Gentle quantum leakage is proposed as a measure of information leakage to arbitrary eavesdroppers that aim to avoid detection. Gentle (also sometimes referred to as weak or non-demolition) measurements are used to encode the desire of the eavesdropper to evade detection. The gentle quantum leakage meets important axioms proposed for measures of information leakage including positivity, independence, and unitary invariance. Global depolarizing noise, an important family of physical noise in quantum devices, is shown to reduce gentle quantum leakage (and hence can be used as a mechanism to ensure privacy or security). A lower bound for the gentle quantum leakage based on asymmetric approximate cloning is presented. This lower bound relates information leakage to mutual incompatibility of quantum states. A numerical example, based on the encoding in the celebrated BB84 quantum key distribution algorithm, is used to demonstrate the results.
Quantum key distribution (QKD) is an important branch of quantum information science as it holds promise for unconditionally secure communication. For QKD research, a central issue is to improve the final secure key rate (SKR) and the maximal transmission distance. To address this issue, most works focused on reducing the information leakage of QKD. In this paper, we propose a novel approach to further reduce the information leakage by specially considering the overlap between the information leakage of quantum part and post-processing part. The overlap means that the information leakage of post-processing part caused solely by multi-photon pulses is considered twice in previous studies, i.e., both in quantum part and post-processing part. Since the information carried by multi-photon pulses has been considered as completely known by Eve through the photon-number-splitting attack in quantum part, there is no need to consider it in post-processing part repetitively during the SKR calculation. Therefore, our approach can theoretically reduce the information leakage of a QKD protocol. Based on this idea, we derive the formulas to calculate the amount of information leakage for decoy-BB84 and sending-or-not-sending twin-field protocols. Simulation results for these two typical protocols also demonstrate that our approach evidently improves the SKR as well as the maximal transmission distance under practical experimental parameters.
Barycentric and pairwise quantum Renyi leakages are proposed as two measures of information leakage for privacy and security analysis in quantum computing and communication systems. These quantities both require minimal assumptions on the eavesdropper, i.e., they do not make any assumptions on the eavesdropper's attack strategy or the statistical prior on the secret or private classical data encoded in the quantum system. They also satisfy important properties of positivity, independence, post-processing inequality, and unitary invariance. The barycentric quantum Renyi leakage can be computed by solving a semi-definite program and the pairwise quantum Renyi leakage possesses an explicit formula. The barycentric and pairwise quantum Renyi leakages form upper bounds on the maximal quantum leakage, the sandwiched quantum
α-mutual information, the accessible information, and the Holevo's information. Furthermore, differentially-private quantum channels are shown to bound these measures of information leakage. Global and local depolarizing channels, that are common models of noise in quantum computing and communication, restrict private or secure information leakage. Finally, a privacy-utility trade-off formula in quantum machine learning using variational circuits is developed. The privacy guarantees can only be strengthened, i.e., information leakage can only be reduced, if the performance degradation grows larger and vice versa.