Quantum Key Distribution Without Shared Reference Frame Under Unital Noise
2026-06-22 • Cryptography and Security
Cryptography and Security
AI summaryⓘ
The authors study how to securely share keys using quantum communication when the connection between parties is noisy and they cannot align their measurement setups, a situation common in satellite communication. They present two methods: one constructs a mathematical description of the noise without needing aligned setups and finds the best states to send; the other gradually finds the best measurement settings step-by-step. Both methods end up allowing known quantum key protocols like BB84 to work optimally despite these challenges.
quantum key distributionqubit channelPauli transfer matrixshared reference frameBB84 protocolsix-state protocolquantum noisesatellite communicationBloch vectorquantum cryptography
Authors
Junaid ur Rehman, Shehbaz Tariq, Symeon Chatzinotas
Abstract
We consider a general and practical scenario of quantum key distribution (QKD) over an unknown, stationary, unital qubit channel. Furthermore, due to practical limitations, e.g., relative movement and rotation of communicating parties, a global shared reference frame cannot be established. This scenario can routinely appear in satellite QKD. We propose two methods to overcome the physical qubit noise and the lack of shared reference frame. The first proposed approach involves constructing the Pauli transfer matrix (PTM) description of the channel, which we achieve without requiring a shared reference frame, by absorbing the lack of shared reference frame in the channel definition. This is followed by the identification of singular vectors of PTM as the Bloch vectors for optimal signal states. In the optimized local bases, the resulting correlations are equivalent, up to outcome relabeling, to those of a Pauli channel, allowing us to show the optimality of the BB84 and six-state QKD protocols under these conditions. The second approach, called the sequential basis matching (SBM) involves sequentially identifying the channel-optimized local bases that enable QKD. We show that both of these approaches result in the same effective key exchange rate for QKD.