Entropic Quantum Central Limit Theorem and Quantum Inverse Sumset Theorem

• URL: http://arxiv.org/abs/2401.14385v1
• Date: Thu, 25 Jan 2024 18:43:24 GMT
• Title: Entropic Quantum Central Limit Theorem and Quantum Inverse Sumset Theorem
• Authors: Kaifeng Bu, Weichen Gu, Arthur Jaffe
• Abstract summary: We establish an entropic, quantum central limit theorem and quantum inverse sumset theorem in discrete-variable quantum systems. A byproduct of this work is a magic measure to quantify the nonstabilizer nature of a state, based on the quantum Ruzsa divergence.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We establish an entropic, quantum central limit theorem and quantum inverse sumset theorem in discrete-variable quantum systems describing qudits or qubits. Both results are enabled by using our recently-discovered quantum convolution. We show that the exponential rate of convergence of the entropic central limit theorem is bounded by the magic gap. We also establish an ``quantum, entropic inverse sumset theorem,'' by introducing a quantum doubling constant. Furthermore, we introduce a ``quantum Ruzsa divergence'', and we pose a conjecture called ``convolutional strong subaddivity,'' which leads to the triangle inequality for the quantum Ruzsa divergence. A byproduct of this work is a magic measure to quantify the nonstabilizer nature of a state, based on the quantum Ruzsa divergence.

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