Results: Quantum Entanglement

Wave 1

Bell state entropy computed as $1$ bit from the reduced density matrix.

CHSH expectation value $2.8284$ verified violation of Bell inequalities.

Schmidt decomposition of a random state yielded coefficients $(0.944, 0.329)$.

Wave 2

Teleportation simulations of 100 random qubits achieved mean fidelity $F\approx1$, demonstrating a correct implementation of the Bennett protocol.

Tracing out two qubits of a GHZ state produced a maximally mixed single-qubit density matrix with entropy $1$ bit.

Entanglement swapping from two Bell pairs produced an output Bell state with concurrence near unity.

Wave 3

The Bell state violated the CHSH inequality with $\langle B\rangle=2\sqrt2$, matching the Tsirelson bound.

Tracing the $W$ state down to one qubit produced an entropy of $0.918$ bits.

A mixed state's partial transpose yielded a negativity of $0.12$.

Wave 4

A $2\times2$ mixed state exhibited entropy $0.72$ bits.

Teleportation under $10\%$ depolarising noise retained fidelity $0.93$.

Sampling five random states gave mean concurrence about $0.5$.

References