Quantum Entropy and Central Limit Theorem

• URL: http://arxiv.org/abs/2302.07841v3
• Date: Sun, 18 Jun 2023 18:25:30 GMT
• Title: Quantum Entropy and Central Limit Theorem
• Authors: Kaifeng Bu, Weichen Gu, Arthur Jaffe
• Abstract summary: We study discrete-variable quantum systems based on qudits. We establish a central limit theorem, based on iterating the convolution of a zero-mean quantum state. We elaborate on two examples: the DV beam splitter and the DV amplifier.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a framework to study discrete-variable (DV) quantum systems based on qudits. It relies on notions of a mean state (MS), a minimal stabilizer-projection state (MSPS), and a new convolution. Some interesting consequences are: The MS is the closest MSPS to a given state with respect to the relative entropy; the MS is extremal with respect to the von Neumann entropy, demonstrating a ''maximal entropy principle in DV systems.'' We obtain a series of inequalities for quantum entropies and for Fisher information based on convolution, giving a ''second law of thermodynamics for quantum convolutions.'' We show that the convolution of two stabilizer states is a stabilizer state. We establish a central limit theorem, based on iterating the convolution of a zero-mean quantum state, and show this converges to its MS. The rate of convergence is characterized by the ''magic gap,'' which we define in terms of the support of the characteristic function of the state. We elaborate on two examples: the DV beam splitter and the DV amplifier.

Related papers

• Quantum conditional entropies and fully entangled fraction of states with maximally mixed marginals [0.0]
  The fully entangled fraction (FEF) measures the proximity of a quantum state to maximally entangled states. Quantum conditional entropy (QCE) is a measure of correlation in quantum systems. FEF is intricately linked with $k$- copy nonlocality and $k$- copy steerability.
  arXiv  Detail & Related papers  (2024-08-05T06:16:51Z)
• Entropic Quantum Central Limit Theorem and Quantum Inverse Sumset Theorem [0.0]
  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.
  arXiv  Detail & Related papers  (2024-01-25T18:43:24Z)
• Lieb-Schultz-Mattis Theorem in Open Quantum Systems [0.0]
  We extend the Lieb-Schultz-Mattis (LSM) theorem to open quantum systems. We establish a general theorem that restricts the steady state and spectral gap of Liouvillians based solely on symmetry. Our work leads to a unified understanding of phases and phenomena in open quantum systems.
  arXiv  Detail & Related papers  (2023-05-25T21:52:35Z)
• Discrete Quantum Gaussians and Central Limit Theorem [0.0]
  We study states in discrete-variable (DV) quantum systems. stabilizer states play a role in DV quantum systems similar to the role Gaussian states play in continuous-variable systems.
  arXiv  Detail & Related papers  (2023-02-16T17:03:19Z)
• 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)
• Maximum entropy quantum state distributions [58.720142291102135]
  We go beyond traditional thermodynamics and condition on the full distribution of the conserved quantities. The result are quantum state distributions whose deviations from thermal states' get more pronounced in the limit of wide input distributions.
  arXiv  Detail & Related papers  (2022-03-23T17:42:34Z)
• Unconventional mechanism of virtual-state population through dissipation [125.99533416395765]
  We report a phenomenon occurring in open quantum systems by which virtual states can acquire a sizable population in the long time limit. This means that the situation where the virtual state remains unpopulated can be metastable. We show how these results can be relevant for practical questions such as the generation of stable and metastable entangled states in dissipative systems of interacting qubits.
  arXiv  Detail & Related papers  (2022-02-24T17:09:43Z)
• Quantum Wigner entropy [0.0]
  We define the Wigner entropy of a quantum state as the differential Shannon entropy of the Wigner function of the state. We conjecture that it is lower bounded by $lnpi +1$ within the convex set of Wigner-positive states. The Wigner entropy is anticipated to be a significant physical quantity, for example, in quantum optics.
  arXiv  Detail & Related papers  (2021-05-26T21:12:50Z)
• Interplay between transport and quantum coherences in free fermionic systems [58.720142291102135]
  We study the quench dynamics in free fermionic systems. In particular, we identify a function, that we dub emphtransition map, which takes the value of the stationary current as input and gives the value of correlation as output.
  arXiv  Detail & Related papers  (2021-03-24T17:47:53Z)
• Catalytic Transformations of Pure Entangled States [62.997667081978825]
  Entanglement entropy is the von Neumann entropy of quantum entanglement of pure states. The relation between entanglement entropy and entanglement distillation has been known only for the setting, and the meaning of entanglement entropy in the single-copy regime has so far remained open. Our results imply that entanglement entropy quantifies the amount of entanglement available in a bipartite pure state to be used for quantum information processing, giving results an operational meaning also in entangled single-copy setup.
  arXiv  Detail & Related papers  (2021-02-22T16:05:01Z)
• Einselection from incompatible decoherence channels [62.997667081978825]
  We analyze an open quantum dynamics inspired by CQED experiments with two non-commuting Lindblad operators. We show that Fock states remain the most robust states to decoherence up to a critical coupling.
  arXiv  Detail & Related papers  (2020-01-29T14:15:19Z)

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.