Designing generalized elegant Bell inequalities in higher dimensions from a Tsirelson bound

Abstract

Elegant Bell inequality is well known for its distinctive property, being maximally violated by maximal entanglement, mutually unbiased bases, and symmetric informationally complete positive operator-valued measure elements. Despite its significance in quantum information theory demonstrated based on its unique violation feature, it remains the only known one with the characteristic. We present a method to construct Bell inequalities with violation feature analogous to elegant Bell inequality in higher local dimensions from a simple, analytic quantum bound. A Bell inequality with the generalized violation feature is derived in three dimension for the first time. It exhibits larger violation than existing Bell inequalities of similar classes, including the original elegant Bell inequality, while requiring arguably small number of measurements.

References in corpus (38)

• Bell nonlocality
• Device-independent security of quantum cryptography against collective attacks
• Random Numbers Certified by Bell's Theorem
• Symmetric Informationally Complete Quantum Measurements
• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• On mutually unbiased bases
• From Bell's Theorem to Secure Quantum Key Distribution
• A new proof for the existence of mutually unbiased bases
• Fully device independent quantum key distribution
• Secure device-independent quantum key distribution with causally independent measurement devices
• Device independent quantum random number generation
• The SIC Question: History and State of Play
• Optimal randomness certification from one entangled bit
• Quantum Random Access Codes using Single $d$-level Systems
• Generic Bell inequalities for multipartite arbitrary dimensional systems
• SIC~POVMs and Clifford groups in prime dimensions
• Bell inequalities tailored to maximally entangled states
• Quantum Secret Sharing with Multi-level Mutually (Un-)Biased Bases
• Enhanced entanglement criterion via symmetric informationally complete measurements
• Device-Independent Quantum Key Distribution with Random Key Basis
• Mutually unbiased bases and symmetric informationally complete measurements in Bell experiments
• Causality and Cirel'son bounds
• Reexamination of a multisetting Bell inequality for qudits
• Maximal nonlocality from maximal entanglement and mutually unbiased bases, and self-testing of two-qutrit quantum systems
• Connections Between Mutually Unbiased Bases and Quantum Random Access Codes
• Correlations in star networks: from Bell inequalities to network inequalities
• Optimal quantum preparation contextuality in $n$-bit parity-oblivious multiplexing task
• Linking Entanglement Detection and State Tomography via Quantum 2-Designs
• Multi-setting Bell inequality for qudits
• Experimental certification of an informationally complete quantum measurement in a device-independent protocol
• Self-testing properties of Gisin's elegant Bell inequality
• Device-independent certification of two bits of randomness from one entangled bit and Gisin's elegant Bell inequality
• Exploring the geometry of qutrit state space using symmetric informationally complete probabilities
• Intermediate states in quantum cryptography and Bell inequalities
• Designing Bell inequalities from a Tsirelson bound
• Device-independent self-testing of unsharp measurements
• Scalable implementation of $(d+1)$ mutually unbiased bases for $d$-dimensional quantum key distribution
• Simple conditions constraining the set of quantum correlations