[Paper Review] Experimental study for Yuen-Kim protocol of quantum key distribution with unconditional secure

Osamu Hirota, Kentaro Kato+1 more|ArXiv.org|Dec 9, 2002

Quantum Information and Cryptography1 references3 citations

TL;DR

This paper proposes an experimental implementation of the Yuen-Kim quantum key distribution protocol using intensity modulation/direct detection (IMDD) in optical fiber, achieving unconditional security by leveraging non-commuting coherent state signals and quantum detection theory. The scheme uses a pairwise M-ary intensity modulation to encode bits, ensuring Eve’s minimum error probability approaches 1/2, while Bob maintains a lower error rate, enabling secure key exchange even under classical noise and eavesdropping with partial signal interception.

ABSTRACT

In this report, we simulate practical feature of Yuen-Kim protocol for quantum key distribution with unconditional secure. In order to demonstrate them experimentally by intensity modulation/direct detection(IMDD) optical fiber communication system, we use simplified encoding scheme to guarantee security for key information(1 or 0). That is, pairwise M-ary intensity modulation scheme is employed. Furthermore, we give an experimental implementation of YK protocol based on IMDD.

Motivation & Objective

• To demonstrate a practical implementation of the Yuen-Kim quantum key distribution protocol using conventional optical fiber communication systems.
• To achieve unconditional security in quantum key distribution by exploiting quantum detection theory rather than the no-cloning theorem.
• To design and simulate a system based on intensity modulation/direct detection (IMDD) that ensures Bob’s error rate is always lower than Eve’s, even under eavesdropping with partial signal access.
• To evaluate the impact of increasing the number of basis states (M) on the error probabilities of Eve and Bob, and to optimize secure communication distance.

Proposed method

• The protocol uses a two-mode coherent state |Ψ₀⟩ = |α/√2⟩₁ ⊗ |α/√2⟩₂ as the base state, with bit encoding via rotation using the operator exp(−iJ_zϕ_b), resulting in |Ψ_b⟩ = |e^{−iϕ_b/2}α/√2⟩₁ ⊗ |e^{iϕ_b/2}α/√2⟩₂.
• A stream cipher expands a short key K into a long key K*, which selects from M uniformly distributed basis states for encoding.
• The scheme employs a pairwise M-ary intensity modulation to encode 2M bits per M basis sets, increasing the number of non-commuting signal states.
• Eve’s minimum error probability is bounded using quantum detection theory, with a lower bound derived from the fidelity between neighboring states: P_e^* (2) = ½(1 − √(1 − exp(−|α₁ − α₂|²))).
• Bob’s error probability is calculated independently of M, given by P_e(B) = ½(1 − √(1 − |⟨α₁|α_{M/2+1}⟩|²)), ensuring consistent decoding performance.
• An experimental setup using a 1.3 µm laser diode, pattern generator, modulator, optical divider (simulating Eve), and InGaAs PIN detector is used to simulate 10 km fiber with variable attennuation (10–200 km equivalent).

Experimental results

Research questions

• RQ1 Can the Yuen-Kim protocol achieve unconditional security in a practical IMDD optical fiber system?
• RQ2 How does increasing the number of basis states (M) affect the error probabilities of Eve and Bob?
• RQ3 Can Bob maintain a lower error rate than Eve even when Eve intercepts a fraction of the signal (η << 1)?
• RQ4 What is the maximum secure communication distance under realistic channel losses and eavesdropping conditions?
• RQ5 Does the use of non-commuting coherent states ensure that Eve cannot distinguish bit states with error probability below 1/2?

Key findings

• When Eve is opaque (e.g., full signal interception), Bob’s error rate increases to nearly 1/2, indicating detection of eavesdropping, regardless of channel length.
• When Eve is translucent (η << 1), her error probability increases with M, approaching 1/2 asymptotically, while Bob’s error rate remains stable and significantly lower.
• The error probability for Eve’s minimum detection error is bounded below by P_e^*(2) = ½(1 − √(1 − exp(−|α₁ − α₂|²))), which increases with amplitude difference between neighboring states.
• Bob’s error probability is independent of M and given by P_e(B) = ½(1 − √(1 − |⟨α₁|α_{M/2+1}⟩|²)), ensuring reliable decoding across all M values.
• The system achieves secure key distribution at 1.2 Gbps over 10 km fiber, with a minimum detectable signal power of −30 dBm and dark current of 7 nA.
• With 20 dB total loss (100 km equivalent), the transmitter power of −10 dBm supports secure communication, and increasing M enhances Eve’s error rate, improving security.