Consecutive Measurement Tradeoffs in Quantum Cryptography

Abstract

Mistrustful quantum cryptographic protocols encode information in incompatible observables, so that any attempt by a dishonest party to access multiple pieces of information necessarily involves a tradeoff. A natural class of such strategies proceeds via consecutive measurements, where each measurement disturbs the state and influences subsequent information extraction. We introduce consecutive measurement theorems (CMTs) as a unified framework to quantify this tradeoff and argue that they capture the fundamental limitations underlying security in mistrustful quantum cryptography. Our main result is a tight characterization of the achievable region of success probabilities for single and consecutive measurements, strictly improving all previously known bounds. We further establish robust variants expressed in terms of fidelity and trace distance that remain valid under perturbations. These results yield strengthened and unified security guarantees for a range of primitives, including relativistic bit commitment, quantum oblivious transfer and quantum private query, and clarify the role of measurement disturbance as the key limitation on adversarial information extraction.