Quantum Teleportation Protocol Calculator
Estimate the end-to-end fidelity of a quantum teleportation protocol over a lossy channel given entanglement quality, detector efficiency, and distance. Use this when designing quantum networks or comparing protocol variants.
About this calculator
Quantum teleportation transmits an unknown qubit state from sender (Alice) to receiver (Bob) using a shared entangled pair and a classical communication channel, consuming the entanglement in the process. The overall success fidelity combines several multiplicative factors: entanglement fidelity F_ent (how close the shared pair is to a perfect Bell state), measurement efficiency η_m (probability of a successful Bell-state measurement), channel transmission T (fraction of photons surviving the optical path), and exponential photon loss with distance d. For the standard protocol, F = F_ent · η_m · T · exp(−d/50 km). Probabilistic protocols add a 0.5 factor because success occurs only half the time. Relay-assisted protocols use a shorter effective attenuation length of 30 km. The 50 km scale corresponds approximately to the attenuation length of telecom-wavelength photons in standard optical fibre (~0.2 dB/km).
How to use
Consider the standard protocol with F_ent = 0.95, η_m = 0.85, T = 0.90, and distance d = 20 km. Compute each factor: exponential loss = exp(−20/50) = exp(−0.4) ≈ 0.670. Multiply all factors: F = 0.95 · 0.85 · 0.90 · 0.670 = 0.95 · 0.85 = 0.8075; then 0.8075 · 0.90 = 0.7268; then 0.7268 · 0.670 ≈ 0.487. The teleportation fidelity is approximately 0.487, below the classical limit of 2/3 ≈ 0.667, indicating that channel loss and imperfections at this distance dominate. Reducing distance or improving detector efficiency would raise fidelity above the classical threshold.
Frequently asked questions
What fidelity is needed for quantum teleportation to outperform classical communication?
For teleportation of an arbitrary qubit state, the classical fidelity limit is 2/3 ≈ 0.667. Any teleportation protocol achieving fidelity above this threshold demonstrates genuine quantum advantage, because no classical strategy can exceed it on average over all input states. Maximally entangled Bell states enable unit fidelity in the absence of noise. In practice, real experiments report fidelities of 0.80–0.99 over short distances using high-quality entangled photon pairs and efficient superconducting nanowire detectors. Exceeding the 2/3 threshold is the minimum requirement for a meaningful quantum network link.
How does distance affect the success probability of quantum teleportation over optical fibre?
Photon loss in standard single-mode optical fibre is approximately 0.2 dB/km at telecom wavelengths (1550 nm), corresponding to an attenuation length of about 50 km before the transmission drops to 1/e ≈ 37%. The fidelity model here uses exp(−d/50 km) to capture this loss. At 50 km only 37% of photons survive; at 100 km only 14% survive. Beyond roughly 100–150 km, direct fibre transmission becomes impractical without quantum repeaters, which use entanglement swapping and purification to extend range without amplifying the quantum signal.
What is the difference between standard and probabilistic quantum teleportation protocols?
Standard quantum teleportation deterministically transfers the qubit state to Bob once Alice performs a Bell-state measurement and sends the two-bit classical result. The probabilistic variant succeeds only 50% of the time because it uses a measurement that cannot distinguish all four Bell states with linear optics, but it requires simpler and cheaper equipment. The relay-assisted (third) protocol inserts intermediate quantum repeater nodes, which shorten the effective transmission distance per segment to around 30 km and partially restore fidelity at the cost of additional hardware complexity and synchronisation. The choice of protocol depends on the fidelity requirements, available hardware, and acceptable latency.