Shun Kawakami

The Bennett-Brassard 1984 (BB84) protocol is one of the simplest protocols for implementing quantum key distribution (QKD). In the protocol, the sender and the receiver iteratively choose one of two complementary measurement bases. Regarding the basis choice by the receiver, a passive setup has been adopted in a number of its implementations, including satellite QKD and time-bin encoding. However, conventional theoretical techniques to prove the security of the BB84 protocol are not applicable if the receiver chooses their measurement basis passively, rather than actively, with a biased probability, followed by measurement with threshold detectors. Here we present a fully analytical security proof against coherent attacks for such a decoy-state BB84 protocol with the receiver’s passive basis choice and measurement with threshold detectors. Numerical simulations under practical situations show that the difference in secure key rate between the active and passive implementations of the protocol is negligible except for long communication distances.

The decoy-state Bennett–Brassard 1984 (BB84) quantum key distribution (QKD) protocol is widely regarded as the de facto standard for practical implementations. On the receiver side, passive basis choice is attractive because it significantly reduces the need for random number generators and eliminates the need for optical modulators. Despite these advantages, a finite-key analytical security proof for the decoy-state BB84 protocol, where the basis is chosen passively with a biased probability, has been lacking. In this work, we present a simple analytical finite-key security proof for this setting, yielding a closed-form secret-key rate formula that can be directly evaluated using experimentally accessible parameters. Numerical simulations show that the key rates of passive- and active-measurement implementations are nearly identical, indicating that passive measurement does not compromise key-generation efficiency in practical QKD systems.

Time-bin encoding is more favorable in fiber-based implementation of quantum key distribution (QKD) than polarization encoding as it avoids issues inherent for polarization encoding, such as birefringence, caused by optical fibers. QKD only with passive devices is desirable to prevent side-channel attacks possible in the case of use of active devices such as modulators. The Bennett-Brassard 1984 (BB84) protocol is a strong candidate for an implementation with satisfying these; it can be implemented using time bins with a passive delayed interferometer that inevitably generates "satellite time bins", two pulses outside the phase-interference timing. Although time-bin encoding BB84 has been frequently demonstrated, there is no consensus whether satellite time bins can be used to extract a key. Besides, there is no security proof for either case. Here, we prove the security of time-bin encoding BB84 protocol with a passive delayed interferometer and threshold detectors. If satellite time bins are used for key generation, we show that an additional operation is necessary for security. The result is not limited only to BB84 but can be applied to Bennett-Brassard-Mermin 1992 and quantum conference key agreement based on time bins.