Original title: Non-local Magic: closed-form solution and equivalence with magic of purification
Michele Viscardi, Lorenzo Leone, Alioscia Hamma · September 2026
In quantum computing, some states possess a property called non-stabilizerness, or magic, which is necessary for complex calculations. Non-local magicA measure of how much a quantum state cannot be simplified using local operations on its parts. measures the magic shared between two quantum systems that cannot be eliminated using local operations on each part alone. Calculating this value usually requires a difficult search over all possible local operations. Researchers tackled this problem by studying a specific measure called the log-stabilizer fidelity. They found an exact formula to calculate non-local magic directly, using only numbers called the Schmidt spectrumA set of numbers that describe the entanglement between two parts of a bipartite state.. Next, they introduced the magic of purificationThe smallest amount of quantum magic needed to represent a mixed state as a pure state. to measure the magic in mixed, imperfect states. Ultimately, they discovered that non-local magic equals the smallest magic of purification across a certain set of these states.
Imagine two people writing letters to each other, but the content gets distorted based on their physical setup. Normally, to measure how distorted the communication is, you'd have to try every possible arrangement of their setup. Here, the researchers show that the distortion can be calculated directly from a simple feature of how the letters were initially mixed, without trying all arrangements. In this paper, the two people represent the two parts of a quantum system, the distorted communication is the non-local magic, and the simple feature is the Schmidt spectrum.
This gives quantum physicists a straightforward formula instead of a hard optimization for measuring state complexity. It simplifies assessing resources for quantum information tasks.
The results are specific to the log-stabilizer fidelity measure and bipartite states. The abstract does not address whether similar closed-form solutions exist for other fidelity measures or for multipartite systems.
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Non-local Magic: closed-form solution and equivalence with magic of purification — Michele Viscardi, Lorenzo Leone, Alioscia Hamma
Abstract licence: CC0
Explanation generated by Synthesis from the abstract — it is not the original paper. This is a preprint, so it hasn't necessarily been peer reviewed.