Physical implementability for reversible magic state manipulation

Abstract

Abstract Magic states are essential for achieving universal quantum computation, yet the reversibility and efficiency of exact magic state manipulations remain less explored. Here we show that magic states in odd dimensions can be exactly and reversibly transformed under operations that preserve both the trace of states and positivity of discrete Wigner representation. Using the stochastic formalism, we demonstrate that magic mana emerges as the unique measure for such reversible magic state transformations. We propose the concept of physical implementability for characterizing the hardness and cost of maintaining reversibility. Our findings show that, analogous to the entanglement theory, going beyond the positivity constraint enables an exact reversible theory of magic manipulation. Physical implementability for quantum resource transformation provides a perspective for understanding and quantifying quantum resources, contributing to an operational framework for understanding the cost of reversible quantum resource manipulation.