# Quantification and manipulation of magic states

## TL;DR

This paper investigates the possibility of converting one magic state into another using stabilizer-preserving quantum operations in a single-copy setting, providing a mathematical framework and criteria for such transformations.

## Contribution

It formulates the magic state conversion problem as an SDP feasibility problem and derives necessary and sufficient conditions using a variant of the Farkas Lemma.

## Key findings

- Provides a procedure to determine the existence of stabilizer-preserving conversions.
- Derives a complete set of magic monotones for state conversion.
- Establishes necessary and sufficient conditions for single-shot magic state transformations.

## Abstract

Magic states can be used as a resource to circumvent the restrictions due to stabilizer-preserving operations, and magic-state conversion has not been studied in the single-copy regime thus far. Here we solve the question of whether a stabilizer-preserving quantum operation exists that can convert between two given magic states in the single-shot regime. We first phrase this question as a feasibility problem for a semi-definite program (SDP), which provides a procedure for constructing a stabilizer-preserving quantum operation (free channel) if it exists. Then we employ a variant of the Farkas Lemma to derive necessary and sufficient conditions for existence, and this method is used to construct a complete set of magic monotones.