Identifying local unitary equivalence based on reduction of quantum states

• URL: http://arxiv.org/abs/2607.20266v1
• Date: Wed, 22 Jul 2026 15:19:37 GMT
• Title: Identifying local unitary equivalence based on reduction of quantum states
• Abstract summary: Local unitary equivalence is central to quantification entanglement and classification.<n>We map each state to a reduced state" by nullifying the highest-multiplicity eigenvalue.<n>We prove the local unitary equivalence of the original states is equivalent to that of their reduced counterparts.
• Score: 1.2598422062985142
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Local unitary equivalence is central to entanglement quantification and classification. Identifying the local unitary equivalence remains a formidable challenge. We address this problem for a class of quantum states with one highly degenerate eigenvalue and the rest non-degenerate simple eigenvalues that are pivotal to structured resources in quantum resource theory. We introduce a ``reduction" procedure that maps each state to a ``reduced state" by nullifying the highest-multiplicity eigenvalue and prove that the local unitary equivalence of the original states is equivalent to that of their reduced counterparts. For the resulting pure or non-degenerate reduced states, we employ the existing invariants or fixed-point subgroup criteria to establish a complete discrimination framework, although the existing criteria can not directly identify the local unitary equivalence of the original states. We also verify the local unitary equivalence of two families of single-parameterized multipartite mixed states constructed by perturbing absolutely maximally entangled states from distinct combinatorial origins, demonstrating the efficacy and generality of our approach.

Related papers

• Characterizing Heterogeneous Rates in Finite Mixture Estimation via Partial Optimal Transport [88.55403215843967]
  Voronoi-based partial optimal transport (VPOT) for obtaining refined local and global convergence guarantees for the maximum likelihood estimator of the mixing measure.<n>Results hold in arbitrary fixed dimension without requiring mixing proportions to be uniformly bounded away from zero or prior knowledge of the true number of mixture components.
  arXiv  Detail & Related papers  (2026-09-15T04:32:53Z)
• Distributed Learning of Quantum State Tomography Robust to Readout Errors [28.619101416652395]
  This paper introduces a unified framework for joint regional quantum state tomography with readout errors.<n>A multiqubit system is partitioned in overlapping regions, each region is assigned to a local density operator and a local confusion matrix.<n>We show that joint estimation improves state recovery over fixed-readout reconstruction, recovers a substantial portion of oracle performance, and reveals a clear tradeoff between state estimation performance, communication, and computation.
  arXiv  Detail & Related papers  (2026-04-15T21:22:08Z)
• Revisiting the Role of State Texture in Gate Identification and Fixed-Point Resource Theories [40.119993515374325]
  We revisit a protocol for identifying controlled-NOT gates versus single-qubit-only gates in quantum circuits.<n>We show that a more general fidelity-based formulation succeeds for nearly all laboratory bases.<n>We introduce a family of "fixed-point resource theories" that includes fixed-point instances of the theories of state texture, genuine coherence, purity, and athermality.
  arXiv  Detail & Related papers  (2026-02-26T00:22:58Z)
• Conclusive Local State Marking: More Nonlocality With No Entanglement [0.0]
  Nonlocality exhibited by ensembles of composite quantum states is a striking nonclassical feature of quantum theory.<n>We show that certain ensembles of product states can exhibit a stronger form of nonlocality than entangled ensembles traditionally considered highly nonlocal.
  arXiv  Detail & Related papers  (2025-06-11T05:59:42Z)
• Local Unitary Equivalence of Tripartite Quantum States In Terms of Trace Identities [0.0]
  We present a modified version of the proof given Jing-Yang-Zhao's paper "Local Unitary Equivalence of Quantum States"<n>We are able to generalize this correspondence to tripartite quantum states.
  arXiv  Detail & Related papers  (2025-03-08T14:52:14Z)
• General detectability measure [45.85698554568285]
  Distinguishing resource states from resource-free states is a fundamental task in quantum information.<n>We derived the optimal exponential decay rate of the failure probability for detecting a given $n$-tensor product state.
  arXiv  Detail & Related papers  (2025-01-16T05:39:22Z)
• Local unitary equivalence of arbitrary-dimensional multipartite quantum states [19.34942152423892]
  Local unitary equivalence is an ingredient for quantifying and classifying entanglement. We find a variety of local unitary invariants for arbitrary-dimensional bipartite quantum states. We apply these invariants to estimate concurrence, a vital entanglement measure.
  arXiv  Detail & Related papers  (2024-02-21T02:57:46Z)
• Locally unidentifiable subset of quantum states and its resourcefulness in secret password distribution [0.0]
  We introduce a hitherto unexplored form of quantum nonlocality, termed local subset unidentifiability. We show that this nonlocality is stronger than other existing forms of quantum nonlocality. We anticipate potential applications of this nonlocality for future quantum technologies.
  arXiv  Detail & Related papers  (2022-09-22T12:17:11Z)
• Non-standard entanglement structure of local unitary self-dual models as a saturated situation of repeatability in general probabilistic theories [61.12008553173672]
  We show the existence of infinite structures of quantum composite system such that it is self-dual with local unitary symmetry. We also show the existence of a structure of quantum composite system such that non-orthogonal states in the structure are perfectly distinguishable.
  arXiv  Detail & Related papers  (2021-11-29T23:37:58Z)
• Unextendible entangled bases and more nonlocality with less entanglement [0.0]
  We show that the phenomenon of more nonlocality with less entanglement can be observed for two qubits, while still being at the single-copy level. The results are potentially useful for secure quantum communication technologies with an optimal amount of resources.
  arXiv  Detail & Related papers  (2021-03-16T15:33:44Z)
• Localisation in quasiperiodic chains: a theory based on convergence of local propagators [68.8204255655161]
  We present a theory of localisation in quasiperiodic chains with nearest-neighbour hoppings, based on the convergence of local propagators. Analysing the convergence of these continued fractions, localisation or its absence can be determined, yielding in turn the critical points and mobility edges. Results are exemplified by analysing the theory for three quasiperiodic models covering a range of behaviour.
  arXiv  Detail & Related papers  (2021-02-18T16:19:52Z)
• Unifying Two Notions of Nonlocality in Quantum Theory [0.0]
  We prove that a full product basis can create entangled states if and only if the full bases or any subspace of it become irreducible in the process of LOCC discrimination. For a set having entangled states, we modify the quantity accordingly and show that it can provide an explanation for the phenomena of more nonlocality with less entanglement.
  arXiv  Detail & Related papers  (2020-09-09T12:13:39Z)

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.