Quantification and manipulation of magic states

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.

10 pages, 3 figures

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• Gaussian quantum resource theories
• Magic-state resource theory for the ground state of the transverse-field Ising model
• Nonstabilizerness determining the hardness of direct fidelity estimation
• Characterization of an operational quantum resource in a critical many-body system
• Generating steady quantum coherence and magic through an autonomous thermodynamic machine by utilizing a spin bath
• Resource theory of quantum uncomplexity
• Quantifying dynamical magic with completely stabilizer preserving operations as free
• Constraints on magic state protocols from the statistical mechanics of Wigner negativity
• Quantum Non-Local Nonstabilizerness
• Non-stabilizerness in kinetically-constrained Rydberg atom arrays
• Resource theory of quantum coherence with probabilistically non-distinguishable pointers and corresponding wave-particle duality
• The axiomatic and the operational approaches to resource theories of magic do not coincide
• Geometric-Like imaginarity: quantification and state conversion
• Unified Framework for Calculating Convex Roof Resource Measures
• Choi-Defined Resource Theories
• Quantum coherence with incomplete set of pointers and corresponding wave-particle duality
• Resource distillation in convex Gaussian resource theories
• Enhancement of non-Stabilizerness within Indefinite Causal Order
• Mathematical methods for resource-based type theories