Device-independent certification of maximal randomness from pure entangled two-qutrit states using non-projective measurements

Abstract

While it has recently been demonstrated how to certify the maximal amount of randomness from any pure two-qubit entangled state in a device-independent way [E. Woodhead et al., Phys. Rev. Research 2, 042028(R)(2020)], the problem of optimal randomness certification from entangled states of higher local dimension remains open. Here we introduce a method for device-independent certification of the maximal possible amount of $2{\log }_{2}3$ random bits using pure bipartite entangled two-qutrit states and extremal nine-outcome general non-projective measurements. To this aim, we exploit the extended Bell scenario introduced recently in [S. Sarkar et al., arXiv:2110.15176], which combines a device-independent method for certification of the full Weyl-Heisenberg basis in three-dimensional Hilbert spaces together with a one-sided device-independent method for certification of two-qutrit partially entangled states.

arXiv comment9 pages, 1 figure

References in corpus (18)

• Random Numbers Certified by Bell's Theorem
• Quantum Random Number Generators
• A new proof for the existence of mutually unbiased bases
• Quantum random number generation
• Self-testing of quantum systems: a review
• Certified randomness in quantum physics
• Classical randomness in quantum measurements
• Experimentally Generated Randomness Certified by the Impossibility of Superluminal Signals
• Optimal randomness certification from one entangled bit
• High speed self-testing quantum random number generation without detection loophole
• Randomness in Quantum Mechanics: Philosophy, Physics and Technology
• Bell inequalities tailored to maximally entangled states
• 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
• Maximal nonlocality from maximal entanglement and mutually unbiased bases, and self-testing of two-qutrit quantum systems
• Maximal randomness from partially entangled states
• Device-independent certification of two bits of randomness from one entangled bit and Gisin's elegant Bell inequality

Cited by in corpus (9)

• Certification of incompatible measurements using quantum steering
• Unbounded Sharing of Nonlocality Using Projective Measurements
• Certification of the maximally entangled state using non-projective measurements
• Network quantum steering enables randomness certification without seed randomness
• Certification of unbounded randomness with arbitrary noise
• Robustness of Higher Dimensional Nonlocality against dual noise and sequential measurements
• Quantum bounds and device-independent security with rank-one qubit measurements
• Guarantees on the structure of experimental quantum networks
• Maximal device-independent randomness in every dimension