Hoi-Fung Chau

In quantum Shannon theory, various kinds of quantum entropies are used to characterize the capacities of noisy physical systems. Among them, min-entropy and its smooth version attract wide interest especially in the field of quantum cryptography as they can be used to bound the information obtained by an adversary. However, calculating the exact value or non-trivial bounds of min-entropy are extremely difficult because the composite system dimension may scale exponentially with the dimension of its subsystem. Here, we develop a one-shot lower bound calculation technique for the min-entropy of a classical-quantum state that is applicable to both finite and infinite dimensional reduced quantum states. Moreover, we show our technique is of practical interest in at least three situations. First, it offers an alternative tight finite-data analysis for the BB84 quantum key distribution scheme. Second, it gives the best finite-key bound known to date for a variant of device independent quantum key distribution protocol. Third, it provides a security proof for a novel source-independent continuous-variable quantum random number generation protocol. These results show the effectiveness and wide applicability of our approach.

Photons play an important role in quantum information processing as they are easy to manipulate locally and transfer over a long distance. Photonic qubits are widely used in tasks such as linear optical quantum computing (LOQC), quantum sensing/metrology, and quantum communication. However, to date, efficient high-speed single photon sources are still difficult to make. Here, we propose that we can use "classical" phase-randomized coherent states, combined with post-processing, to perform various quantum information processing tasks. Specifically, we divide the tasks into two scenarios: ones with a circuit of a known Hilbert space dimension, describable by a unitary matrix, such as LOQC and metrology, as well as ones with an unknown channel, such as quantum communication. We propose methods that can hugely improve the numerical precision and applicable dimensions in both scenarios, including a machine learning method for the former and a linear interpolation method for the latter, opening up a wide variety of applications that can be implemented with easily attainable coherent light sources and threshold detectors, such as quantum metrology or universal fully-passive state preparation.