Generic bound coherence under strictly incoherent operations

TL;DR

This paper analytically characterizes the limits of quantum coherence distillation under strictly incoherent operations, revealing that almost all states are bound and only pure or rank-one submatrix states are distillable, highlighting fundamental operational restrictions.

Contribution

It provides a complete analytical criterion for asymptotic distillability under SIO and PIO, and demonstrates that almost all quantum states exhibit bound coherence, advancing understanding of coherence resource theory.

Findings

Maximal distillation rates under SIO and PIO coincide for all states.

Almost every quantum state is undistillable, except pure and rank-one submatrix states.

Distillation fidelity can be efficiently computed via semidefinite programming.

Abstract

We compute analytically the maximal rates of distillation of quantum coherence under strictly incoherent operations (SIO) and physically incoherent operations (PIO), showing that they coincide for all states, and providing a complete description of the phenomenon of bound coherence. In particular, we establish a simple, analytically computable necessary and sufficient criterion for the asymptotic distillability under SIO and PIO. We use this result to show that almost every quantum state is undistillable --- only pure states as well as states whose density matrix contains a rank-one submatrix allow for coherence distillation under SIO or PIO, while every other quantum state exhibits bound coherence. This demonstrates fundamental operational limitations of SIO and PIO in the resource theory of quantum coherence. We show that the fidelity of distillation of a single bit of coherence under SIO can be efficiently computed as a semidefinite program, and investigate the generalization of this result to provide an understanding of asymptotically achievable distillation fidelity.