Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Revisiting optimal eavesdropping in quantum cryptography: Characterizing initial state and unitary evolution for optimal interaction

Atanu Acharyya, Goutam Paul

Published Dec 12, 2017• 0 citations
OpenAlex

Related papers

Revisiting Optimal Eavesdropping in Quantum Cryptography: Choice of Interaction Is Unique up to Rotation of the Underlying Basis.

Atanu Acharyya, Goutam Paul

•Oct 23, 2016•0 citations

Optimal eavesdropping in quantum cryptography with six states

Villa Gualino, Viale Settimio Severo

•Jan 1, 2008•1 citation

Optimal eavesdropping in semi-quantum key distribution

Hasnaa Hajji, M. El Baz, Walter O. Krawec

Physics Letters A•Dec 3, 2025•2 citations

Revisiting optimal eavesdropping in quantum cryptography: Optimal interaction is unique up to rotation of the underlying basis

Atanu Acharyya, Goutam Paul

A general framework of optimal eavesdropping on BB84 protocol was provided by Fuchs et al. [Phys. Rev. A 56, 1163 (1997)]. An upper bound on mutual information was derived, which could be achieved by a specific type of interaction and the corresponding measurement. However, uniqueness of optimal interaction was posed as an unsolved problem there and it has remained open for almost two decades now. In this paper, we solve this open problem and establish the uniqueness of optimal interaction up to rotation. The specific choice of optimal interaction by Fuchs et al. is shown to be a special case of the form derived in our work.

arXiv:1610.07148•Physical Review A•Feb 21, 2017•4 citations

Characterizing Optimal-speed unitary time evolution of pure and quasi-pure quantum states

Rodríguez, John A. Mora, Brian Grajales, Marcelo Terra Cunha +1 more

We present a characterization of the Hamiltonians that generate optimal-speed unitary time evolution and the associated dynamical trajectory, where the initial states are either pure states or quasi-pure quantum states. We construct the manifold of pure states as an orbit under the conjugation action of the Lie group $\SU(n)$ on the manifold of one-dimensional orthogonal projectors, obtaining an isometry with the flag manifold $\SU(n)/\textnormal{S}(\textnormal{U}(1)\times \textnormal{U}(n-1 ))$. From this construction, we show that Hamiltonians generating optimal-speed time evolution are fully characterized by equigeodesic vectors of $\SU(n)/\textnormal{S}(\textnormal{U}(1)\times \textnormal{U}(n-1))$. We later extend that result to quasi-pure quantum states.

arXiv:2408.07794•Aug 14, 2024•0 citations

Security Against Eavesdropping in Quantum Cryptography

Norbert Lütkenhaus, Stephen Mark Barnett

Springer eBooks•Jan 1, 1997•1 citation
A general framework of optimal eavesdropping on BB84 protocol was provided by Fuchs et al. [Phys. Rev. A 56, 1163 (1997)]. An upper bound on mutual information was derived, which could be achieved by a specific type of interaction and the corresponding measurement. However, uniqueness of optimal interaction was posed as an unsolved problem there and it has remained open for almost two decades now. In this paper, we solve this open problem and establish the uniqueness of optimal interaction up to rotation. The specific choice of optimal interaction by Fuchs et al. is shown to be a special case of the form derived in our work.
We present a characterization of the Hamiltonians that generate optimal-speed unitary time evolution and the associated dynamical trajectory, where the initial states are either pure states or quasi-pure quantum states. We construct the manifold of pure states as an orbit under the conjugation action of the Lie group $\SU(n)$ on the manifold of one-dimensional orthogonal projectors, obtaining an isometry with the flag manifold $\SU(n)/\textnormal{S}(\textnormal{U}(1)\times \textnormal{U}(n-1 ))$. From this construction, we show that Hamiltonians generating optimal-speed time evolution are fully characterized by equigeodesic vectors of $\SU(n)/\textnormal{S}(\textnormal{U}(1)\times \textnormal{U}(n-1))$. We later extend that result to quasi-pure quantum states.