Toshihiko Sasaki

We developed new concentration inequalities for a quantum state on an N -qudit system or measurement outcomes on it that apply to an adversarial setup, where an adversary prepares the quantum state. Our one-sided concentration inequalities for a quantum state require the N -qudit system to be permutation invariant and are thus de-Finetti type, but they are tighter than the one previously obtained. We show that the bound can further be tightened if each qudit system has an additional symmetry. Furthermore, our concentration inequality for the outcomes of independent and identical measurements on an N -qudit quantum system has no assumption on the adversarial quantum state and is much tighter than the conventional one obtained through Azuma’s inequality. We numerically demonstrate the tightness of our bounds in simple quantum information processing tasks.

Practical quantum key distribution (QKD) protocols require a finite-size security proof. The phase error correction (PEC) approach is one of the general strategies for security analyses that has successfully proved finite-size security for many protocols. However, the asymptotically optimal key rate cannot, in general, be achieved with the conventional PEC approach due to the reduction to the estimation problem of the classical quantity, the phase error rate. In this work, we propose a new PEC-type strategy that can provably achieve the asymptotically optimal key rate. The key piece for this is a virtual protocol based on the universal source compression with quantum side information, which is of independent interest. Combined with the reduction method to collective attacks, this enables us to directly estimate the phase error pattern rather than the estimation via the phase error rate, and thus leads to asymptotically tight analyses. As a result, the security of any permutation-symmetrizable QKD protocol gets reduced to the estimation problem of the single conditional R\'enyi entropy, which can be efficiently solved by a convex optimization.

The trusted device scenario is the assumption that an adversary cannot access imperfections in the detectors such as electronic noise, aiming at improving the key rate of quantum key distribution (QKD) protocol. In the case of trusted Gaussian noises in the detectors of continuous-variable (CV) QKD, there is a method based on rescaling that is applicable to any protocol using homodyne or heterodyne detectors. Here, we are interested in what kind of CV-QKD protocols tend to benefit more from the trusted scenario. Using prior research that extended the covariance matrix analysis from Gaussian modulation to discrete modulation, we evaluated the quantitative effect of rescaling on the key rate with arbitrary modulation. Our results revealed that the performance asymptotically improves in any discrete modulation protocol, and this improvement is more significant compared to Gaussian modulation. Additionally, we developed a method to address unbalanced heterodyne measurements, where the noise and transmittance of the two homodyne detectors differ. This allows for a more realistic measurement model to be addressed with discrete modulation.

Continuous Variable (CV) quantum key distribution (QKD) is a promising candidate for practical implementations due to its compatibility with the existing communication technology. A trusted device scenario assuming that an adversary has no access to imperfections in the detector is expected to provide significant improvement in the key rate, but such an endeavor so far was made separately for specific protocols and for specific proof techniques. Here, we develop a simple and general treatment that can incorporate the effects of Gaussian trusted noises for any protocol that uses homodyne/heterodyne measurements. In our method, a rescaling of the outcome of a noisy homodyne/heterodyne detector renders it equivalent to the outcome of a noiseless detector with a tiny additional loss, thanks to a noise-loss equivalence well-known in quantum optics. Since this method is independent of protocols and security proofs, it is applicable to Gaussian-modulation and discrete-modulation protocols and to any proof techniques developed so far and yet to be discovered as well.