Alternatives of entanglement depth and metrological entanglement criteria
arXiv:2408.15350 · doi:10.22331/q-2025-04-18-1718
Abstract
We work out the general theory of one-parameter families of partial entanglement properties and the resulting entanglement depth-like quantities. Special cases of these are the depth of partitionability, the depth of producibility (or simply entanglement depth) and the depth of stretchability, which are based on one-parameter families of partial entanglement properties known earlier. We also construct some further physically meaningful properties, for instance the squareability, the toughness, the degree of freedom, and also several ones of entropic motivation. Metrological multipartite entanglement criteria with the quantum Fisher information fit naturally into this framework. Here we formulate these for the depth of squareability, which therefore turns out to be the natural choice, leading to stronger bounds than the usual entanglement depth. Namely, the quantum Fisher information turns out to provide a lower bound not only on the maximal size of entangled subsystems, but also on the average size of entangled subsystems for a random choice of elementary subsystems. We also formulate criteria with convex quantities for both cases, which are much stronger than the original ones. In particular, the quantum Fisher information puts a lower bound on the average size of entangled subsystems. We also argue that one-parameter partial entanglement properties, which carry entropic meaning, are more suitable for the purpose of defining metrological bounds.
arXiv commentv3: revised version, accepted in Quantum; 32+18 pages, 22 figures, 814 relation signs;
References in corpus (78)
- Quantum entanglement
- Mixed State Entanglement and Quantum Error Correction
- Concentrating Partial Entanglement by Local Operations
- Quantum metrology
- Quantum metrology with nonclassical states of atomic ensembles
- Entanglement Measures and Purification Procedures
- Quantum Resource Theories
- Quantum Nonlocality without Entanglement
- 14-qubit entanglement: creation and coherence
- Many-particle entanglement with Bose--Einstein condensates
- Nonlinear atom interferometer surpasses classical precision limit
- Entanglement, Non-linear Dynamics, and the Heisenberg Limit
- Quantum metrology from a quantum information science perspective
- Squeezing and entanglement in a Bose-Einstein condensate
- Entanglement monotones
- Fisher information and multiparticle entanglement
- Classification of mixed three-qubit states
- Multipartite entanglement and high precision metrology
- Quantum spin dynamics and entanglement generation with hundreds of trapped ions
- Implementation of Cavity Squeezing of a Collective Atomic Spin
- Entanglement and Extreme Spin Squeezing
- Twin matter waves for interferometry beyond the classical limit
- Fisher Information and entanglement of non-Gaussian spin states
- A Schmidt number for density matrices
- Violation of local uncertainty relations as a signature of entanglement
- Taming multiparticle entanglement
- Classification of multi-qubit mixed states: separability and distillability properties
- Separability and distillability of multiparticle quantum systems
- Scalable Spin Squeezing for Quantum-Enhanced Magnetometry with Bose-Einstein Condensates
- Detecting multiparticle entanglement of Dicke states
- Multipartite entanglement in spin chains
- Deterministic Squeezed States with Joint Measurements and Feedback
- Schmidt number witnesses and bound entanglement
- Optimal spin squeezing inequalities detect bound entanglement in spin models
- Entanglement with Negative Wigner Function of Three Thousand Atoms Heralded by One Photon
- Quantum metrology with a scanning probe atom interferometer
- Reduced back-action for phase sensitivity 10 times beyond the standard quantum limit
- Extremal properties of the variance and the quantum Fisher information
- Beating the classical precision limit with spin-1 Dicke state of more than 10000 atoms
- 0.75 atoms improve the clock signal of 10,000 atoms
- Sufficient conditions for three-particle entanglement and their tests in recent experiments
- Useful Multiparticle Entanglement and Sub-Shot-Noise Sensitivity in Experimental Phase Estimation
- Multipartite entanglement measures
- Deterministic generation of multiparticle entanglement by quantum Zeno dynamics
- Partial separability and entanglement criteria for multiqubit quantum states
- Spin squeezing inequalities for arbitrary spin
- Measurement-induced nonlocal entanglement in a hot, strongly-interacting atomic system
- Metrological Detection of Multipartite Entanglement from Young Diagrams
- Generation of macroscopic singlet states in a cold atomic ensemble
- Witnessing Multipartite Entanglement without Entanglement Witness Operators
- Entanglement Detection in Optical Lattices of Bosonic Atoms with Collective Measurements
- Roofs and Convexity
- Generation of macroscopic singlet states in atomic ensembles
- Entanglement detection in the vicinity of arbitrary Dicke states
- Energy and multipartite entanglement in multidimensional and frustrated spin models
- The correlation theory of the chemical bond
- Separability criteria and entanglement witnesses for symmetric quantum states
- Detecting metrologically useful entanglement in the vicinity of Dicke states
- Partial separability revisited: Necessary and sufficient criteria
- Uncertainty relations with the variance and the quantum Fisher information based on convex decompositions of density matrices
- k-stretchability of entanglement, and the duality of k-separability and k-producibility
- Entanglement and extreme spin squeezing of unpolarized states
- Entanglement and extreme planar spin squeezing
- Improving sum uncertainty relations with the quantum Fisher information
- Construction of multi-qubit optimal genuine entanglement witnesses
- Squeezed Ground States in a Spin-1 Bose-Einstein Condensate
- The classification of multipartite quantum correlation
- Bounding the amount of entanglement from witness operators
- Construction of three-qubit biseparable states distinguishing kinds of entanglement in a partial separability classification
- The role of phases in detecting three-qubit entanglement
- Construction of three qubit genuine entanglement with bi-partite positive partial transposes
- Separability of three qubit Greenberger-Horne-Zeilinger diagonal states
- Dichotomy of entanglement depth for symmetric states
- Separability criterion for three-qubit states with a four dimensional norm
- On the convex cones arising from classifications of partial entanglement in the three qubit system
- Continuity of the relative entropy of resource
- There exist infinitely many kinds of partial separability/entanglement
- Polytope structures for Greenberger-Horne-Zeilinger diagonal states