Experimental Device-Independent Certification of a SIC-POVM

Enabling Computation of Correlation Bounds for Finite-Dimensional Quantum Systems via Symmetrization

“…These lower bounds were verified to be achieved with projective measurements up to machine precision. The results show that the obtained upper bounds are either optimal or close to optimal, depending on d. In analogy with previous works [32][33][34][35][36], we find that the gap between optimal quantum correlations and those obtained under projective measurements is small.…”

“…To this end, we introduce a family of CCPs, prove that they enable self-tests of d-dimensional symmetric informationally complete (SIC) POVMs, then use symmetrised semidefinite relaxations to bound the correlations attainable under projective measurements. This allows us to go beyond previously studied qubit systems [32][33][34][35][36] and robustly certify the nonprojectiveness of SIC-POVMs subject to imperfections.…”

“…Non-projective measurements have diverse applications in quantum theory [32,[40][41][42][43][44][45][46]. This has motivated interest in their blackbox certification [32][33][34][35][36]. Using semidefinite relaxations (whose complexity scale quickly with dimension) as a primary tool, these works limit themselves to qubits.…”

Mutually unbiased bases and symmetric informationally complete measurements in Bell experiments

“…Furthermore, they are useful for entanglement witnessing [39], have found applications in quantum key distribution [40,41] and enable optimal random number generation from a singlet state [42]. In addition, SICs are at the heart of many protocols for certifying the nonprojective nature of a measurement [43][44][45][46]. Moreover, SICs exhibit interesting connections to several areas of mathematics, for instance Lie and Jordan algebras [47] and algebraic number theory [48,49].…”