估计随机多部量子态的纠缠

IF 5.1 2区 物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY
Quantum Pub Date : 2025-10-01 DOI:10.22331/q-2025-10-01-1870
Khurshed P. Fitter, Cécilia Lancien, Ion Nechita
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引用次数: 0

摘要

给定多部纯量子态的真正多部纠缠可以通过其纠缠的几何度量来量化,该度量直到对数,仅仅是相应单位张量与积单位张量的最大重叠,这个量也被称为张量的内射范数。我们在这项工作中的一般目标是估计随机采样张量的内射范数。为此,我们研究并比较了各种算法,这些算法要么基于广泛使用的交替最小二乘法,要么基于一种新的归一化梯度下降方法,并且适用于对称或非对称随机张量。我们首先在对称实高斯张量的情况下对它们各自的性能进行了比较,这些实高斯张量的渐近平均内射范数是解析已知的。在确定了我们提出的归一化梯度下降算法通常表现最好之后,我们然后使用它来获得复高斯张量(即,直到归一化,均匀分布的多部纯量子态)的平均内射范数的数值估计,具有或不具有置换不变性。我们还估计了由高斯局部张量构成的随机矩阵积态的平均内射范数,不论有无平移不变性。所有这些结果构成了在各种随机多部纯态模型中典型存在的真正多部纠缠量的第一个数值估计。最后,根据我们的数值结果,我们对随机高斯张量(实张量和复张量)和高斯MPS在物理维的渐近极限下的内射模提出了两个猜想。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Estimating the entanglement of random multipartite quantum states
Genuine multipartite entanglement of a given multipartite pure quantum state can be quantified through its geometric measure of entanglement, which, up to logarithms, is simply the maximum overlap of the corresponding unit tensor with product unit tensors, a quantity that is also known as the injective norm of the tensor. Our general goal in this work is to estimate this injective norm of randomly sampled tensors. To this end, we study and compare various algorithms, based either on the widely used alternating least squares method or on a novel normalized gradient descent approach, and suited to either symmetrized or non-symmetrized random tensors. We first benchmark their respective performances on the case of symmetrized real Gaussian tensors, whose asymptotic average injective norm is known analytically. Having established that our proposed normalized gradient descent algorithm generally performs best, we then use it to obtain numerical estimates for the average injective norm of complex Gaussian tensors (i.e., up to normalization, uniformly distributed multipartite pure quantum states), with or without permutation-invariance. We also estimate the average injective norm of random matrix product states constructed from Gaussian local tensors, with or without translation-invariance. All these results constitute the first numerical estimates on the amount of genuinely multipartite entanglement typically present in various models of random multipartite pure states. Finally, motivated by our numerical results, we posit two conjectures on the injective norms of random Gaussian tensors (real and complex) and Gaussian MPS in the asymptotic limit of the physical dimension.
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来源期刊
Quantum
Quantum Physics and Astronomy-Physics and Astronomy (miscellaneous)
CiteScore
9.20
自引率
10.90%
发文量
241
审稿时长
16 weeks
期刊介绍: Quantum is an open-access peer-reviewed journal for quantum science and related fields. Quantum is non-profit and community-run: an effort by researchers and for researchers to make science more open and publishing more transparent and efficient.
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