Continuous-Variable Quantum Teleportation

Braunstein-Kimble protocol — EPR entanglement, homodyne detection, displacement operations

Phase Space: Input & Output States

Wigner Function of Teleported State

Fidelity vs Squeezing Parameter

Protocol & Theory

Braunstein-Kimble (1998):
1. Create EPR pair: r = squeezing
2. Alice measures (x̂_in−x̂_a, p̂_in+p̂_a)
3. Bob displaces: D̂(x_m, p_m)|ψ⟩
Fidelity (coherent input):
F = 1/(1 + e^(−2r)) → 1 as r→∞
Classical limit: F_cl = 1/2 (r=0)
Squeezing r1.0
Fidelity F
Classical bound0.500
Output noise Δx²
EPR correlations