Third-Order Local Randomized Measurements for Finite-size Entanglement Certification

• URL: http://arxiv.org/abs/2604.13165v1
• Date: Tue, 14 Apr 2026 18:00:02 GMT
• Title: Third-Order Local Randomized Measurements for Finite-size Entanglement Certification
• Abstract summary: Entanglement is certified when its minimum eigenvalue $mathcalE_4()$ becomes negative.<n>We prove that all separable states satisfy $barmathfrakM()succeq0$, and that the sign of $mathcalE_4()$ can be inferred from single-copy randomized measurements.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Randomized measurements access nonlinear functionals without full tomography, yet turning third-order local single-copy data into a strong entanglement test remains difficult. We convert the reduction criterion into an experimentally measurable separability criterion by testing it on squared affine combinations of the identity, the local marginals, and the state itself. This yields a $4\times4$ matrix $\bar{\mathfrak{M}}(ρ)$ built from experimentally accessible second- and third-order local invariants. Entanglement is certified when its minimum eigenvalue $\mathcal{E}_4(ρ)$ becomes negative. We prove that all separable states satisfy $\bar{\mathfrak{M}}(ρ)\succeq0$, and that the sign of $\mathcal{E}_4(ρ)$ can be inferred from single-copy randomized measurements with dimension-independent sample complexity. For isotropic states on $d\times d$, the second-order purity criterion detects entanglement only for $p\sim d^{-1/2}$, whereas our third-order witness reaches $p\sim 2/d$, close to the separability threshold $p\sim 1/d$. A complementary nonisotropic benchmark shows that the affine marginal directions become essential once the local states are not maximally mixed.

Related papers

• Exact Entanglement Swapping through Single-Occupancy Measurements in Gaussian Fermion States [0.0]
  We determine the entanglement structure of the conditional state obtained by measuring $m$ corresponding rungs in two identical copies.<n>We find that the entanglement entropy between the unmeasured parts of the two copies is independent of the initial state.<n>The success probability is given by $P_m=det C_Ldet(I_m-C_L)=det(C_LRC_RL)$, determined solely by the initial correlations.
  arXiv  Detail & Related papers  (2026-08-30T18:01:55Z)
• Robust Average-Reward Markov Decision Processes: Minimax-Optimal Learning via Plug-in Reductions [51.50375419691955]
  Distributionally robust Markov decision processes provide a principled framework for sequential decision making under model uncertainty.<n>We study how many samples are necessary and sufficient to learn an $varepsilon$-optimal robust policy under the average-reward criterion.
  arXiv  Detail & Related papers  (2026-08-06T19:49:48Z)
• Detecting entanglement of non-Gaussian continuous-variable states from single-copy homodyne measurements [0.047056701241378535]
  Non-Gaussian entanglement detection remains an experimental challenge.<n>$p_3$-PPT criterion detects entanglement using moments of the partial transpose of the density matrix.<n>We introduce a single-copy homodyne protocol that detects bipartite CV entanglement via the same criterion.
  arXiv  Detail & Related papers  (2026-06-27T02:55:23Z)
• Optimal Dimension-Free Sampling for Regularized Classification [56.72526267755301]
  We prove optimal sampling bounds achieving $(1pmvarepsilon)$-relative error for a broad class of Lipschitz continuous classification loss functions.<n>This includes important functions such as logistic and sigmoid loss, hinge loss, and ReLU loss, as prominent and popular representative examples.
  arXiv  Detail & Related papers  (2026-05-22T15:05:33Z)
• Mean Testing under Truncation beyond Gaussian [3.9925887361256134]
  truncation induces a bias of order $O(_P,pvarepsilon1-1/p)$ for distributions with magnitudes of magnitude at most $_P,p$.<n>We show that under a directional median regularity assumption, truncation bias improves to linear order $O(varepsilon)$.<n>Our results provide a unified framework for mean testing under truncation, connecting finite-moment, sub-Gaussian, and median-regular structural regimes.
  arXiv  Detail & Related papers  (2026-05-02T09:13:50Z)
• Fixed-PVM Born Rule Uniqueness from Fisher Non-Expansion and Operational Calibration [0.0]
  We prove that three primitives force the Born rule for this fixed measurement.<n>The main readout theorem is dimensionwise, fixed-PVM, and pure-state only.
  arXiv  Detail & Related papers  (2026-04-30T02:31:19Z)
• Optimal Scalar Quantization for Matrix Multiplication: Closed-Form Density and Phase Transition [50.36362492608702]
  We study entrywise scalar quantization of two matrices prior to multiplication.<n>We obtain a closed-form optimal point density [ star(u) propto exp!left(-fracu26right)bigl( (1-2)+2u22bigr), qquad u=fracx_X,, and prove a correlation-driven phase transition.
  arXiv  Detail & Related papers  (2026-03-20T01:53:44Z)
• On the Sparsifiability of Correlation Clustering: Approximation Guarantees under Edge Sampling [6.908972852063454]
  Correlation Clustering (CC) is a fundamental unsupervised learning primitive.<n>We study how much edge information is needed to retain LP-based guarantees.<n>We show via Yao's minimax principle that without pseudometric structure, any algorithm observing $o(n)$ uniformly random edges incurs an approximation ratio.
  arXiv  Detail & Related papers  (2026-02-14T09:12:15Z)
• Instance-optimal high-precision shadow tomography with few-copy measurements: A metrological approach [2.956729394666618]
  We study the sample complexity of shadow tomography in the high-precision regime.<n>We use possibly adaptive measurements that act on $O(mathrmpolylog(d))$ number of copies of $$ at a time.
  arXiv  Detail & Related papers  (2026-02-04T19:00:00Z)
• Entanglement detection via third-order local invariants from randomized measurements [0.0]
  We compute all third-order local invariants accessible via randomised measurements and employ them to derive separability criteria.<n>The reconstruction of the invariants yields experimentally accessible entanglement criteria for multipartite states with arbitrary local dimensions.
  arXiv  Detail & Related papers  (2025-06-23T05:41:07Z)
• Dimension-free Private Mean Estimation for Anisotropic Distributions [55.86374912608193]
  Previous private estimators on distributions over $mathRd suffer from a curse of dimensionality. We present an algorithm whose sample complexity has improved dependence on dimension.
  arXiv  Detail & Related papers  (2024-11-01T17:59:53Z)
• Learning with Norm Constrained, Over-parameterized, Two-layer Neural Networks [54.177130905659155]
  Recent studies show that a reproducing kernel Hilbert space (RKHS) is not a suitable space to model functions by neural networks. In this paper, we study a suitable function space for over- parameterized two-layer neural networks with bounded norms.
  arXiv  Detail & Related papers  (2024-04-29T15:04:07Z)
• A New Framework for Variance-Reduced Hamiltonian Monte Carlo [88.84622104944503]
  We propose a new framework of variance-reduced Hamiltonian Monte Carlo (HMC) methods for sampling from an $L$-smooth and $m$-strongly log-concave distribution. We show that the unbiased gradient estimators, including SAGA and SVRG, based HMC methods achieve highest gradient efficiency with small batch size. Experimental results on both synthetic and real-world benchmark data show that our new framework significantly outperforms the full gradient and gradient HMC approaches.
  arXiv  Detail & Related papers  (2021-02-09T02:44:24Z)
• SDP Achieves Exact Minimax Optimality in Phase Synchronization [19.909352968029584]
  We study the phase synchronization problem with noisy measurements $Y=z*z*+sigma WinmathbbCntimes ntimes n. We prove that SDP achieves error bound $ (1+o)fracnp22np$ under a squared $ell$ loss.
  arXiv  Detail & Related papers  (2021-01-07T03:14:05Z)
• The Sample Complexity of Robust Covariance Testing [56.98280399449707]
  We are given i.i.d. samples from a distribution of the form $Z = (1-epsilon) X + epsilon B$, where $X$ is a zero-mean and unknown covariance Gaussian $mathcalN(0, Sigma)$. In the absence of contamination, prior work gave a simple tester for this hypothesis testing task that uses $O(d)$ samples. We prove a sample complexity lower bound of $Omega(d2)$ for $epsilon$ an arbitrarily small constant and $gamma
  arXiv  Detail & Related papers  (2020-12-31T18:24:41Z)
• How isotropic kernels perform on simple invariants [0.5729426778193397]
  We investigate how the training curve of isotropic kernel methods depends on the symmetry of the task to be learned. We show that for large bandwidth, $beta = fracd-1+xi3d-3+xi$, where $xiin (0,2)$ is the exponent characterizing the stripe of the kernel at the origin.
  arXiv  Detail & Related papers  (2020-06-17T09:59:18Z)
• Sample Complexity of Asynchronous Q-Learning: Sharper Analysis and Variance Reduction [63.41789556777387]
  Asynchronous Q-learning aims to learn the optimal action-value function (or Q-function) of a Markov decision process (MDP) We show that the number of samples needed to yield an entrywise $varepsilon$-accurate estimate of the Q-function is at most on the order of $frac1mu_min (1-gamma)5varepsilon2+ fract_mixmu_min (1-gamma)$ up to some logarithmic factor.
  arXiv  Detail & Related papers  (2020-06-04T17:51:00Z)

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.