Quantum Key Distribution Rate Calculator
Free Quantum Key Distribution Rate Calculator for physics. Enter variables to compute results using verified scientific formulas with step-by-step
Formula
R = (f_rep * mu * eta * 0.5) * [1 - (1+f_ec) * H(QBER)]
Where f_rep is the pulse repetition rate, mu is the mean photon number, eta is the total channel and detector efficiency, 0.5 accounts for basis reconciliation in BB84, f_ec is the error correction efficiency (typically 1.16), and H(QBER) is the binary Shannon entropy of the quantum bit error rate.
Worked Examples
Example 1: Metropolitan QKD Link (50 km)
Problem: Calculate the secure key rate for a BB84 system with 1 GHz pulse rate, mu = 0.1, 50 km fiber (0.2 dB/km loss), 85% detector efficiency, 100 Hz dark counts, 3% QBER.
Solution: Channel loss = 0.2 * 50 = 10 dB\nChannel transmission = 10^(-10/10) = 10%\nDetection probability = 0.1 * 0.10 * 0.85 = 0.0085\nSignal rate = 1e9 * 0.0085 = 8,500,000 counts/s\nSifted rate = 8,500,000 * 0.5 = 4,250,000 bits/s\nEffective QBER = (0.03*8.5M + 0.5*200)/(8.5M + 200) = 3.0%\nH(0.03) = 0.1945\nSecure fraction = 1 - 0.1945 - 1.16*0.1945 = 58.0%\nSecure key rate = 4,250,000 * 0.58 = 2,465,000 bps
Result: Secure Key Rate: 2,465 kbps | QBER: 3.0% | Channel Loss: 10 dB
Example 2: Long-Distance QKD Link (200 km)
Problem: Same system parameters but over 200 km fiber. How does performance change?
Solution: Channel loss = 0.2 * 200 = 40 dB\nChannel transmission = 10^(-40/10) = 0.01%\nDetection probability = 0.1 * 0.0001 * 0.85 = 8.5e-6\nSignal rate = 1e9 * 8.5e-6 = 8,500 counts/s\nDark count total = 200 Hz\nEffective QBER = (0.03*8500 + 100)/(8500 + 200) = 4.08%\nH(0.0408) = 0.2457\nSecure fraction = 1 - 0.2457 - 1.16*0.2457 = 46.9%\nSecure key rate = (8700*0.5) * 0.469 = 2,040 bps
Result: Secure Key Rate: 2.0 kbps | QBER: 4.08% | Channel Loss: 40 dB
Frequently Asked Questions
What is quantum key distribution and how does it achieve unconditional security?
Quantum key distribution (QKD) is a method for two parties (traditionally Alice and Bob) to establish a shared secret key with security guaranteed by the laws of quantum physics rather than computational assumptions. Unlike classical cryptography, which can be broken by sufficiently powerful computers, QKD security relies on the no-cloning theorem, which states that an unknown quantum state cannot be perfectly copied. Any eavesdropping attempt necessarily disturbs the quantum states being transmitted, introducing detectable errors in the QBER. The BB84 protocol, the most widely implemented QKD scheme, encodes key bits in the polarization states of single photons. After transmission, error correction and privacy amplification produce a final shared key that is provably secure.
What factors determine the secure key generation rate?
The secure key rate depends on several interconnected factors. The source repetition rate (pulse frequency) sets the maximum possible rate. The mean photon number per pulse (typically 0.1 for weak coherent sources) determines the probability of sending a photon. Channel loss, measured in dB/km multiplied by distance, reduces the fraction of photons reaching the receiver. Detector efficiency determines what fraction of arriving photons are actually detected. Dark count rate adds noise that increases the effective QBER. The error correction efficiency factor (typically 1.16 for practical implementations) determines how much key material is consumed during error correction. All these factors combine multiplicatively, making the key rate exponentially sensitive to distance.
What is the decoy state protocol and how does it improve key rates?
The decoy state protocol is a practical enhancement to BB84 that allows higher mean photon numbers while maintaining security against photon number splitting attacks. Instead of using a single intensity, Alice randomly varies the pulse intensity between signal states (higher mu) and decoy states (lower mu). By comparing detection rates at different intensities, Alice and Bob can accurately estimate the transmission and error rate for single-photon pulses specifically, which is what determines security. This enables mean photon numbers of 0.5 or higher compared to 0.1 for standard BB84, improving key rates by a factor of 1.5 to 3. The decoy state method has become standard in commercial QKD systems and is essential for practical long-distance key distribution.
What are the key kinematics equations?
The four main kinematics equations relate displacement (d), initial velocity (v0), final velocity (v), acceleration (a), and time (t): v = v0 + at, d = v0t + 0.5at^2, v^2 = v0^2 + 2ad, and d = 0.5(v + v0)t. These apply only to constant acceleration.
Is my data stored or sent to a server?
No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.
Is Quantum Key Distribution Rate Calculator free to use?
Yes, completely free with no sign-up required. All calculators on NovaCalculator are free to use without registration, subscription, or payment.