Entanglement distillation on symmetric two-qutrit entangled states of rank five

• URL: http://arxiv.org/abs/2509.21258v1
• Date: Thu, 25 Sep 2025 14:52:56 GMT
• Title: Entanglement distillation on symmetric two-qutrit entangled states of rank five
• Authors: Zihua Song, Lin Chen, Yongge Wang,
• Abstract summary: Entanglement distillation is a key step in quantum information, both theoretically and practically.<n>It has been proven that non-positive-partial transpose (NPT) entangled states of rank at most four is 1-distillable under local operation and classical communications.
• Score: 4.146329485823113
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Entanglement distillation is a key step in quantum information, both theoretically and practically. It has been proven that non-positive-partial transpose (NPT) entangled states of rank at most four is 1-distillable under local operation and classical communications. In this paper we investigate the distillation of a more complex family of NPT entangled states, namely a family of symmetric two-qutrit states $\r$ of rank five with given eigenvectors. We explicitly construct five families of such states by requiring four of the five eigenvalues to be the same. We respectively show that some of them are 1-distillable. It turns out that such states may be not 1-distillable for some interval of eigenvalues. We provide some conditions for eigenvalues that allow $\r$ to be 1-distillable or to be 1-undistillable.

Related papers

• Extracting conserved operators from a projected entangled pair state [5.607590231264275]
  Given a tensor network state, how can we determine conserved operators (including Hamiltonians) for which the state is an eigenstate?<n>We show that our method is still able to extract from exact or variational iPEPS to good precision both frustration-free and non-frustration-free parent Hamiltonians.<n>In particular, we find a 4-site-plaquette local Hamiltonian that approximately has the short-range RVB state as the ground state.
  arXiv  Detail & Related papers  (2025-11-25T18:43:47Z)
• Practical Criteria for Entanglement and Nonlocality in Systems with Additive Observables [44.99833362998488]
  For general bipartite mixed states, a sufficient and necessary mathematical condition for certifying entanglement and/or (Bell) non-locality remains unknown.<n>We derive very simple, handy criteria for detecting entanglement or non-locality in many cases.<n>We illustrate these results by analyzing the potential detection of entanglement and nonlocality in Higgs to ZZ decays at the LHC.
  arXiv  Detail & Related papers  (2025-03-21T16:48:04Z)
• On the extreme points of sets of absolulely separable and PPT states [6.9607365816307]
  The absolutely separable (resp. PPT) states remain separable (resp. positive partial transpose) under any global unitary operation. We show that each extreme point has at most three distinct eigenvalues. We also demonstrate that any extreme point in qutrit-qudit system has at most seven distinct eigenvalues.
  arXiv  Detail & Related papers  (2024-09-22T07:17:25Z)
• Efficient conversion from fermionic Gaussian states to matrix product states [48.225436651971805]
  We propose a highly efficient algorithm that converts fermionic Gaussian states to matrix product states.<n>It can be formulated for finite-size systems without translation invariance, but becomes particularly appealing when applied to infinite systems.<n>The potential of our method is demonstrated by numerical calculations in two chiral spin liquids.
  arXiv  Detail & Related papers  (2024-08-02T10:15:26Z)
• Catalytic and asymptotic equivalence for quantum entanglement [44.99833362998488]
  Many-copy entanglement manipulation procedures allow for highly entangled pure states from noisy states.<n>We show that using an entangled catalyst cannot enhance the singlet distillation rate of a distillable quantum state.<n>Our findings provide a comprehensive understanding of the capabilities and limitations of both catalytic and state transformations of entangled states.
  arXiv  Detail & Related papers  (2023-05-05T12:57:59Z)
• Entanglement distillation in terms of Schmidt rank and matrix rank [7.238541917115604]
  We distill non-positive-partial-transpose (NPT) bipartite states of some given Schmidt rank and matrix rank. We show that all bipartite states of Schmidt rank two are locally equivalent to classical-classical states, and all bipartite states of Schmidt rank three are 1-undistillable.
  arXiv  Detail & Related papers  (2023-04-12T01:50:21Z)
• Growing Schr\"odinger's cat states by local unitary time evolution of product states [0.0]
  We show that, typically, a macroscopically-entangled state naturally grows after a single projective measurement of just one spin in the trivial eigenstate. We identify a condition under which what is growing is a "Schr"odinger's cat state"
  arXiv  Detail & Related papers  (2022-10-27T16:21:28Z)
• Coherent dynamics in a five-level atomic system [62.997667081978825]
  coherent control of multi-partite quantum systems is one of the central prerequisites in quantum information processing. Laser-cooled neon atoms in the metastable state of state $1s2 2s2 2p5 3s$ are prepared. Coherence properties of the prepared states are studied using Ramsey and spin echo measurements.
  arXiv  Detail & Related papers  (2022-10-21T11:44:15Z)
• Rydberg ions in coherent motional states: A new method for determining the polarizability of Rydberg ions [71.05995184390709]
  We present a method for measuring the polarizability of Rydberg ions confined in a Paul trap. The method is easy-to-implement and applicable to different Rydberg states regardless of their principal or angular quantum numbers.
  arXiv  Detail & Related papers  (2022-08-23T17:56:50Z)
• Experimental demonstration of optimal unambiguous two-out-of-four quantum state elimination [52.77024349608834]
  A core principle of quantum theory is that non-orthogonal quantum states cannot be perfectly distinguished with single-shot measurements. Here we implement a quantum state elimination measurement which unambiguously rules out two of four pure, non-orthogonal quantum states.
  arXiv  Detail & Related papers  (2022-06-30T18:00:01Z)
• Constructions of $k$-uniform states from mixed orthogonal arrays [18.378398718548016]
  We study $k$-uniform states in heterogeneous systems whose local dimensions are mixed. We present two constructions of $2$-uniform states in heterogeneous systems. We show that some $k$-uniform bases can not be distinguished by local operations and classical communications.
  arXiv  Detail & Related papers  (2020-06-07T08:35:22Z)
• Entanglement as upper bounded for the nonlocality of a general two-qubit system [16.676050048472963]
  We systematically investigate the relationship between entanglement and nonlocality of a general two-qubit system. We find that the nonlocality of two different two-qubit states can be optimally stimulated by the same nonlocality test setting.
  arXiv  Detail & Related papers  (2020-04-17T16:42:27Z)
• Qutrit and Ququint Magic States [0.0]
  Non-stabilizer eigenstates of Clifford operators are natural candidates for endpoints of magic state distillation routines. We provide an explicit bestiary of all inequivalent non-stabilizer Clifford eigenstates for qutrits and ququints.
  arXiv  Detail & Related papers  (2020-03-16T12:54:09Z)

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.