Complete characterization of qubit masking

TL;DR

This paper fully characterizes which single-qubit states can be masked using linear operators, proving that only states on a spherical circle on the Bloch sphere are maskable, and provides explicit maskers and secret sharing protocols.

Contribution

It proves the maximal maskable set of qubit states is a spherical circle on the Bloch sphere and confirms a previous conjecture, providing explicit maskers and applications.

Findings

Nonzero linear operators cannot mask a nonzero measure set of states.

Maskable states are exactly those on a spherical circle on the Bloch sphere.

Explicit unitary maskers are constructed for all maskable sets.

Abstract

We study the problem of information masking through nonzero linear operators that distribute information encoded in single qubits to the correlations between two qubits. It is shown that a nonzero linear operator cannot mask any nonzero measure set of qubit states. We prove that the maximal maskable set of states on the Bloch sphere with respect to any masker is the ones on a spherical circle. Any states on a spherical circle on the Bloch sphere are maskable, which also proves the conjecture on maskable qubit states given by Modi et al. [Phys. Rev. Lett. 120, 230501 (2018)]. we provide explicitly operational unitary maskers for all maskable sets. As applications, different protocols for secret sharing are introduced.