Quantum Ruzsa Divergence to Quantify Magic

• URL: http://arxiv.org/abs/2401.14385v2
• Date: Fri, 07 Feb 2025 03:50:45 GMT
• Title: Quantum Ruzsa Divergence to Quantify Magic
• Authors: Kaifeng Bu, Weichen Gu, Arthur Jaffe,
• Abstract summary: We investigate the behavior of quantum entropy under quantum convolution and its application in magic. We introduce a new quantum divergence based on quantum convolution, called the quantum Ruzsa divergence, to study the stabilizer structure of quantum states.
• Score: 0.0
• License:
• 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.

Related papers

• The multimode conditional quantum Entropy Power Inequality and the squashed entanglement of the extreme multimode bosonic Gaussian channels [53.253900735220796]
  Inequality determines the minimum conditional von Neumann entropy of the output of the most general linear mixing of bosonic quantum modes. Bosonic quantum systems constitute the mathematical model for the electromagnetic radiation in the quantum regime.
  arXiv  Detail & Related papers  (2024-10-18T13:59:50Z)
• Extracting randomness from quantum 'magic' [4.607344782066309]
  We show that when a subsystem of a quantum state is measured, the resultant projected ensemble of the unmeasured subsystem can exhibit a high degree of randomness. Our findings suggest an efficient approach for leveraging magic as a resource to generate random quantum states.
  arXiv  Detail & Related papers  (2024-02-15T18:33:21Z)
• Unraveling the Mystery of Quantum Measurement with A New Space-Time Approach to Relativistic Quantum Mechanics [9.116661570248171]
  Quantum measurement is a fundamental concept in the field of quantum mechanics. Despite its significance, four fundamental issues continue to pose significant challenges to the broader application of quantum measurement. We employ a new space-time approach to relativistic quantum mechanics to address these issues systematically.
  arXiv  Detail & Related papers  (2023-06-01T13:25:08Z)
• A vertical gate-defined double quantum dot in a strained germanium double quantum well [48.7576911714538]
  Gate-defined quantum dots in silicon-germanium heterostructures have become a compelling platform for quantum computation and simulation. We demonstrate the operation of a gate-defined vertical double quantum dot in a strained germanium double quantum well. We discuss challenges and opportunities and outline potential applications in quantum computing and quantum simulation.
  arXiv  Detail & Related papers  (2023-05-23T13:42:36Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• Quantum entanglement without superposition [0.0]
  Superposition states are at the origin of many paradoxes in quantum mechanics. quantum jumps are a key feature of this approach, in blatant contrast with the continuity of the deterministic Schr"odinger equation.
  arXiv  Detail & Related papers  (2022-12-09T13:56:35Z)
• Relation between Quantum Coherence and Quantum Entanglement in Quantum Measurements [3.8073142980733]
  We set up resource theories of quantum coherence and quantum entanglement for quantum measurements. For this, we conceive a relative entropy type quantity to account for the quantum resources of quantum measurements. Our results confirm that the understanding on the link between quantum coherence and quantum entanglement is valid even for quantum measurements which do not generate any quantum resource.
  arXiv  Detail & Related papers  (2022-02-25T12:24:32Z)
• Towards understanding the power of quantum kernels in the NISQ era [79.8341515283403]
  We show that the advantage of quantum kernels is vanished for large size datasets, few number of measurements, and large system noise. Our work provides theoretical guidance of exploring advanced quantum kernels to attain quantum advantages on NISQ devices.
  arXiv  Detail & Related papers  (2021-03-31T02:41:36Z)
• Experimental Validation of Fully Quantum Fluctuation Theorems Using Dynamic Bayesian Networks [48.7576911714538]
  Fluctuation theorems are fundamental extensions of the second law of thermodynamics for small systems. We experimentally verify detailed and integral fully quantum fluctuation theorems for heat exchange using two quantum-correlated thermal spins-1/2 in a nuclear magnetic resonance setup.
  arXiv  Detail & Related papers  (2020-12-11T12:55:17Z)
• Quantum Zeno effect for open quantum systems [6.553031877558699]
  We prove the quantum Zeno effect in open quantum systems governed by quantum dynamical semigroups. We also prove the existence of a novel strong quantum Zeno limit for quantum operations.
  arXiv  Detail & Related papers  (2020-10-08T17:00:05Z)
• Jumptime unraveling of Markovian open quantum systems [68.8204255655161]
  We introduce jumptime unraveling as a distinct description of open quantum systems. quantum jump trajectories emerge, physically, from continuous quantum measurements. We demonstrate that quantum trajectories can also be ensemble-averaged at specific jump counts.
  arXiv  Detail & Related papers  (2020-01-24T09:35:32Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.