Gaussian unsteerable channels and computable quantifications of Gaussian steering

• URL: http://arxiv.org/abs/2409.00878v2
• Date: Sat, 2 Nov 2024 08:33:13 GMT
• Title: Gaussian unsteerable channels and computable quantifications of Gaussian steering
• Authors: Taotao Yan, Jie Guo, Jinchuan Hou, Xiaofei Qi, Kan He,
• Abstract summary: Current quantum resource theory for Gaussian steering for continuous-variable systems is flawed and incomplete. We introduce the class of the Gaussian unsteerable channels and the class of maximal Gaussian unsteerable channels. We also propose two quantifications $mathcalJ_jj$ of $(m+n)$-mode Gaussian steering from $A$ to $B$.
• Score: 2.3000719681099735
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The current quantum resource theory for Gaussian steering for continuous-variable systems is flawed and incomplete. Its primary shortcoming stems from an inadequate comprehension of the architecture of Gaussian channels transforming Gaussian unsteerable states into Gaussian unsteerable states, resulting in a restricted selection of free operations. In the present paper, we explore in depth the structure of such $(m+n)$-mode Gaussian channels, and introduce the class of the Gaussian unsteerable channels and the class of maximal Gaussian unsteerable channels, both of them may be chosen as the free operations, which completes the resource theory for Gaussian steering from $A$ to $B$ by Alice's Gaussian measurements. We also propose two quantifications $\mathcal{J}_{j}$ $(j=1,2)$ of $(m+n)$-mode Gaussian steering from $A$ to $B$. The computation of the value of $\mathcal{J}_{j}$ is straightforward and efficient, as it solely relies on the covariance matrices of Gaussian states, eliminating the need for any optimization procedures. Though $\mathcal{J}_{j}$s are not genuine Gaussian steering measures, they have some nice properties such as non-increasing under certain Gaussian unsteerable channels. Additionally, we compare ${\mathcal J}_2$ with the Gaussian steering measure $\mathcal N_3$, which is based on the Uhlmann fidelity, revealing that ${\mathcal J}_2$ is an upper bound of $\mathcal N_3$ at certain class of $(1+1)$-mode Gaussian pure states. As an illustration, we apply $\mathcal J_2$ to discuss the behaviour of Gaussian steering for a special class of $(1+1)$-mode Gaussian states in Markovian environments, which uncovers the intriguing phenomenon of rapid decay in quantum steering.

Related papers

• GaussianFormer-2: Probabilistic Gaussian Superposition for Efficient 3D Occupancy Prediction [55.60972844777044]
  3D semantic occupancy prediction is an important task for robust vision-centric autonomous driving. Most existing methods leverage dense grid-based scene representations, overlooking the spatial sparsity of the driving scenes. We propose a probabilistic Gaussian superposition model which interprets each Gaussian as a probability distribution of its neighborhood being occupied.
  arXiv  Detail & Related papers  (2024-12-05T17:59:58Z)
• Sum-of-squares lower bounds for Non-Gaussian Component Analysis [33.80749804695003]
  Non-Gaussian Component Analysis (NGCA) is the statistical task of finding a non-Gaussian direction in a high-dimensional dataset. Here we study the complexity of NGCA in the Sum-of-Squares framework.
  arXiv  Detail & Related papers  (2024-10-28T18:19:13Z)
• A Unified Framework for Uniform Signal Recovery in Nonlinear Generative Compressed Sensing [68.80803866919123]
  Under nonlinear measurements, most prior results are non-uniform, i.e., they hold with high probability for a fixed $mathbfx*$ rather than for all $mathbfx*$ simultaneously. Our framework accommodates GCS with 1-bit/uniformly quantized observations and single index models as canonical examples. We also develop a concentration inequality that produces tighter bounds for product processes whose index sets have low metric entropy.
  arXiv  Detail & Related papers  (2023-09-25T17:54:19Z)
• Constraints on Gaussian Error Channels and Measurements for Quantum Communication [0.0]
  We study joint Gaussian measurements on two modes $mathsfA$ and $mathsfB$ that take place after independent single-mode Gaussian error channels. We show that, for any Gaussian measurement, if $l_mathsfA + l_mathsfB + n_mathsfA + n_mathsfB geq 1$ then the effective total measurement is separable and unsuitable for teleportation or entanglement swapping of arbitrary input states.
  arXiv  Detail & Related papers  (2022-06-23T17:18:13Z)
• Random matrices in service of ML footprint: ternary random features with no performance loss [55.30329197651178]
  We show that the eigenspectrum of $bf K$ is independent of the distribution of the i.i.d. entries of $bf w$. We propose a novel random technique, called Ternary Random Feature (TRF) The computation of the proposed random features requires no multiplication and a factor of $b$ less bits for storage compared to classical random features.
  arXiv  Detail & Related papers  (2021-10-05T09:33:49Z)
• Fundamental limitations to key distillation from Gaussian states with Gaussian operations [4.642647756403864]
  We prove that the key is bounded by the R'enyi-$2$ entanglement of formation $E_F,2mathrmscriptscriptstyle G$. We conjecture that the factor of $2$ is spurious, which would imply that $E_F,2mathrmscriptscriptstyle G$ coincides with the secret key rate of Gaussian states.
  arXiv  Detail & Related papers  (2020-10-29T16:26:46Z)
• Convergence of Sparse Variational Inference in Gaussian Processes Regression [29.636483122130027]
  We show that a method with an overall computational cost of $mathcalO(log N)2D(loglog N)2)$ can be used to perform inference.
  arXiv  Detail & Related papers  (2020-08-01T19:23:34Z)
• Optimal Robust Linear Regression in Nearly Linear Time [97.11565882347772]
  We study the problem of high-dimensional robust linear regression where a learner is given access to $n$ samples from the generative model $Y = langle X,w* rangle + epsilon$ We propose estimators for this problem under two settings: (i) $X$ is L4-L2 hypercontractive, $mathbbE [XXtop]$ has bounded condition number and $epsilon$ has bounded variance and (ii) $X$ is sub-Gaussian with identity second moment and $epsilon$ is
  arXiv  Detail & Related papers  (2020-07-16T06:44:44Z)
• Near-Optimal SQ Lower Bounds for Agnostically Learning Halfspaces and ReLUs under Gaussian Marginals [49.60752558064027]
  We study the fundamental problems of agnostically learning halfspaces and ReLUs under Gaussian marginals. Our lower bounds provide strong evidence that current upper bounds for these tasks are essentially best possible.
  arXiv  Detail & Related papers  (2020-06-29T17:10:10Z)
• Curse of Dimensionality on Randomized Smoothing for Certifiable Robustness [151.67113334248464]
  We show that extending the smoothing technique to defend against other attack models can be challenging. We present experimental results on CIFAR to validate our theory.
  arXiv  Detail & Related papers  (2020-02-08T22:02:14Z)
• A computable multipartite multimode Gaussian correlation measure and the monogamy relation for continuous-variable systems [4.205209248693658]
  A computable multipartite multimode Gaussian quantum correlation measure is proposed. $mathcal M(k)$ satisfies the hierarchy condition that a multipartite quantum correlation measure should obey.
  arXiv  Detail & Related papers  (2020-01-05T14:25:09Z)

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.