Classifying Density Matrices of 2 and 3 Qubit States Up To LU Equivalence

• URL: http://arxiv.org/abs/2404.07338v3
• Date: Wed, 14 Aug 2024 16:16:40 GMT
• Title: Classifying Density Matrices of 2 and 3 Qubit States Up To LU Equivalence
• Authors: Isaac Dobes, Naihuan Jing,
• Abstract summary: We present a modified version of the proof given Jing-Yang-Zhao's paper titled "Local Unitary Equivalence of Quantum States" We are able to generalize this correspondence to $3$-qubits. All of these results can be extended to $2$ and $3$ qudits if we relax the notion of LU equivalence to quasi-LU equivalence.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper we present a modified version of the proof given Jing-Yang-Zhao's paper titled "Local Unitary Equivalence of Quantum States and Simultaneous Orthogonal Equivalence," which established the correspondance between local unitary equivalence and simultaneous orthogonal equivalence of $2$-qubits. Our modified proof utilizes a hypermatrix algebra framework, and through this framework we are able to generalize this correspondence to $3$-qubits. Finally, we apply a generalization of Specht's criterion (first proved in "Specht's Criterion for Systems of Linear Mappings" by V. Futorney, R. A. Horn, and V. V. Sergeichuk) to reduce the problem of local unitary equivalence of $3$-qubits to checking trace identities and a few other easy-to-check properties. We also note that all of these results can be extended to $2$ and $3$ qudits if we relax the notion of LU equivalence to quasi-LU equivalence, as defined in the aforementioned paper by Jing et. al.

Related papers

• 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" We are able to generalize this correspondence to tripartite quantum states.
  arXiv  Detail & Related papers  (2025-03-08T14:52:14Z)
• Algorithm to Verify Local Equivalence of Stabilizer States [0.0]
  We present an algorithm for verifying the local unitary equivalence of graph and stabilizer states. Our approach reduces the problem to solving a system of linear equations in modular arithmetic.
  arXiv  Detail & Related papers  (2024-10-04T22:51:11Z)
• Unified Framework for Matchgate Classical Shadows [0.0]
  Estimating quantum fermionic properties is a computationally difficult yet crucial task for the study of electronic systems. Recent developments have begun to address this challenge by introducing classical shadows protocols. We propose an approach that unifies these different protocols, proving their equivalence, and deriving from it an optimal sampling scheme.
  arXiv  Detail & Related papers  (2024-09-05T18:01:00Z)
• Separability transitions in topological states induced by local decoherence [0.0]
  We study states with intrinsic topological order subjected to local decoherence from the perspective of separability. We focus on toric codes and the X-cube fracton state and provide evidence for the existence of decoherence-induced separability transitions.
  arXiv  Detail & Related papers  (2023-09-21T08:28:17Z)
• A class of entanglement witnesses and a realignment-like criterion [0.0]
  This framework facilitates the construction of Entanglement Witnesses (EWs) A sufficient condition for positivity is presented. We illustrate effectiveness of this criterion considering examples of Positive Partial Transpose (PPT) entangled states in $3 times 3$ and $3 times 4$ dimensions.
  arXiv  Detail & Related papers  (2023-08-14T09:07:21Z)
• Equivalence Between SE(3) Equivariant Networks via Steerable Kernels and Group Convolution [90.67482899242093]
  A wide range of techniques have been proposed in recent years for designing neural networks for 3D data that are equivariant under rotation and translation of the input. We provide an in-depth analysis of both methods and their equivalence and relate the two constructions to multiview convolutional networks. We also derive new TFN non-linearities from our equivalence principle and test them on practical benchmark datasets.
  arXiv  Detail & Related papers  (2022-11-29T03:42:11Z)
• Threshold size for the emergence of a classical-like behaviour [68.8204255655161]
  We design a procedure to estimate the minimum size beyond which a system is amenable to a classical-like description. The specific case of a magnetic system is considered, with details of a gedanken experiment presented and thoroughly commented.
  arXiv  Detail & Related papers  (2022-03-25T11:31:14Z)
• Three-fold way of entanglement dynamics in monitored quantum circuits [68.8204255655161]
  We investigate the measurement-induced entanglement transition in quantum circuits built upon Dyson's three circular ensembles. We obtain insights into the interplay between the local entanglement generation by the gates and the entanglement reduction by the measurements.
  arXiv  Detail & Related papers  (2022-01-28T17:21:15Z)
• 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)
• Practical Verification of Quantum Properties in Quantum Approximate Optimization Runs [9.661732401406587]
  We show that measurements in no more than 3 out of the possible $3N$ bases can reconstruct the single-qubit reduced density matrices and measure the ability to create coherent superpositions. We demonstrate that a subset of such observables can serve as entanglement witnesses for QAOA-MaxCut states, and further argue that they are especially well tailored for this purpose by defining and computing an entanglement potency metric on witnesses.
  arXiv  Detail & Related papers  (2021-05-04T17:33:15Z)
• GroupifyVAE: from Group-based Definition to VAE-based Unsupervised Representation Disentanglement [91.9003001845855]
  VAE-based unsupervised disentanglement can not be achieved without introducing other inductive bias. We address VAE-based unsupervised disentanglement by leveraging the constraints derived from the Group Theory based definition as the non-probabilistic inductive bias. We train 1800 models covering the most prominent VAE-based models on five datasets to verify the effectiveness of our method.
  arXiv  Detail & Related papers  (2021-02-20T09:49:51Z)
• Bipartite quantum measurements with optimal single-sided distinguishability [0.0]
  We look for a basis with optimal single-sided mutual state distinguishability in $Ntimes N$ Hilbert space. In the case $N=2$ of a two-qubit system our solution coincides with the elegant joint measurement introduced by Gisin. We show that the one-party measurement that distinguishes the states of an optimal basis of the composite system leads to a local quantum state tomography.
  arXiv  Detail & Related papers  (2020-10-28T10:30:35Z)
• 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)

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.