More on genuine multi-entropy and holography

• URL: http://arxiv.org/abs/2504.16589v2
• Date: Thu, 24 Apr 2025 12:52:52 GMT
• Title: More on genuine multi-entropy and holography
• Authors: Norihiro Iizuka, Simon Lin, Mitsuhiro Nishida,
• Abstract summary: We give a prescription on how to construct $rm GM[mathttq]$ systematically for any $mathttq$.<n>For general $mathttq$, $rm GM[mathttq]$ contains $N (mathttq)-p(mathttq-1)-1$ number of free parameters.<n>These give $N (mathttq)+1$ number of new diagnostics for genuine $mathttq
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: By generalizing the construction of genuine multi-entropy ${\rm GM}[\mathtt{q}]$ for genuine multi-partite entanglement proposed in the previous paper arXiv:2502.07995, we give a prescription on how to construct ${\rm GM}[\mathtt{q}]$ systematically for any $\mathtt{q}$. The crucial point is that our construction naturally fits to the partition number $p(\mathtt{a})$ of integer $\mathtt{a}$. For general $\mathtt{q}$, ${\rm GM}[\mathtt{q}]$ contains $N (\mathtt{q}) = p(\mathtt{q})-p(\mathtt{q}-1)-1$ number of free parameters. Furthermore, these give $N (\mathtt{q})+1$ number of new diagnostics for genuine $\mathtt{q}$-partite entanglement. Especially for $\mathtt{q}=4$ case, this reproduces not only the known diagnostics pointed out by arXiv:1406.2663, but also a new diagnostics for quadripartite entanglement. We also study these ${\rm GM}[\mathtt{q}]$ for $\mathtt{q} = 4, 5$ in holography and show that these are of the order of ${\cal{O}}\left(1/G_N \right)$ both analytically and numerically. Our results give evidence that genuine multipartite entanglement is ubiquitous in holography. We discuss the connection to quantum error correction and the role of genuine multipartite entanglement in bulk reconstruction.

Related papers

• Algorithmic contiguity from low-degree conjecture and applications in correlated random graphs [0.0]
  We provide evidence of computational hardness for two problems.<n>One of the main ingredient in our proof is to derive certain forms of emphalgorithm contiguity between two probability measures.<n>This framework provides a useful tool for performing reductions between different tasks.
  arXiv  Detail & Related papers  (2025-02-14T00:24:51Z)
• The Communication Complexity of Approximating Matrix Rank [50.6867896228563]
  We show that this problem has randomized communication complexity $Omega(frac1kcdot n2log|mathbbF|)$. As an application, we obtain an $Omega(frac1kcdot n2log|mathbbF|)$ space lower bound for any streaming algorithm with $k$ passes.
  arXiv  Detail & Related papers  (2024-10-26T06:21:42Z)
• Provably learning a multi-head attention layer [55.2904547651831]
  Multi-head attention layer is one of the key components of the transformer architecture that sets it apart from traditional feed-forward models. In this work, we initiate the study of provably learning a multi-head attention layer from random examples. We prove computational lower bounds showing that in the worst case, exponential dependence on $m$ is unavoidable.
  arXiv  Detail & Related papers  (2024-02-06T15:39:09Z)
• SQ Lower Bounds for Learning Mixtures of Linear Classifiers [43.63696593768504]
  We show that known algorithms for this problem are essentially best possible, even for the special case of uniform mixtures. The key technical ingredient is a new construction of spherical designs that may be of independent interest.
  arXiv  Detail & Related papers  (2023-10-18T10:56:57Z)
• SQ Lower Bounds for Learning Bounded Covariance GMMs [46.289382906761304]
  We focus on learning mixtures of separated Gaussians on $mathbbRd$ of the form $P= sum_i=1k w_i mathcalN(boldsymbol mu_i,mathbf Sigma_i)$. We prove that any Statistical Query (SQ) algorithm for this problem requires complexity at least $dOmega (1/epsilon)$.
  arXiv  Detail & Related papers  (2023-06-22T17:23:36Z)
• Learning a Single Neuron with Adversarial Label Noise via Gradient Descent [50.659479930171585]
  We study a function of the form $mathbfxmapstosigma(mathbfwcdotmathbfx)$ for monotone activations. The goal of the learner is to output a hypothesis vector $mathbfw$ that $F(mathbbw)=C, epsilon$ with high probability.
  arXiv  Detail & Related papers  (2022-06-17T17:55:43Z)
• Low-degree learning and the metric entropy of polynomials [44.99833362998488]
  We prove that any (deterministic or randomized) algorithm which learns $mathscrF_nd$ with $L$-accuracy $varepsilon$ requires at least $Omega(sqrtvarepsilon)2dlog n leq log mathsfM(mathscrF_n,d,|cdot|_L,varepsilon) satisfies the two-sided estimate $$c (1-varepsilon)2dlog
  arXiv  Detail & Related papers  (2022-03-17T23:52:08Z)
• The decoherence-free subalgebra of Gaussian Quantum Markov Semigroups [0.0]
  We show that $mathcalN(mathcalT)$ is a type I von Neumann algebra $Linfty(mathbbRd_c;mathbbC)barotimesmathcalB(Gamma(Gamma(mathbbCd))$ determined, up to unitary equivalence, by two natural numbers $d_c,d_fleq d$.
  arXiv  Detail & Related papers  (2021-12-27T16:50:53Z)
• Uncertainties in Quantum Measurements: A Quantum Tomography [52.77024349608834]
  The observables associated with a quantum system $S$ form a non-commutative algebra $mathcal A_S$. It is assumed that a density matrix $rho$ can be determined from the expectation values of observables. Abelian algebras do not have inner automorphisms, so the measurement apparatus can determine mean values of observables.
  arXiv  Detail & Related papers  (2021-12-14T16:29:53Z)
• Threshold Phenomena in Learning Halfspaces with Massart Noise [56.01192577666607]
  We study the problem of PAC learning halfspaces on $mathbbRd$ with Massart noise under Gaussian marginals. Our results qualitatively characterize the complexity of learning halfspaces in the Massart model.
  arXiv  Detail & Related papers  (2021-08-19T16:16:48Z)
• StoqMA meets distribution testing [0.0]
  We provide a novel connection between $mathsfStoqMA$ and distribution testing via reversible circuits. We show that both variants of $mathsfStoqMA$ that without any ancillary random bit and with perfect soundness are contained in $mathsfNP$. Our results make a step towards collapsing the hierarchy $mathsfMA subseteq mathsfStoqMA subseteq mathsfSBP$ [BBT06], in which all classes are contained in $
  arXiv  Detail & Related papers  (2020-11-11T12:30:42Z)

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.