Twin-Field PLOB Comparison

Compare an achieved twin-field secret-bit rate with the repeaterless PLOB bound.

Description

A repeaterless PLOB bound provides a theoretical secret-bit-per-channel-use reference for a pure-loss channel.

A repeaterless PLOB bound provides a theoretical secret-bit-per-channel-use reference for a pure-loss channel. The achieved rate must use a compatible normalization.^{[1, 2]}

Compare an achieved twin-field secret-bit rate with the repeaterless PLOB bound.

When to use Twin-Field PLOB Comparison

Use this tool to compare an achieved twin-field secret-bit rate with the repeaterless PLOB bound.

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 Twin-Field PLOB Comparison 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 channelTransmittance, achievedSecretBitsPerUse using the field table and calculation rules, then run the tool.
Read plobBoundBitsPerUse, boundRatio, exceedsPlobBound. 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
channelTransmittance	Channel transmittance	number; minimum: 0; maximum: 1	Required
achievedSecretBitsPerUse	Achieved secret bits per use	number; minimum: 0	Required

Enter transmittance from zero inclusive to one exclusive and nonnegative achieved bits/use. Return bound, ratio and strict exceedance flag. At zero transmittance, ratio is a zero placeholder even if achieved rate is positive.

bound=−log2(1−η); ratio=achieved/bound

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
plobBoundBitsPerUse	Repeaterless PLOB bound	number; minimum: 0
boundRatio	Achieved-to-bound ratio	number; minimum: 0
exceedsPlobBound	Exceeds PLOB bound	boolean

json

{
  "input": {
    "channelTransmittance": 0.1,
    "achievedSecretBitsPerUse": 0.2
  },
  "output": {
    "plobBoundBitsPerUse": 0.15200309344504995,
    "boundRatio": 1.3157626957921171,
    "exceedsPlobBound": true
  }
}

Limitations and assumptions

No protocol security proof, finite-key analysis or channel-use convention is checked.

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. A successfully returned false flag is an evaluated outcome; its meaning is explained above.

Alternative or Complementary methods

Use Repeater-Link Success: Estimate independent quantum-repeater chain success across repeated attempts. For a complementary task, use Decoy-State Intensity Score: Score supplied signal and decoy intensities from observed gains; this is not a security proof.

Further background: Fundamental limits of repeaterless quantum communications.

References

Twin-Field PLOB Comparison — tool.io
Fundamental limits of repeaterless quantum communications — Pirandola, Laurenza, Ottaviani and Banchi

Similar or alternative tools

Repeater-Link Success
Estimate independent quantum-repeater chain success across repeated attempts.
Decoy-State Intensity Score
Score supplied signal and decoy intensities from observed gains; this is not a security proof.