A low order Bargmann invariant hierarchy for set coherence

• URL: http://arxiv.org/abs/2605.10003v1
• Date: Mon, 11 May 2026 05:28:15 GMT
• Title: A low order Bargmann invariant hierarchy for set coherence
• Abstract summary: Set coherence is a basis-independent form of quantum coherence.<n>We show that fourth-order, ordering-sensitive Bargmann invariants give the first universal pairwise criterion for set coherence.
• Score: 5.255419607027447
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Set coherence is a basis-independent relational form of quantum coherence: a finite family of quantum states is set incoherent exactly when all its members are diagonal in one common basis. We determine how much low-order Bargmann data are needed to decide this property. For two states, second-order data are complete for qubits but fail for qutrits, while complete third-order data are sufficient for qutrits but fail already in dimension four. We then show that fourth-order, ordering-sensitive Bargmann invariants give the first universal pairwise criterion for set coherence. Applied to all unordered pairs, this criterion yields a complete test for arbitrary finite families. The result provides a low-order hierarchy connecting cyclic trace invariants with the noncommutativity that prevents a common incoherent basis.

Related papers

• Byzantine Accountability Without Consensus: Strong Eventual Consistency for Non-Associative, Stochastic, Robust Aggregation [0.0]
  ACFA replicates a content-addressed OR-Set of signed contributions and a grow-only set of self-authenticating equivocation proofs.<n>A prototype (10 nodes, 3 Byzantine) passes 16/16 falsification checks.
  arXiv  Detail & Related papers  (2026-07-11T13:23:06Z)
• Essential Unitarity for Higher-Order Quantum Computation [0.0]
  Morphisms are polarized boundary linkings composed by execution, with a unit-free monoidal sum providing reversible control and branching.<n> Essential unitarity is the unique predicate compatible with dagger-monoidal structure, coherence reindexing, and currying.<n>The framework realizes the coherent quantum switch and other one-slot, equal-ratio, purity-preserving supermaps as coherent pure-comb dilations.
  arXiv  Detail & Related papers  (2026-06-02T17:55:36Z)
• Balanced Aggregation: Understanding and Fixing Aggregation Bias in GRPO [70.38763678943648]
  Reinforcement learning with verifiable rewards (RLVR) has become a central paradigm for improving reasoning and code generation in large language models.<n>Standard GRPO uses sequence aggregation, while recent work has advocated token aggregation as a better alternative.<n>We show that these two rules induce different optimization biases; token aggregation introduces sign-length coupling, while sequence aggregation implicitly downweights longer responses.
  arXiv  Detail & Related papers  (2026-04-14T09:48:46Z)
• An order-oriented approach to scoring hesitant fuzzy elements [4.991981804514581]
  This paper proposes a unified framework, where each score is explicitly defined with respect to a given order.<n>We introduce a class of functions, called dominance functions, for ranking hesitant fuzzy elements.<n>We show that these can be employed to construct fuzzy preference relations on typical hesitant fuzzy sets and support group decision-making.
  arXiv  Detail & Related papers  (2026-02-18T19:48:37Z)
• Indefinite Causal Order from Failure-to-Glue: Contextual Semantics and Parametric Time [0.0]
  Indefinite causal order (ICO) has been studied via higher-order quantum processes.<n>PartI develops a category-theoretic formulation of definite-order explainability as a gluing problem.<n>PartII applies this framework to a quantum-gravity motivated setting.
  arXiv  Detail & Related papers  (2026-01-23T06:44:44Z)
• Multi-state imaginarity and coherence in qubit systems [3.7112567233163003]
  We provide a unitary-invariant framework to pinpoint imaginarity and coherence in sets of qubit states.<n>We also show that the set of imaginarity-free multi-states is not convex, and that third-order invariants completely characterize multi-state imaginarity of single-qubits but not of higher-dimensional systems.
  arXiv  Detail & Related papers  (2025-07-20T09:34:57Z)
• Closing the Gap Between the Upper Bound and the Lower Bound of Adam's Iteration Complexity [51.96093077151991]
  We derive a new convergence guarantee of Adam, with only an $L$-smooth condition and a bounded noise variance assumption. Our proof utilizes novel techniques to handle the entanglement between momentum and adaptive learning rate.
  arXiv  Detail & Related papers  (2023-10-27T09:16:58Z)
• Convergence of Adam Under Relaxed Assumptions [72.24779199744954]
  We show that Adam converges to $epsilon$-stationary points with $O(epsilon-4)$ gradient complexity under far more realistic conditions. We also propose a variance-reduced version of Adam with an accelerated gradient complexity of $O(epsilon-3)$.
  arXiv  Detail & Related papers  (2023-04-27T06:27:37Z)
• Hierarchy of topological order from finite-depth unitaries, measurement and feedforward [0.0]
  Single-site measurements provide a loophole, allowing for finite-time state preparation in certain cases. We show how this observation imposes a complexity hierarchy on long-range entangled states based on the minimal number of measurement layers required to create the state, which we call "shots" This hierarchy paints a new picture of the landscape of long-range entangled states, with practical implications for quantum simulators.
  arXiv  Detail & Related papers  (2022-09-13T17:55:36Z)
• Stochastic Gradient Descent-Ascent and Consensus Optimization for Smooth Games: Convergence Analysis under Expected Co-coercivity [49.66890309455787]
  We introduce the expected co-coercivity condition, explain its benefits, and provide the first last-iterate convergence guarantees of SGDA and SCO. We prove linear convergence of both methods to a neighborhood of the solution when they use constant step-size. Our convergence guarantees hold under the arbitrary sampling paradigm, and we give insights into the complexity of minibatching.
  arXiv  Detail & Related papers  (2021-06-30T18:32:46Z)
• 3D Correspondence Grouping with Compatibility Features [51.869670613445685]
  We present a simple yet effective method for 3D correspondence grouping. The objective is to accurately classify initial correspondences obtained by matching local geometric descriptors into inliers and outliers. We propose a novel representation for 3D correspondences, dubbed compatibility feature (CF), to describe the consistencies within inliers and inconsistencies within outliers.
  arXiv  Detail & Related papers  (2020-07-21T02:39:48Z)
• Quantum Communication Complexity of Distribution Testing [114.31181206328276]
  Two players each receive $t$ samples from one distribution over $[n]$. The goal is to decide whether their two distributions are equal, or are $epsilon$-far apart. We show that the quantum communication complexity of this problem is $tildeO$(tepsilon2))$ qubits when distributions have low $l$-norm.
  arXiv  Detail & Related papers  (2020-06-26T09:05:58Z)

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.