A generalized measurement key intercept at approximately 6 percent QBER against 4-PSK BB84

Abstract

Existing intercept and resend models for BB84 quantum key distribution (QKD) with weak coherent pulses (WCPs) may underestimate how well an eavesdropper can discriminate states using generalized measurements. We model a simplified protocol with no phase randomization, so Eve discriminates among coherent states directly. Under idealized conditions, Eve performs a full intercept and resend while introducing a quantum bit error rate (QBER) within the Helstrom bound. At amplitude 1.0, the Helstrom bound gives a minimum error of 9.2%. The resulting QBER between Alice and Bob ranges from 1/2 the Helstrom bound (when errors fall entirely on the wrong basis) to 2/3 the Helstrom bound (symmetric errors). When Alice and Bob tolerate errors above these thresholds, Eve defeats privacy amplification and recovers the full key.