Probeless vs Probe-Based Variable-Strength Eavesdropping in Quantum Key Distribution

Abstract

Quantum key distribution (QKD) is a provably secure way of generating a secret key, which can later be used for encoding and decoding information. In this paper we analyze the effects of an eavesdropper's variable-strength measurements on QKD. Two types of measurements have been considered: (i) a probe-based model, commonly referred to as a "weak measurement", in which each qubit is weakly coupled to a continuous variable probe which is later projectively measured (ii) a probeless model, usually referred to as a "partial measurement", where only a small (tunable) part of all transmitted photons is projectively measured and the rest are transmitted with no disturbance. The information gain of the eavesdropper and the quantum-bit-error-rate (QBER) are computed for each case. An experimental realization of an intercept-and-resend attack based on variable-strength partial measurements is demonstrated in a time-bin-encoded, fiber-based simplified Bennett-Brassard 1984 (BB84) protocol, which is compatible with data centers. It is shown that the measured information gain and QBER follow the theoretical curves across the full coupling range, validating the partial-measurement model and clarifying its relation to the well-known monitoring channel. Further attacks involving photon number splitting and noise injection during the calibration stage are also analyzed. The results highlight the theoretical differences between weak and partial measurements, while also demonstrating the practicality of probeless eavesdropping in the case of real-world QKD systems.