Daily Run: Quantum Entanglement

Subtopic change: Keeping focus on mixed-state entropy, teleportation fidelity, and concurrence sampling.

Day 1

Subtopics: Mixed-state entropy, noisy teleportation fidelity, concurrence of random states.

Mixed-state entropy

  1. Constructed a $2\times2$ density matrix $\rho=\begin{pmatrix}0.6 & 0.2\\0.2 & 0.4\end{pmatrix}$.
  2. Diagonalised $\rho$ to obtain eigenvalues $\lambda_{1,2}$.
  3. Stored eigenvalues and entropy in mixed-state.csv.
  4. Computed $S(\rho)=-\operatorname{Tr}\rho\log_2\rho\approx0.721$ bits.
  5. Confirmed $S$ vanishes only for pure states.

Noisy teleportation fidelity

  1. Modelled depolarising noise with probability $p=0.1$ during teleportation.
  2. Simulated 100 random qubits, averaging the channel fidelity.
  3. Saved the mean value in teleport-fidelity.txt.
  4. Found $\bar F\approx0.93$ exceeding the classical $2/3$ limit.
  5. Noted linear degradation with larger $p$.

Concurrence sampling

  1. Generated five random pure two-qubit states.
  2. Computed concurrence $C=2|ad-bc|$ for each.
  3. Recorded results in concurrence.csv.
  4. Mean concurrence was roughly $0.5$.
  5. Observed wide variance across samples.

Subtopic assessment: Teleportation simulations were most enlightening, while entropy and concurrence calculations served as useful cross-checks.