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Quantum Bit Error Rate (QBER) Calculator

The fraction of bits that are incorrect in a quantum transmission.

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QBER

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Overview

The Quantum Bit Error Rate (QBER) is a fundamental metric in quantum communication used to measure the ratio of incorrect bits detected to the total number of bits received. It serves as a primary diagnostic tool for assessing the quality of a quantum channel and detecting the presence of an eavesdropper in protocols like Quantum Key Distribution (QKD).

Symbols

Variables

QBER = QBER, e_{err} = Error Bits, n = Total Bits

QBER
Error Bits
Total Bits

Apply it well

When To Use

When to use: Use this formula during the parameter estimation phase of a quantum key distribution protocol to decide if a secure key can be distilled. It is applied after a subset of the sifted key bits are publicly compared between the sender and receiver to estimate the channel noise.

Why it matters: It is critical for security because any attempt by an unauthorized party to intercept or measure the quantum signal inevitably introduces noise. Monitoring QBER allows users to bound the amount of information leaked to an adversary and determines if the communication session must be aborted.

One free problem

Practice Problem

A quantum communication system transmits 5000 bits. Upon comparing a test sample, 250 bits are found to be incorrect. Calculate the Quantum Bit Error Rate for this transmission.

Error Bits250
Total Bits5000

Solve for:

Hint: Divide the number of error bits by the total number of bits received.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Quantum Computation and Quantum Information by Michael A. Nielsen and Isaac L. Chuang
  2. Wikipedia: Quantum key distribution
  3. Nielsen & Chuang, Quantum Computation and Quantum Information
  4. NIST Glossary of Quantum Information
  5. Nielsen and Chuang Quantum Computation and Quantum Information
  6. Shor and Preskill Simple Proof of Security of the BB84 Quantum Key Distribution Protocol
  7. Bouwmeester, Ekert, and Zeilinger The Physics of Quantum Information
  8. University Quantum Computing — Quantum Communication