Quantum Ruzsa Divergence to Quantify Magic
arXiv:2401.14385 · doi:10.1109/TIT.2025.3543276
Abstract
In this work, we investigate the behavior of quantum entropy under quantum convolution and its application in quantifying magic. We first establish an entropic, quantum central limit theorem (q-CLT), where the rate of convergence is bounded by the magic gap. We also introduce a new quantum divergence based on quantum convolution, called the quantum Ruzsa divergence, to study the stabilizer structure of quantum states. We conjecture a ``convolutional strong subadditivity'' inequality, which leads to the triangle inequality for the quantum Ruzsa divergence. In addition, we propose two new magic measures, the quantum Ruzsa divergence of magic and quantum-doubling constant, to quantify the amount of magic in quantum states. Finally, by using the quantum convolution, we extend the classical, inverse sumset theory to the quantum case. These results shed new insight into the study of the stabilizer and magic states in quantum information theory.
V3. 16 pages, close to the published version V2.29 pages V1.23 pages
References in corpus (37)
- Universal Quantum Computation with ideal Clifford gates and noisy ancillas
- Quantum information can be negative
- High-fidelity parallel entangling gates on a neutral atom quantum computer
- The Resource Theory of Stabilizer Computation
- Application of a resource theory for magic states to fault-tolerant quantum computing
- Negative Quasi-Probability as a Resource for Quantum Computation
- Hudson's Theorem for finite-dimensional quantum systems
- Improved classical simulation of quantum circuits dominated by Clifford gates
- Trading classical and quantum computational resources
- A Sharp Fannes-type Inequality for the von Neumann Entropy
- Stabilizer Rényi entropy
- Simulation of quantum circuits by low-rank stabilizer decompositions
- Convex resource theory of non-Gaussianity
- A quantum central limit theorem for non-equilibrium systems: Exact local relaxation of correlated states
- Quantifying quantum speedups: improved classical simulation from tighter magic monotones
- Sumset and inverse sumset theorems for Shannon entropy
- Resource theory of non-Gaussian operations
- A polynomial-time classical algorithm for noisy random circuit sampling
- The entropy power inequality for quantum systems
- Sumset and Inverse Sumset Inequalities for Differential Entropy and Mutual Information
- On the statistical complexity of quantum circuits
- A generalization of the Entropy Power Inequality to Bosonic Quantum Systems
- Limits on classical communication from quantum entropy power inequalities
- Efficient classical simulation of Clifford circuits with nonstabilizer input states
- Entropy bounds on abelian groups and the Ruzsa divergence
- Quantum Entropy and Central Limit Theorem
- Entropy and set cardinality inequalities for partition-determined functions
- Continuous-variable entanglement distillation and non-commutative central limit theorems
- Entropy power inequalities for qudits
- Further extensions of Clifford circuits and their classical simulation complexities
- Exchange relation planar algebras of small rank
- Convergence rates for the quantum central limit theorem
- Magic Resource Can Enhance the Quantum Capacity of Channels
- Classical simulation of quantum circuits by half Gauss sums
- Central limit theorems for the large-spin asymptotics of quantum spins
- On a generalized Central Limit Theorem and Large Deviations for Homogeneous Open Quantum Walks
- Sumsets and entropy revisited