Detecting the dimensionality of genuine multi-particle entanglement

Abstract

Complex forms of quantum entanglement can arise in two qualitatively different ways; either between many qubits or between two particles with higher-than-qubit dimension. While the many-qubit frontier and the high-dimension frontier both are well-established, state-of-the-art quantum technology is becoming increasingly able to create and manipulate entangled states that simltaneously feature many particles and high dimension. Here, we investigate generic states that can be considered both genuinely high-dimensional and genuine multi-particle entangled. We consider a natural quantity that characterises this key property. To detect it, we develop three different classes of criteria. These enable us both to probe the ultimate noise tolerance of this form of entanglement and to make detection schemes using sparse or even minimal measurement resources. The approach provides a simple way of benchmarking entanglement dimensionality in the multi-particle regime and general, platform-independent, detection methods that readily apply to experimental use.

Corrected relations to Schmidt number vectors

References in corpus (17)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Entanglement detection
• Quantum computational advantage using photons
• Scalable multi-particle entanglement of trapped ions
• Experimental entanglement of six photons in graph states
• Entanglement Certification $-$ From Theory to Experiment
• Taming multiparticle entanglement
• The structure of multidimensional entanglement in multipartite systems
• Quantifying photonic high-dimensional entanglement
• Semidefinite Programming in Quantum Information Science
• Inverse-design of high-dimensional quantum optical circuits in a complex medium
• Separability criteria for several classes of $n$-partite quantum states
• Greenberger-Horne-Zeilinger paradoxes from qudit graph states
• Resource-efficient high-dimensional entanglement detection via symmetric projections
• Preparation of multiphoton high-dimensional GHZ state
• Construction of efficient Schmidt number witnesses for high-dimensional quantum states
• Criteria for non-$k$-separability of $n$-partite quantum states

Cited by in corpus (9)

• Enhanced Schmidt number criteria based on correlation trace norms
• Observation of Genuine High-dimensional Multi-partite Non-locality in Entangled Photon States
• Maximal steady-state entanglement in autonomous quantum thermal machines
• Observation of a Multimode Displaced Squeezed State in High-Harmonic Generation
• Simulating quantum instruments with projective measurements and quantum post-processing
• Entanglement Transfer in a Composite Electron-Ion-Photon System
• Detecting high-dimensional entanglement by randomized product projections
• Supersinglets can be self-tested with perfect quantum strategies
• Entanglement Structure Certification Based on Energy-Restricted State Discrimination