Honest-party lockability of distillable key
- Fields
- Topics
Problem
Can loss of one qubit held by an honest party reduce the two-way distillable secret key by an arbitrarily large amount? Let \(K_D(A:B)_\rho\) denote the asymptotic secret-key rate obtainable from \(\rho_{AB}\) by local operations and public two-way classical communication, with an adversary holding a purification. The question is whether there are finite-dimensional states \(\rho^{(r)}_{A_ra:B_r}\), with \(\dim a=2\), such that
Equation (1) is the \(AB\)-locking question: the discarded qubit belongs to Alice rather than being transferred to the adversary.
Source
Christandl et al. explicitly ask whether distillable key is lockable when the discarded subsystem is held by an honest party [CEH+07].
Progress
Christandl and collaborators proved that transferring a bounded subsystem to the adversary cannot cause an unbounded loss of distillable key. They explicitly left the distinct honest-party, or \(AB\)-, locking problem open, even for classical tripartite states [CEH+07].
Horodecki and collaborators established non-lockability bounds for restricted families of private states. They identify the arbitrary-state version of Eq. (1) as unresolved, including a specified product-system special case [HSK+21].
Comment
The unresolved scope is \(AB\)-lockability of \(K_D\) for arbitrary states, as formalized in Eq. (1). It excludes both the non-lockable adversary-side operation and the restricted private-state families covered by existing bounds.