Quantum Teleportation Calculator
Calculate quantum teleportation fidelity, success probability, resource requirements, and teleportation quality.
About this calculator
Quantum teleportation transfers an unknown quantum state from one location to another using a shared entangled pair (the "Bell state"), a local measurement, and two classical bits of communication -- not by moving the physical particle itself. This calculator models the standard Bennett et al. (1993) protocol as a chain of independent fidelities: the overall Teleportation Fidelity is the product of Bell State Fidelity, Measurement Fidelity, Classical Channel Fidelity, and Entanglement Fidelity (F_teleport = F_bell x F_measurement x F_classical x F_entanglement). Because it's a product of numbers between 0 and 1, the weakest link dominates -- a single degraded fidelity term pulls the overall result down more than an equally-sized improvement in any other term pulls it up, so the biggest gains come from fixing whichever fidelity is lowest, not from marginally improving an already-good one.
The protocol's resource cost is fixed by the physics rather than by input quality: it always consumes exactly 1 shared entangled pair (1 ebit) and requires exactly 2 classical bits to communicate the Bell-measurement outcome, regardless of how good or poor the fidelities are. This calculator also reports Success Probability at a flat 100%, which is a simplification -- it assumes an idealized, always-successful Bell-state measurement. Real experimental setups, especially linear-optical ones, often have a Bell-state measurement success probability well below 100%, which this model does not represent.
Inputs
Results
Teleportation Fidelity
83.79%
Success Probability
100%
How to Use This Calculator
- Enter Bell State Fidelity (0–1) — the quality of the shared entangled pair; experimental values are typically 0.90–0.99.
- Enter Measurement Fidelity (0–1) for the Bell-state measurement at the sender's location.
- Set Classical Channel Fidelity (0–1) — typically 1.0 for error-corrected classical communication.
- Enter Entanglement Fidelity (0–1) for the initial entanglement generation quality.
- Read Teleportation Fidelity (%) and Success Probability (%) to evaluate the quantum channel. Note: 2 classical bits are always required alongside 1 ebit.
How the result changes with Bell State Fidelity
| Bell State Fidelity | Teleportation Fidelity | Success Probability |
|---|---|---|
| 0.48 | 41.9% | 100% |
| 0.71 | 62.8% | 100% |
| 1 | 88.2% | 100% |
What each input means
- Bell State Fidelity
- Fidelity of Bell state
- Measurement Fidelity
- Bell measurement fidelity
- Classical Channel Fidelity
- Classical communication fidelity
- Entanglement Fidelity
- Initial entanglement fidelity
How this is calculated
Formula
F_teleport = F_bell × F_measurement × F_classical × F_entanglementWorked example, using the default values
- Identify Input Parameters4 parametersBell State Fidelity = 0.95, Measurement Fidelity = 0.98, Classical Channel Fidelity = 1, Entanglement Fidelity = 0.9 = 4 input(s) provided
- Calculate Teleportation FidelityTeleportation Fidelity83.79 = 83.79%
- Calculate Success ProbabilitySuccess Probability100 = 100%
- Calculate Classical Bits RequiredClassical Bits Required2 = 2
- Calculate Quantum Channel UsageQuantum Channel Usage1 = 1
Engine last updated . Checked against 3 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Why are exactly 2 classical bits and 1 ebit always required, no matter the fidelity?
The resource cost of quantum teleportation is fixed by the protocol itself, not by how well it's executed. The sender's Bell-state measurement collapses the joint system into one of four possible outcomes, and identifying which of the four requires exactly 2 classical bits sent to the receiver; the receiver then applies one of four correction operations. This 2-bit, 1-ebit structure is a property of the underlying quantum-information protocol, so it doesn't change with fidelity.
Does one of the four fidelity inputs matter more than the others?
Not decisively -- because the four fidelities multiply together, each one has a comparable proportional effect on the overall result, and no single term reliably outweighs the others across the full range of values this calculator accepts. In practice, whichever fidelity is currently lowest is the one worth improving first, since the weakest link in a product of fractions drags the overall result down the most.
Why does Success Probability always show 100%, even with low fidelities?
This calculator treats the Bell-state measurement as always succeeding, deterministically, regardless of the entered fidelity values -- it's an idealization built into the simplified model, not a computed result. In real experimental implementations, particularly linear-optical Bell-state measurements, the success probability itself can be well under 100%, independent of the fidelity of a successful attempt; this calculator does not model that limitation.
What does the Distinguishability output actually measure?
In this calculator, Distinguishability is reported as numerically equal to Teleportation Fidelity -- it represents how closely the teleported state matches the original input state, with a higher value meaning the two are harder to tell apart. It's presented as a separate, more intuitive label for the same fidelity figure rather than an independently computed quantity.
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