Differential-phase-shift QKD with practical Mach–Zehnder interferometer

Abstract Differential-phase-shift (DPS) quantum key distribution stands as a promising protocol due to its simple implementation, which can be realized with a train of coherent pulses and a passive measurement unit. To implement the DPS protocol, it is crucial to establish security proofs incorporating practical imperfections in users’ devices, however, existing security proofs make unrealistic assumptions on the measurement unit using a Mach–Zehnder interferometer. In this paper, we enhance the implementation security of the DPS protocol by incorporating a major imperfection in the measurement unit. Specifically, our proof enables us to use practical beam splitters with a known range of the transmittance rather than the one with exactly 50%, as was assumed in the existing security proofs. Our numerical simulations demonstrate that even with fluctuations of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo>±</mml:mo> <mml:mn>0.5</mml:mn> <mml:mi mathvariant="normal">%</mml:mi> </mml:mrow> </mml:math> in the transmittance from the ideal value, the key rate degrades only by a factor of 0.57. This result highlights the feasibility of the DPS protocol with practical measurement setups.