Pseudomagic Quantum States

Abstract

Notions of nonstabilizerness, or "magic", quantify how non-classical quantum states are in a precise sense: states exhibiting low nonstabilizerness preclude quantum advantage. We introduce 'pseudomagic' ensembles of quantum states that, despite low nonstabilizerness, are computationally indistinguishable from those with high nonstabilizerness. Previously, such computational indistinguishability has been studied with respect to entanglement, introducing the concept of pseudoentanglement. However, we demonstrate that pseudomagic neither follows from pseudoentanglement nor implies it. In terms of applications, the study of pseudomagic offers fresh insights into the theory of quantum scrambling: it uncovers states that, even though they originate from non-scrambling unitaries, remain indistinguishable from scrambled states to any physical observer. Additional applications include new lower bounds on state synthesis problems, property testing protocols, and implications for quantum cryptography. Our work is driven by the observation that only quantities measurable by a computationally bounded observer - intrinsically limited by finite-time computational constraints - hold physical significance. Ultimately, our findings suggest that nonstabilizerness is a 'hide-able' characteristic of quantum states: some states are much more magical than is apparent to a computationally bounded observer.

32 pages, 3 figures, 1 table. Updated with the published version

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Cited by in corpus (32)

• Stabilizer entropies are monotones for magic-state resource theory
• Pauli Spectrum and Non-stabilizerness of Typical Quantum Many-Body States
• Magic spreading in random quantum circuits
• Entanglement-magic separation in hybrid quantum circuits
• Magic-induced computational separation in entanglement theory
• Probing quantum complexity via universal saturation of stabilizer entropies
• Pseudorandom unitaries are neither real nor sparse nor noise-robust
• Entanglement and Stabilizer entropies of random bipartite pure quantum states
• Anticoncentration and state design of random tensor networks
• Pseudorandom density matrices
• Dynamics of Pseudoentanglement
• A nonstabilizerness monotone from stabilizerness asymmetry
• Extracting randomness from magic quantum states
• The non-stabilizerness of fermionic Gaussian states
• Efficient distributed inner product estimation via Pauli sampling
• Efficient witnessing and testing of magic in mixed quantum states
• Maximal Magic for Two-qubit States
• Black Box Work Extraction and Composite Hypothesis Testing
• Hardness of observing strong-to-weak symmetry breaking
• Uncovering Quantum Many-body Scars with Quantum Machine Learning
• Faster computation of nonstabilizerness
• Rise and fall of nonstabilizerness via random measurements
• Pseudochaotic Many-Body Dynamics as a Pseudorandom State Generator
• On the Hardness of Measuring Magic
• Anticoncentration in Clifford Circuits and Beyond: From Random Tensor Networks to Pseudo-Magic States
• Pseudoentanglement from tensor networks
• Fast computational deep thermalization
• Characterization of non-adaptive Clifford channels
• Universal work extraction in quantum thermodynamics
• An Algorithm for Estimating $\alpha$-Stabilizer Rényi Entropies via Purity
• Shallow quantum circuit for generating extremely low-entangled approximate state designs
• Pseudoentanglement Ain't Cheap