Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2506.18303 · Quantum Science and Technology

Entanglement detection via third-order local invariants from randomized measurements

Giovanni Scala, Anindita Bera, Gniewomir Sarbicki

Published Nov 10, 2025• 2 citations
arXivHTMLPDF

Abstract

Abstract We compute all third-order local invariants accessible via randomized measurements and employ them to derive separability criteria. The reconstruction of the invariants yields experimentally accessible entanglement criteria for multipartite states with arbitrary local dimensions. The results show that third-order invariants capture inter-subsystem correlations beyond second-order spectral criteria within more feasible entanglement detection protocols than full tomography. As an example, for Werner states in d = 3, the entanglement is detected for p > 1 2 for the second-order correlations and it is improved to p > 1 10 3 at the third-order.

DOI
10.1088/2058-9565/ae1d4b

Related papers

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

Giovanni Scala, Gniewomir Sarbicki

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.

quant-pharXiv:2604.13165•Apr 16, 2026•0 citations

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

Giovanni Scala, Corrado Cosimo Mattiacci, Dorota Pietryka +1 more

Certifying entanglement in high-dimensional systems usually requires full state tomography, whose cost grows rapidly with the system dimension. Local randomized measurements offer a scalable alternative, but existing tests based on second-order correlations access only limited information about the state. Here, we derive a finite-size entanglement certificate that extends local randomized measurements to third order. The additional third-order information reveals entanglement that remains undetected at second order, while a dimension-independent concentration bound provides rigorous control of finite-sample errors. Our result opens a practical route to extracting stronger entanglement information from experimental platforms without the dimension-dependent overhead of state tomography.

quant-pharXiv:2609.08635•Sep 9, 2026•0 citations

Enhanced separability criteria based on symmetric measurements

Yu Lu, Hao-Fan Wang, Meng Su +2 more

We present separability criteria based on local symmetric measurements. These experimental plausible criteria are shown to be more efficient in detecting entanglement than the current counterparts by detailed examples. Furthermore, we generalize the separability criteria from bipartite to arbitrary multipartite systems. These criteria establish a richer connection between the quantum entanglement and the probabilities of local measurement outcomes.

quant-pharXiv:2512.22514•Advanced Quantum Technologies•Dec 30, 2025•0 citations

Complete entanglement detection using polynomial invariants

Thomas C. Fraser, Vjosa Blakaj, Roberto Rubboli +2 more

Existing methods for deciding whether a bipartite quantum state is separable or entangled typically fall into one of two categories: they are either complete but require access to an explicit density matrix followed by numerical optimization, or they can be evaluated directly by measuring the quantum system but are incomplete, in the sense that they cannot detect all forms of entanglement. In this work, we overcome both limitations in a unified framework. First, we bypass numerical optimization by deriving separability criteria in the form of universal bounds on tensor powers of separable states. We prove that these bounds are complete: every entangled state violates them for sufficiently large tensor powers. Second, we explicitly construct a corresponding complete family of nonlinear entanglement witnesses, which can detect all forms of entanglement without requiring an explicit density matrix. The witnesses we construct are moreover basis-independent, in the sense that they are invariant under conjugation by local unitaries. Altogether, our results expand the toolbox for entanglement detection in arbitrary local dimensions in a manifestly invariant way.

quant-pharXiv:2606.16712•Jun 16, 2026•0 citations

Quantum Separability Criteria Based on Symmetric Measurements

Yu Lu, Wen Zhou, Meng Su +3 more

We propose experimentally feasible separability criteria for bipartite systems based on local symmetric measurements. Through detailed examples, we demonstrate that our criteria can detect entanglement more effectively compared to existing counterparts. Furthermore,we demonstrate the potential for our results to be generalized to general multipartite systems.

quant-pharXiv:2512.10380•Physical Review A•Dec 12, 2025•0 citations

Detection of $k$-nonseparable $n$-partite quantum states

Ting Gao, Yan Hong

The detection of multipartite entanglement in arbitrary dimensional systems is investigated. We derive useful $k$-separability criteria of mixed $n$-partite ($n\geq 3$) quantum states to detect $k$-nonseparable $n$-partite quantum states. Our criteria can be expressed by the elements of the density matrix, which allows a simple and practical evaluation and computation. They are experimentally accessible without quantum state tomography.

arXiv:1207.1596•Jul 6, 2012•0 citations
Abstract We compute all third-order local invariants accessible via randomized measurements and employ them to derive separability criteria. The reconstruction of the invariants yields experimentally accessible entanglement criteria for multipartite states with arbitrary local dimensions. The results show that third-order invariants capture inter-subsystem correlations beyond second-order spectral criteria within more feasible entanglement detection protocols than full tomography. As an example, for Werner states in d = 3, the entanglement is detected for p > 1 2 for the second-order correlations and it is improved to p > 1 10 3 at the third-order.
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 4×44\times44×4 matrix Mˉ(ρ)\bar{\mathfrak{M}}(ρ)Mˉ(ρ) built from experimentally accessible second- and third-order local invariants. Entanglement is certified when its minimum eigenvalue E4(ρ)\mathcal{E}_4(ρ)E4​(ρ) becomes negative. We prove that all separable states satisfy Mˉ(ρ)⪰0\bar{\mathfrak{M}}(ρ)\succeq0Mˉ(ρ)⪰0, and that the sign of E4(ρ)\mathcal{E}_4(ρ)E4​(ρ) can be inferred from single-copy randomized measurements with dimension-independent sample complexity. For isotropic states on d×dd\times dd×d, the second-order purity criterion detects entanglement only for p∼d−1/2p\sim d^{-1/2}p∼d−1/2, whereas our third-order witness reaches p∼2/dp\sim 2/dp∼2/d, close to the separability threshold p∼1/dp\sim 1/dp∼1/d. A complementary nonisotropic benchmark shows that the affine marginal directions become essential once the local states are not maximally mixed.
Certifying entanglement in high-dimensional systems usually requires full state tomography, whose cost grows rapidly with the system dimension. Local randomized measurements offer a scalable alternative, but existing tests based on second-order correlations access only limited information about the state. Here, we derive a finite-size entanglement certificate that extends local randomized measurements to third order. The additional third-order information reveals entanglement that remains undetected at second order, while a dimension-independent concentration bound provides rigorous control of finite-sample errors. Our result opens a practical route to extracting stronger entanglement information from experimental platforms without the dimension-dependent overhead of state tomography.
Existing methods for deciding whether a bipartite quantum state is separable or entangled typically fall into one of two categories: they are either complete but require access to an explicit density matrix followed by numerical optimization, or they can be evaluated directly by measuring the quantum system but are incomplete, in the sense that they cannot detect all forms of entanglement. In this work, we overcome both limitations in a unified framework. First, we bypass numerical optimization by deriving separability criteria in the form of universal bounds on tensor powers of separable states. We prove that these bounds are complete: every entangled state violates them for sufficiently large tensor powers. Second, we explicitly construct a corresponding complete family of nonlinear entanglement witnesses, which can detect all forms of entanglement without requiring an explicit density matrix. The witnesses we construct are moreover basis-independent, in the sense that they are invariant under conjugation by local unitaries. Altogether, our results expand the toolbox for entanglement detection in arbitrary local dimensions in a manifestly invariant way.
Detection of kkk-nonseparable nnn-partite quantum states
The detection of multipartite entanglement in arbitrary dimensional systems is investigated. We derive useful kkk-separability criteria of mixed nnn-partite (n≥3n\geq 3n≥3) quantum states to detect kkk-nonseparable nnn-partite quantum states. Our criteria can be expressed by the elements of the density matrix, which allows a simple and practical evaluation and computation. They are experimentally accessible without quantum state tomography.