theoretically secure in the same manner as the (classical) One-Time Pad or Vigenère cipher is. I think your interpretation of "perfect secrecy" is ...
- 14.4k
2
votes
Accepted
how to mix (or time average) two density matrix?
Your question is a bit confusing because it is not clear what you mean by "combine two channels into an 8 qubit channel", but maybe the following suffices?:
Prepare $\rho_1$ on qubits $q_0$ ...
- 2,204
2
votes
Computing the expected value of a spin - 1 particle component given density matrix
This reads like it is some kind of homework assignment, so I won't compute the full answer.
For a density matrix, the expectation value of any operator $\hat{O}$ is given by $\langle \hat{O} \rangle = ...
- 536
1
vote
Expansion of multi-qubit density matrix in the Pauli matrix basis
Let $P_x$ denote any $n$-qubit Pauli matrix indexed by $x$, It is easy to see that $Tr(P_xP_y)=0$ for any two different Pauli matrices $P_x \ne P_y$. Denoting $\rho = \sum_y P_y c_y$, this property ...
- 41
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