Quantum Teleportation Fidelity Calculator

Calculator Form

Example Data Table

Formula Used

For a qubit pure-state check, the calculator uses the fidelity relation:

F = |⟨ψ|φ⟩|²

with |ψ⟩ = α|0⟩ + β|1⟩ and |φ⟩ = α′|0⟩ + β′|1⟩.

The overlap becomes:

⟨ψ|φ⟩ = α*α′ + β*β′

For benchmark analysis with system dimension d and fully entangled fraction f_e, the average fidelity is:

F_avg = (d f_e + 1) / (d + 1)

The classical benchmark is:

F_classical = 2 / (d + 1)

When d = 2, these become F_avg = (2f_e + 1)/3 and the classical limit 2/3.

How to Use This Calculator

1. Enter the real and imaginary parts of the source qubit amplitudes α and β.
2. Enter the reconstructed or teleported qubit amplitudes α′ and β′.
3. Keep normalization checked if you want automatic qubit normalization.
4. Set the system dimension. Leave it at 2 for standard qubit teleportation.
5. Enter the fully entangled fraction if you want a predicted average fidelity.
6. Enter a measured average fidelity and optional uncertainty for benchmark analysis.
7. Press the calculate button to show the result below the header and above the form.
8. Use the CSV button for spreadsheet work and the PDF button for a printable report.

Quantum Teleportation Fidelity in Physics

Why fidelity matters

Quantum teleportation fidelity measures how closely the recovered qubit matches the original qubit. It is not matter transport. It is quantum state transfer supported by entanglement and classical communication. Because real experiments contain noise, loss, imperfect Bell measurements, drift, and detector limits, fidelity becomes a central quality metric.

State overlap and average performance

Researchers often inspect pure-state overlap first. For qubit states, fidelity is the squared magnitude of the inner product between the source state and the teleported state. A value near one means strong agreement. A lower value can point to phase error, amplitude imbalance, decoherence, or poor calibration. This calculator makes that comparison fast and readable.

Average teleportation fidelity matters as well. One state alone cannot describe channel quality. Experimental teams usually prepare several test states and summarize performance with an average result. When the shared resource is described by the fully entangled fraction, the average fidelity follows a compact expression that depends on system dimension. That relation is useful for theory checks, simulation reviews, and hardware validation.

Benchmarking and interpretation

Benchmarking is essential in physics. For qubits, the widely cited classical threshold is two thirds. Beating that level indicates performance beyond classical measure-and-prepare strategies. In some qubit discussions, researchers also compare with the approximate five-sixths cloning benchmark. That number serves a different purpose, but it still helps frame how strong the teleportation result is.

It is also important to separate fidelity from success probability. A protocol may return very accurate states when it succeeds, yet fail often because of loss or post-selection. Recording both values gives a more honest picture of practical teleportation performance.

Where this tool helps

This page supports direct overlap analysis and benchmark analysis together. You can enter complex amplitudes for the input and teleported qubits, estimate average fidelity from the fully entangled fraction, and compare measured averages against the classical limit. The result panel also reports margins, percentages, normalized states, and a fidelity angle for quick interpretation.

Use this calculator for coursework, lab notebooks, simulation outputs, optics experiments, superconducting qubit studies, and protocol design reviews. Keep amplitudes consistent, normalize when needed, and examine the benchmark margin instead of only the raw score. A careful fidelity workflow gives clearer insight into teleportation quality, resource strength, and experimental reliability.

Frequently Asked Questions