Unveiling NPT bound problem: From Distillability Sets to Inequalities and Multivariable Insights

• URL: http://arxiv.org/abs/2402.18037v1
• Date: Wed, 28 Feb 2024 04:29:10 GMT
• Title: Unveiling NPT bound problem: From Distillability Sets to Inequalities and Multivariable Insights
• Authors: Si-Yuan Qi, Geni Gupur, Yu-Chun Wu, Guo-Ping Guo
• Abstract summary: Equivalence between Positive Partial Transpose (PPT) entanglement and bound entanglement is a long-standing open problem in quantum information theory. We propose a decomposition of the Nundi-Nundistillability verification verification.
• Score: 5.902307331486972
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Equivalence between Positive Partial Transpose (PPT) entanglement and bound entanglement is a long-standing open problem in quantum information theory. So far limited progress has been made, even on the seemingly simple case of Werner states bound entanglement. The primary challenge is to give a concise mathematical representation of undistillability. To this end, we propose a decomposition of the N-undistillability verification into $log(N)$ repeated steps of 1-undistillability verification. For Werner state N-undistillability verification, a bound for N-undistillability is given, which is independent of the dimensionality of Werner states. Equivalent forms of inequalities for both rank one and two matrices are presented, before transforming the two-undistillability case into a matrix analysis problem. A new perspective is also attempted by seeing it as a non-convex multi-variable function, proving its critical points and conjecturing Hessian positivity, which would make them local minimums.

Related papers

• Ultracold Neutrons in the Low Curvature Limit: Remarks on the post-Newtonian effects [49.1574468325115]
  We apply a perturbative scheme to derive the non-relativistic Schr"odinger equation in curved spacetime. We calculate the next-to-leading order corrections to the neutron's energy spectrum. While the current precision for observations of ultracold neutrons may not yet enable to probe them, they could still be relevant in the future or in alternative circumstances.
  arXiv  Detail & Related papers  (2023-12-30T16:45:56Z)
• New Partial Trace Inequalities and Distillability of Werner States [0.0]
  This work presents a new strategy to try to solve the problem by translating the distillability condition on the family of Werner states into a problem of partial trace inequalities. We obtain a new bound for the $2$-distillability of Werner states, which does not depend on the dimension of the system. On the other hand, our second main result provides new partial trace inequalities for bipartite systems, connecting some of them also with the separability of Werner states.
  arXiv  Detail & Related papers  (2023-10-09T13:55:35Z)
• Real-time dynamics of false vacuum decay [49.1574468325115]
  We investigate false vacuum decay of a relativistic scalar field in the metastable minimum of an asymmetric double-well potential. We employ the non-perturbative framework of the two-particle irreducible (2PI) quantum effective action at next-to-leading order in a large-N expansion.
  arXiv  Detail & Related papers  (2023-10-06T12:44:48Z)
• Symmetry Resolved Entanglement of Excited States in Quantum Field Theory III: Bosonic and Fermionic Negativity [0.0]
  We study the resolved R'enyi entropies of quasi-particle excited states in quantum field theory. We compute the ratio of charged moments of the partially transposed reduced density matrix as an expectation value of twist operators. We find that although the operation of partial transposition requires a redefinition for fermionic theories, the ratio of the negativity moments between an excited state and the ground state is universal and identical for fermions and bosons.
  arXiv  Detail & Related papers  (2023-02-06T10:05:58Z)
• Global Nash Equilibrium in Non-convex Multi-player Game: Theory and Algorithms [66.8634598612777]
  We show that Nash equilibrium (NE) is acceptable to all players in a multi-player game. We also show that no one can benefit unilaterally from the general theory step by step.
  arXiv  Detail & Related papers  (2023-01-19T11:36:50Z)
• Exact solution of a family of staggered Heisenberg chains with conclusive pretty good quantum state transfer [68.8204255655161]
  We work out the exact solutions in the one-excitation subspace. We present numerical evidence that pretty good transmission is achieved by chains whose length is not a power of two.
  arXiv  Detail & Related papers  (2022-06-28T18:31:09Z)
• Stochastic approximate state conversion for entanglement and general quantum resource theories [41.94295877935867]
  An important problem in any quantum resource theory is to determine how quantum states can be converted into each other. Very few results have been presented on the intermediate regime between probabilistic and approximate transformations. We show that these bounds imply an upper bound on the rates for various classes of states under probabilistic transformations. We also show that the deterministic version of the single copy bounds can be applied for drawing limitations on the manipulation of quantum channels.
  arXiv  Detail & Related papers  (2021-11-24T17:29:43Z)
• Dimension-free entanglement detection in multipartite Werner states [1.5771347525430772]
  Werner states are multipartite quantum states that are invariant under the diagonal conjugate action of the unitary group. This paper gives a complete characterization of their entanglement that is independent of the underlying local space. For every entangled Werner state there exists a dimension-free entanglement witness.
  arXiv  Detail & Related papers  (2021-08-19T14:41:09Z)
• Lifting the Convex Conjugate in Lagrangian Relaxations: A Tractable Approach for Continuous Markov Random Fields [53.31927549039624]
  We show that a piecewise discretization preserves better contrast from existing discretization problems. We apply this theory to the problem of matching two images.
  arXiv  Detail & Related papers  (2021-07-13T12:31:06Z)
• A new parameterized entanglement monotone [3.267240600491982]
  Entanglement concurrence has been widely used for featuring entanglement in quantum experiments. We propose a new parameterized bipartite entanglement monotone named as $q$-concurrence inspired by general Tsallis entropy.
  arXiv  Detail & Related papers  (2021-01-12T01:38:55Z)
• The Decompositions of Werner and Isotropic States [0.5156484100374059]
  decompositions of separable Werner state, and also isotropic state, are well-known tough issues in quantum information theory. We successfully get the decomposition for arbitrary $Ntimes N$ Werner state in terms of regular simplexes. The decomposition of isotropic state is found to be related to the decomposition of Werner state via partial transposition.
  arXiv  Detail & Related papers  (2020-03-02T07:13:04Z)
• Einselection from incompatible decoherence channels [62.997667081978825]
  We analyze an open quantum dynamics inspired by CQED experiments with two non-commuting Lindblad operators. We show that Fock states remain the most robust states to decoherence up to a critical coupling.
  arXiv  Detail & Related papers  (2020-01-29T14:15:19Z)

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.