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

TL;DR

This work analyzes information–disturbance relations in QKD under variable-strength eavesdropping, contrasting probe-based weak measurements with probeless partial measurements. Using a time-bin BB84 implementation with weak coherent states, it develops a theoretical framework for the monitoring channel and quantifies how $Q$ (QBER) and $G$ (Eve’s information gain) depend on measurement strength $\epsilon$ or $\gamma$, corroborated by fiber-based experiments. It shows that partial measurements can yield higher $G$ for a given $Q$ than weak measurements and extends the study to composite threats such as photon-number-splitting and calibration-time noise injection. The results reinforce that standard abort thresholds and parameter estimation secure QKD under these variable-strength attacks, and they propose practical countermeasures including decoy states, enhanced calibration, and hardware isolation for real-world deployments, with implications for data-center QKD and beyond.

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.

Figures (7)

• Figure 1: Information gain (G) and disturbance (Q) for variable-strength probe-based measurements. Left: Eve's gain as a function of her interaction strength $\epsilon$. When $\epsilon = 0$, Eve guesses the classical bit string without measurement, while for $\epsilon =1$, Eve strongly interacts with Alice's state. Right: Alice and Bob's QBER as a function of $\epsilon$.
• Figure 2: $G$ and $Q$ as functions of the interaction strength, $\epsilon$, are plotted for the Gaussian, partial measurement, rectangular pointer, and triangular pointer. It can be observed that the rectangular and triangular pointers lead to similar performance, whereas the Gaussian pointer is more efficient.
• Figure 3: The ratio between disturbance and information gain, $\frac{Q}{G}$, as a function of the interaction strength $\epsilon$ is plotted for probeless partial measurements and for probe-based variable-strength measurements with a Gaussian pointer, rectangular pointer, and triangular pointer. Among these, partial measurement seems the most efficient due to its definite, sharp outcomes. The Gaussian pointer appears to be more efficient than the rectangular and triangular pointers.
• Figure 4: Heatmaps of the information gain and QBER over the photon rate $\mu$ and interaction strength $\epsilon$.
• Figure 5: A continuous-wave laser at 1550 nm first passes through an intensity modulator and a variable optical attenuator on the encoder side. At the decoder, a 50:50 beamsplitter (BS) passively selects the measurement basis: one arm goes directly to a single-photon avalanche diode (SPAD) for the time (Z) basis, while the other enters an AMZI to enable interference measurements in the phase (X) basis before reaching its SPAD. All detection events are recorded by a time-tagger.