A minimal qutrit counterexample to Conjecture 4.9 of Lesniewski and Ruskai

• URL: http://arxiv.org/abs/2608.15464v1
• Date: Sun, 16 Aug 2026 01:11:59 GMT
• Title: A minimal qutrit counterexample to Conjecture 4.9 of Lesniewski and Ruskai
• Abstract summary: Lesniewski and Ruskai conjectured that the contraction coefficient of every monotone metric under a unital contraction map equals the Hilbert--space on the traceless sub.<n>We disprove the conjecture with an explicit entanglement-breakingtrit channel induced by a doubly $3times3$ matrix.<n>A theorem of Hiai and Ruskai establishes the conjectured identity for all unital qubit maps, so three dimension is minimal among full matrix algebras.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Lesniewski and Ruskai conjectured that the contraction coefficient of every monotone Riemannian metric under a unital stochastic map equals the Hilbert--Schmidt contraction on the traceless subspace. We disprove the conjecture with an explicit entanglement-breaking qutrit channel induced by a doubly stochastic $3\times3$ matrix. A faithful diagonal state and a commuting traceless tangent give, simultaneously for every normalized monotone metric, the exact lower bound $η^{\mathrm{Riem}}_κ(Φ_K)\ge 8896/20007>(62+2\sqrt{61})/225=Λ_2(Φ_K^{\dagger}Φ_K)$. The counterexample is entirely classical on a maximal abelian subalgebra. A theorem of Hiai and Ruskai establishes the conjectured identity for all unital qubit maps, so dimension three is minimal among full matrix algebras.

Related papers

• Nonmaximal sums of maximally monotone operators under Rockafellar's constraint qualification [0.701633634930651]
  We construct counterexamples to Rockafellar's sum conjecture in which two maximally monotone operators satisfy the interior-domain condition but their sum is not maximally monotone.<n>We compute the entire monotone polar of a class of graphs, gives a necessary and sufficient condition for their maximal monotonicity, and shows how a positive rank-one perturbation yields a nonmaximal sum under this condition.
  arXiv  Detail & Related papers  (2026-09-09T17:26:26Z)
• A Complete Classification of Complex Hadamard Matrices of Order Six [0.0]
  Complex Hadamard matrices encode perfectly balanced unitary transformations.<n>Their classification is complete through order five, but order six has remained open for decades.<n>Our work resolves the classification problem and provides a rigorous framework for further investigating order-six Hadamards.
  arXiv  Detail & Related papers  (2026-08-18T17:46:58Z)
• A Direct Route to Markov Chain Convergence via Asymptotic Equivalence with the Target [16.08983109077834]
  We give a self-contained proof of the Markov chain convergence theorem via a criterion called equivalence with the target.<n>A density version of this criterion is verified on general measurable spaces in three cases.<n>In all mentioned settings Birkhoff's ergodic theorem applies, so as to obtain the strong law of large numbers.
  arXiv  Detail & Related papers  (2026-08-04T09:03:20Z)
• The Kikuchi Hierarchy is Sharp for $k$XOR [46.26532142699448]
  We show that a normalized variant of the Kikuchi hierarchy achieves the sharp conjectured trade-off, with no logarithmic loss, at every arity $kge3$.<n>We also prove matching lower bounds in the same model. The inference and refutation upper bounds transfer to more general planting laws and predicates.
  arXiv  Detail & Related papers  (2026-07-31T17:54:11Z)
• Self-Normalized Martingales and Uniform Regret Bounds for Linear Regression [65.82017723631897]
  We show that scale-invariant upper bounds on self-normalized martingales are possible.<n>We derive a self-normalized concentration inequality free of the usual regularization penalties.
  arXiv  Detail & Related papers  (2026-05-02T22:39:00Z)
• Quantum two-dimensional superintegrable systems in flat space: exact-solvability, hidden algebra, polynomial algebra of integrals [41.99844472131922]
  It includes the Smorodinsky-Winternitz potentials I-II (the Holt potential), the Fokas-Lagerstrom model, the 3-body Calogero and Wolfes (equivalently, $G$ rational, or $I_6$) models.<n>It is shown that all of them are exactly-solvable, thus, confirming the Montreal conjecture.<n>Each model is characterized by infinitely-many finite-dimensional invariant subspaces, which form the infinite flag.
  arXiv  Detail & Related papers  (2025-12-30T07:39:35Z)
• Geometry of degenerate quantum states, configurations of $m$-planes and invariants on complex Grassmannians [55.2480439325792]
  We show how to reduce the geometry of degenerate states to the non-abelian connection $A$. We find independent invariants associated with each triple of subspaces. Some of them generalize the Berry-Pancharatnam phase, and some do not have analogues for 1-dimensional subspaces.
  arXiv  Detail & Related papers  (2024-04-04T06:39:28Z)
• Rigorous derivation of the Efimov effect in a simple model [68.8204255655161]
  We consider a system of three identical bosons in $mathbbR3$ with two-body zero-range interactions and a three-body hard-core repulsion of a given radius $a>0$.
  arXiv  Detail & Related papers  (2023-06-21T10:11:28Z)
• Discreteness of asymptotic tensor ranks [7.378597079944368]
  We show that the subrank and the slice rank have no accumulation points, and that over the complex numbers, the slice rank has no accumulation points.<n>Central to our approach are two new general lower bounds on the subrank of tensors, which measures how much a tensor can be diagonalized.<n>Our rely on new lower bounds on the maximum rank in matrix subspaces that are obtained by slicing a three-tensor in the three different directions.
  arXiv  Detail & Related papers  (2023-06-02T17:42:39Z)
• Annihilating Entanglement Between Cones [77.34726150561087]
  We show that Lorentz cones are the only cones with a symmetric base for which a certain stronger version of the resilience property is satisfied. Our proof exploits the symmetries of the Lorentz cones and applies two constructions resembling protocols for entanglement distillation.
  arXiv  Detail & Related papers  (2021-10-22T15:02:39Z)
• Learning with symmetric positive definite matrices via generalized Bures-Wasserstein geometry [40.23168342389821]
  We propose a novel generalization of the Bures-Wasserstein geometry, which we call the GBW geometry. We provide a rigorous treatment to study various differential geometric notions on the proposed novel generalized geometry. We also present experiments that illustrate the efficacy of the proposed GBW geometry over the BW geometry.
  arXiv  Detail & Related papers  (2021-10-20T10:03:06Z)
• Representation of symmetry transformations on the sets of tripotents of spin and Cartan factors [0.0]
  We prove that in order that the description of the spin will be relativistic, it is not enough to preserve the projection lattice equipped with its natural partial order and denoteity. This, in particular, extends a result of Moln'ar to the wider setting of atomic JBW$*$-triples not containing rank-one Cartan factors.
  arXiv  Detail & Related papers  (2021-01-03T17:21:02Z)

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.