Repeater-Link Success
Estimate independent quantum-repeater chain success across repeated attempts.
Description
Independent repeater-link probabilities multiply to form a full-chain attempt probability.
Independent repeater-link probabilities multiply to form a full-chain attempt probability. Repeated independent attempts give a cumulative success probability.1
Estimate independent quantum-repeater chain success across repeated attempts.
When to use Repeater-Link Success
Use this tool to estimate independent quantum-repeater chain success across repeated attempts.
Prepare the optical measurements, geometry, fitted coefficients or caller-selected thresholds requested. Confirm wavelength, radius/diameter, pulse-width, angle and unit conventions before running the calculation.
How to use Repeater-Link Success and understand its results
- Prepare the optical measurements, geometry, fitted coefficients or caller-selected thresholds requested. Confirm wavelength, radius/diameter, pulse-width, angle and unit conventions before running the calculation.
- Enter elementaryLinkSuccessProbability, elementaryLinkCount, attemptCount using the field table and calculation rules, then run the tool.
- Read singleAttemptChainProbability, cumulativeSuccessProbability, expectedAttempts. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| elementaryLinkSuccessProbability | Elementary-link success probability | number; minimum: 0; maximum: 1 | Required |
| elementaryLinkCount | Elementary-link count | integer; minimum: 1 | Required |
| attemptCount | Attempt count | integer; minimum: 1 | Required |
Enter probability from zero through one and positive integer link/attempt counts. Return single-attempt and cumulative success and expected attempts. At q=0, expected attempts is zero as a placeholder.
q=p^links; cumulative=1−(1−q)^attempts; expected=1/q Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| singleAttemptChainProbability | Single-attempt chain probability | number; minimum: 0; maximum: 1 |
| cumulativeSuccessProbability | Cumulative success probability | number; minimum: 0; maximum: 1 |
| expectedAttempts | Expected attempts | number; minimum: 0 |
{
"input": {
"elementaryLinkSuccessProbability": 0.5,
"elementaryLinkCount": 2,
"attemptCount": 3
},
"output": {
"singleAttemptChainProbability": 0.25,
"cumulativeSuccessProbability": 0.578125,
"expectedAttempts": 4
}
}Limitations and assumptions
The placeholder does not represent a finite physical waiting time. Memory, scheduling, swap efficiencies and dependence are not modeled.
Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Twin-Field PLOB Comparison: Compare an achieved twin-field secret-bit rate with the repeaterless PLOB bound. For a complementary task, use SPDC Heralded Rate: Estimate detected SPDC coincidence, singles, and heralding rates from supplied efficiencies.
References
-
Repeater-Link Success — tool.io
Similar or alternative tools
- Twin-Field PLOB Comparison
Compare an achieved twin-field secret-bit rate with the repeaterless PLOB bound.
- SPDC Heralded Rate
Estimate detected SPDC coincidence, singles, and heralding rates from supplied efficiencies.