Kubo-Ando Means and Rigidity of Quantum Positivity Cones

• URL: http://arxiv.org/abs/2605.26272v1
• Date: Mon, 25 May 2026 18:57:05 GMT
• Title: Kubo-Ando Means and Rigidity of Quantum Positivity Cones
• Abstract summary: We show how Kubo--Ando means interact with the positive partial transpose and Schmidt-number cones.<n>We conclude that convex mixing is the uniquely permissible Kubo--Ando operation for preserving entanglement-breaking quantum channels.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate the stability of quantum positivity cones under nonlinear operator means. Specifically, we examine how Kubo--Ando means interact with the separable, positive partial transpose (PPT), and Schmidt-number cones. By analyzing the curvature of operator monotone functions at the identity, we give a strict rigidity phenomenon: weighted arithmetic means are the only Kubo--Ando means that preserve the separable cone in all dimensions. We show that the strictly positive curvature of any non-arithmetic mean explicitly forces a violation of the PPT condition, even in the foundational two-qubit setting, and can strictly increase the Schmidt number of the resulting operator. Finally, using the Choi--Jamiołkowski correspondence, we translate these geometric obstructions to the map-theoretic setting, concluding that convex mixing is the uniquely permissible Kubo--Ando operation for preserving entanglement-breaking quantum channels.

Related papers

• Spin-coherent quantum designs [0.0]
  We show that the canonical finite coherent-state formula reconstructs every operator in the rank-$S$ sector exactly if and only if the sampling points form a spherical $(2J+S)$-design.<n>We derive practical protocols for estimating moments of spin operators from these constructions, with direct applications to polarimetry, magnetometry, and quantum state tomography.
  arXiv  Detail & Related papers  (2026-08-11T18:00:06Z)
• Cumulant-based quantum relative Rényi functional [0.0]
  We introduce a new cumulant-based quantum relative Rényi functional as a candidate quantum Rényi divergence.<n>The functional naturally admits a path-integral-like representation through the Lie-Trotter product expansion.<n>We show that the resulting relative quantumness quantity vanishes if and only if the underlying states commute.
  arXiv  Detail & Related papers  (2026-06-30T06:34:53Z)
• Unitary discretization of the Koopman-von Neumann equation for quantum simulation of fluid and plasma dynamics [45.88028371034407]
  KvN framework embeds the Liouville equation into a Hilbert space with norm-preserving, unitary evolution.<n>Weyl-ordered KvN generator is derived as the unique anti-Hermitian operator symmetrization for real velocity fields.
  arXiv  Detail & Related papers  (2026-05-18T23:27:02Z)
• Operational interpretation of the reverse sandwiched Renyi divergences in composite quantum hypothesis testing [40.82628972269358]
  We study the Hoeffding regime of composite quantum hypothesis testing, in which each hypothesis is specified by a sequence of sets of quantum states.<n>We find that passing from simple to composite hypotheses can fundamentally change which quantum divergence determines the operational limits of discrimination.
  arXiv  Detail & Related papers  (2026-05-04T04:02:55Z)
• Operator Entanglement from Non-Commutative Symmetries [0.0]
  We argue that Hopf-algebra deformations of symmetries carry an intrinsic content of $operator$ $entanglement$ that is enforced by the coproduct-defined notion of composite generators.<n>We compute their operator entanglement in closed form and show that, for Haar-uniform product inputs, their entangling power is fully determined by the latter.
  arXiv  Detail & Related papers  (2025-12-31T11:49:25Z)
• Freeness Reined in by a Single Qubit [36.94429692322632]
  We find that, even in this setting, the correlation functions predicted by free probability theory receive corrections of order $O(1)$.<n>We trace their origin to non-uniformly distributed stationary quantum states, which we characterize analytically and confirm numerically.
  arXiv  Detail & Related papers  (2025-12-15T19:00:09Z)
• Weak coupling limit for quantum systems with unbounded weakly commuting system operators [50.24983453990065]
  This work is devoted to a rigorous analysis of the weak coupling limit (WCL) for the reduced dynamics of an open infinite-dimensional quantum system interacting with electromagnetic field or a reservoir formed by Fermi or Bose particles.<n>We derive in the weak coupling limit the reservoir statistics, which is determined by whose terms in the multi-point correlation functions of the reservoir are non-zero in the WCL.<n>We prove that the resulting reduced system dynamics converges to unitary dynamics with a modified Hamiltonian which can be interpreted as a Lamb shift to the original Hamiltonian.
  arXiv  Detail & Related papers  (2025-05-13T05:32:34Z)
• Error bounds for composite quantum hypothesis testing and a new characterization of the weighted Kubo-Ando geometric means [14.374467687356281]
  We show that in the commutative case, considering weighted geometric means of the states, and in the case of two states per hypothesis, are optimal for this approach.<n>We also extend our results to composite quantum channel discrimination, and show an analogous optimality property of the weighted Kubo-Ando geometric means of two quantum channels.
  arXiv  Detail & Related papers  (2025-03-17T17:06:27Z)
• Quantum Random Walks and Quantum Oscillator in an Infinite-Dimensional Phase Space [45.9982965995401]
  We consider quantum random walks in an infinite-dimensional phase space constructed using Weyl representation of the coordinate and momentum operators. We find conditions for their strong continuity and establish properties of their generators.
  arXiv  Detail & Related papers  (2024-06-15T17:39:32Z)
• Dilation theorem via Schr\"odingerisation, with applications to the quantum simulation of differential equations [29.171574903651283]
  Nagy's unitary dilation theorem in operator theory asserts the possibility of dilating a contraction into a unitary operator. In this study, we demonstrate the viability of the recently devised Schr"odingerisation approach.
  arXiv  Detail & Related papers  (2023-09-28T08:55:43Z)
• Geometry of quantum complexity [0.0]
  Computational complexity is a new quantum information concept that may play an important role in holography. We consider quantum computational complexity for $n$ qubits using Nielsen's geometrical approach.
  arXiv  Detail & Related papers  (2020-11-15T18:41:19Z)
• The Convergence Indicator: Improved and completely characterized parameter bounds for actual convergence of Particle Swarm Optimization [68.8204255655161]
  We introduce a new convergence indicator that can be used to calculate whether the particles will finally converge to a single point or diverge. Using this convergence indicator we provide the actual bounds completely characterizing parameter regions that lead to a converging swarm.
  arXiv  Detail & Related papers  (2020-06-06T19:08:05Z)

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.