Prepare-and-Magic: Semi-Device Independent Magic Certification in the Prepare-and-Measure Scenario
arXiv:2506.02226 · doi:10.1103/wm7m-xnfq
Abstract
Non-stabilizerness is an essential resource for quantum computational advantage, as stabilizer states admit efficient classical simulation. We develop a semi-device-independent framework for certifying non-stabilizer states in prepare-and-measure (PAM) scenarios, relying only on assumptions about the system's dimension. Within this framework, we introduce prepare-and-measure witnesses that can distinguish stabilizer from non-stabilizer states, and we provide analytical proofs that threshold violations of these witnesses certify non-stabilizerness. In the simplest setting: three preparations, two measurements, and qubit systems, surpassing a specific threshold guarantees that at least one prepared state lies outside the stabilizer polytope, while a stronger violation can certify at least two. We extend this approach by linking it to quantum random access codes, also generalizing our results to qutrit systems and introducing a necessary condition for certifying non-stabilizerness based on state overlaps (Gram matrices). These results offer a set of semi-device-independent tools for practically and systematically verifying non-stabilizer states using prepare-and-measure inequalities.
12 + 4 pages, 5 figures
References in corpus (45)
- Universal Quantum Computation with ideal Clifford gates and noisy ancillas
- Improved Simulation of Stabilizer Circuits
- Quantum Resource Theories
- Information Causality as a Physical Principle
- Contextuality supplies the magic for quantum computation
- The Resource Theory of Stabilizer Computation
- Application of a resource theory for magic states to fault-tolerant quantum computing
- Hudson's Theorem for finite-dimensional quantum systems
- Device-independent tests of classical and quantum dimensions
- Semi-device-independent security of one-way quantum key distribution
- Stabilizer Rényi entropy
- Information-Theoretic Implications of Quantum Causal Structures
- Classicality in discrete Wigner functions
- Quantum Random Access Codes using Single -level Systems
- MHz-rate semi-device-independent quantum random number generators based on unambiguous state discrimination
- Self-testing quantum states and measurements in the prepare-and-measure scenario
- Robustness of Magic and Symmetries of the Stabiliser Polytope
- Scalable measures of magic resource for quantum computers
- Semi-device independent random number expansion protocol with n to 1 quantum random access codes
- Self-testing mutually unbiased bases in the prepare-and-measure scenario
- Self-testing non-projective quantum measurements in prepare-and-measure experiments
- Semidefinite Programming in Quantum Information Science
- Set coherence: basis-independent quantification of quantum coherence
- Efficient quantum algorithms for stabilizer entropies
- Experimental magic state distillation for fault-tolerant quantum computing
- Device-Independent Tests of Entropy
- Practical self-testing quantum random number generator based on an energy bound
- Causal modeling the delayed choice experiment
- Correlations in entanglement-assisted prepare-and-measure scenarios
- On the security and degradability of Gaussian channels
- Quantum Online Memory Checking
- Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics
- Entanglement in prepare-and-measure scenarios: many questions, a few answers
- Quantum and classical bounds for two-state overlaps
- Semi-device-independent certification of entanglement in superdense coding
- Device independent certification of a quantum delayed choice experiment
- Semi-definite programming and quantum information
- Inequalities witnessing coherence, nonlocality, and contextuality
- Handbook for Quantifying Robustness of Magic
- General Method for Classicality Certification in the Prepare and Measure Scenario
- Certification of qubits in the prepare-and-measure scenario with large input alphabet and connections with the Grothendieck constant
- Prepare-and-measure scenarios with photon-number constraints
- Bound entangled states are useful in prepare-and-measure scenarios
- On the Geometry of Stabilizer States
- Detecting quantum resources in a semi-device independent framework