Practical Criteria for Entanglement and Nonlocality in Systems with Additive Observables
- URL: http://arxiv.org/abs/2503.17297v1
- Date: Fri, 21 Mar 2025 16:48:04 GMT
- Title: Practical Criteria for Entanglement and Nonlocality in Systems with Additive Observables
- Authors: Alexander Bernal, J. Alberto Casas, Juan Falceto,
- Abstract summary: For general bipartite mixed states, a sufficient and necessary mathematical condition for certifying entanglement and/or (Bell) non-locality remains unknown.<n>We derive very simple, handy criteria for detecting entanglement or non-locality in many cases.<n>We illustrate these results by analyzing the potential detection of entanglement and nonlocality in Higgs to ZZ decays at the LHC.
- Score: 44.99833362998488
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: For general bipartite mixed states, a sufficient and necessary mathematical condition for certifying entanglement and/or (Bell) non-locality remains unknown. In this paper, we examine this question for a broad and physically relevant class of bipartite systems, specifically those possessing an additive observable with a definite value. Such systems include, for example, final states of particle decays or bipartitions of spin chains with well-defined magnetization. We derive very simple, handy criteria for detecting entanglement or non-locality in many cases. For instance, if $\rho_{\left( m p\right)\left( nq\right)} \neq 0$, where the eigenstates $|np\rangle$ or $|mq\rangle$ do not correspond to the given definite value of the additive observable, then the state is necessarily entangled-this condition is very easy to check in practice. If, in addition, the partitioned Hilbert space has dimension 2xd, the condition becomes necessary. Furthermore, if the sectors associated with the eigenstates $|mp\rangle$ or $|nq\rangle$ are non-degenerate, there exists a CHSH inequality that is violated. We illustrate these results by analyzing the potential detection of entanglement and nonlocality in Higgs to ZZ decays at the LHC.
Related papers
- Hamiltonians for Quantum Systems with Contact Interactions [49.1574468325115]
We show that in the limit one obtains the one-body Hamiltonian for the light particle subject to $N$ (non-local) point interactions placed at fixed positions.
We will verify that such non-local point interactions do not exhibit the ultraviolet pathologies that are present in the case of standard local point interactions.
arXiv Detail & Related papers (2024-07-09T14:04:11Z) - $su(d)$-squeezing and many-body entanglement geometry in finite-dimensional systems [0.0]
Generalizing the well-known spin-squeezing inequalities, we study the relation between squeezing of collective $N$-particle $su(d)$ operators and many-body entanglement geometry in multi-particle systems.
arXiv Detail & Related papers (2024-06-19T08:40:11Z) - Mixed-state quantum anomaly and multipartite entanglement [8.070164241593814]
We show a surprising connection between mixed state entanglement and 't Hooft anomaly.<n>We generate simple examples of mixed states with nontrivial long-ranged multipartite entanglement.<n>We also analyze mixed anomaly involving both strong and weak symmetries.
arXiv Detail & Related papers (2024-01-30T19:00:02Z) - The role of shared randomness in quantum state certification with
unentangled measurements [36.19846254657676]
We study quantum state certification using unentangled quantum measurements.
$Theta(d2/varepsilon2)$ copies are necessary and sufficient for state certification.
We develop a unified lower bound framework for both fixed and randomized measurements.
arXiv Detail & Related papers (2024-01-17T23:44:52Z) - Bipartite representations and many-body entanglement of pure states of $N$ indistinguishable particles [0.0]
We analyze a general bipartite-like representation of arbitrary pure states of $N$ indistinguishable particles, valid for both bosons and fermions.
It leads to exact $(M,N-M)$ Schmidt-like expansions of the state for any $MN$ and is directly related to the isospectral reduced $rho(M)$ and $rho(N-M)$.
arXiv Detail & Related papers (2024-01-12T22:22:44Z) - Entanglement and Bell inequalities violation in $H\to ZZ$ with anomalous coupling [44.99833362998488]
We discuss entanglement and violation of Bell-type inequalities for a system of two $Z$ bosons produced in Higgs decays.
We find that a $ZZ$ state is entangled and violates the inequality for all values of the pair (anomalous) coupling constant.
arXiv Detail & Related papers (2023-07-25T13:44:31Z) - Nonlocality under Computational Assumptions [51.020610614131186]
A set of correlations is said to be nonlocal if it cannot be reproduced by spacelike-separated parties sharing randomness and performing local operations.
We show that there exist (efficient) local producing measurements that cannot be reproduced through randomness and quantum-time computation.
arXiv Detail & Related papers (2023-03-03T16:53:30Z) - Scattering data and bound states of a squeezed double-layer structure [77.34726150561087]
A structure composed of two parallel homogeneous layers is studied in the limit as their widths $l_j$ and $l_j$, and the distance between them $r$ shrinks to zero simultaneously.
The existence of non-trivial bound states is proven in the squeezing limit, including the particular example of the squeezed potential in the form of the derivative of Dirac's delta function.
The scenario how a single bound state survives in the squeezed system from a finite number of bound states in the finite system is described in detail.
arXiv Detail & Related papers (2020-11-23T14:40:27Z) - Non-Hermitian N-state degeneracies: unitary realizations via
antisymmetric anharmonicities [0.0]
degeneracy of an $N-$plet of bound states is studied in the framework of quantum theory of closed (i.e., unitary) systems.
For an underlying Hamiltonian $H=H(lambda)$ the degeneracy occurs at a Kato's exceptional point.
arXiv Detail & Related papers (2020-10-28T14:41:52Z) - Bounding the finite-size error of quantum many-body dynamics simulations [6.657101721138396]
We derive rigorous upper bounds on the Finite-size error (FSE) of local observables in real time quantum dynamics simulations from a product state.
Our bounds are practically useful in determining the validity of finite-size results, as we demonstrate in simulations of the one-dimensional (1D) quantum Ising and Fermi-Hubbard models.
arXiv Detail & Related papers (2020-09-25T04:30:25Z)
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.