Limits on broadcasting non-stabilizerness through unrestricted operations

TL;DR

This paper establishes fundamental limits on broadcasting non-stabilizerness, or 'magic', in quantum states, showing that stabilizer operations cannot replicate or clone this resource, and identifying conditions for perfect broadcasting.

Contribution

It proves that stabilizer operations cannot broadcast or clone non-stabilizerness, and derives conditions for perfect broadcasting using unrestricted quantum operations.

Findings

Stabilizer operations cannot replicate non-stabilizerness.

Impossible to clone non-stabilizerness with auxiliary systems.

Conditions for perfect broadcasting of magic states.

Abstract

In the resource theory of non-stabilizerness, we prove that stabilizer operations cannot replicate or broadcast the "magic" resource of all quantum states in an arbitrary finite dimension. Moreover, we show that even in unrestricted scenarios, there are fundamental limits on cloning the non-stabilizerness content of quantum states. When using an auxiliary system as part of the cloning process, we show that it is impossible to broadcast the non-stabilizerness of qubits that possess a greater degree of non-stabilizerness than the known states on which the transformations are based. We also derive the conditions to broadcast magic perfectly using unrestricted operations. Furthermore, we compare non-stabilizerness broadcasting with traditional state cloning methods, such as state-dependent and -independent cloners, which can achieve perfect broadcasting of states with known magic content. Our findings reveal that state-dependent cloning unitaries designed for specific states have lower average non-stabilizerness-generating power than magic-generating unitaries.