High-dimensional entanglement witnessed by correlations in arbitrary bases

Abstract

Certifying entanglement is an important step in the development of many quantum technologies, especially for higher-dimensional systems, where entanglement promises increased capabilities for quantum communication and computation. A key feature distinguishing entanglement from classical correlations is the occurrence of correlations for complementary measurement bases. In particular, mutually unbiased bases (MUBs) are a paradigmatic example that is well-understood and routinely employed for entanglement certification. However, implementing unbiased measurements exactly is challenging and not generically possible for all physical platforms. Here, we extend the entanglement-certification toolbox from correlations in MUBs to arbitrary bases. This practically significant simplification paves the way for efficient characterizations of high-dimensional entanglement in a wide range of physical systems. Furthermore, we introduce a simple three-MUBs construction for all dimensions without using the Wootters-Fields construction, potentially simplifying experimental requirements when measurements in more than two MUBs are needed, especially in high-dimensional settings.

9 + 14 pages, 9 figures, 1 table

References in corpus (9)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Aspects of generic entanglement
• Entanglement Certification $-$ From Theory to Experiment
• Native qudit entanglement in a trapped ion quantum processor
• Resource-efficient high-dimensional entanglement detection via symmetric projections
• Probing the geometry of correlation matrices with randomized measurements
• Detecting high-dimensional entanglement in cold-atom quantum simulators
• Three numerical approaches to find mutually unbiased bases using Bell inequalities
• Experimental high-dimensional entanglement certification and quantum steering with time-energy measurements

Cited by in corpus (7)

• State-Agnostic Approach to Certifying Electron-Photon Entanglement in Electron Microscopy
• Witness based nonlinear detection of quantum entanglement
• Measurement-device-independent Schmidt number certification of all entangled states
• Formulas for Mutually Orthogonal Quantum States in Two-Qubit Systems: Orthogonal Schmidt Decompositions
• Detecting high-dimensional entanglement by randomized product projections
• Certifying entanglement dimensionality by $k$-reduction moments
• Semi-device-independent certification of high-dimensional quantum channels