Enhanced Schmidt number criteria based on correlation trace norms

Abstract

The Schmidt number represents the genuine entanglement dimension of a bipartite quantum state. We derive simple criteria for the Schmidt number of a density matrix in arbitrary local dimensions. They are based on the trace norm of correlations obtained from seminal families of quantum measurements, specifically symmetric informationally complete measurements and mutually unbiased bases. Our criteria are strictly stronger than both the well-known fidelity witness criterion and the computable cross-norms or realignment criterion.

7+3 pages

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Cited by in corpus (8)

• Higher-dimensional entanglement detection and quantum channel characterization using moments of generalized positive maps
• Schmidt number criterion via general symmetric informationally complete measurements
• Estimating the Schmidt numbers of quantum states via symmetric measurements
• Simulating quantum instruments with projective measurements and quantum post-processing
• Measurement-device-independent Schmidt number certification of all entangled states
• A note on Schmidt-number witnesses based on symmetric measurements
• Detecting high-dimensional entanglement by randomized product projections
• On the characterization of partially entanglement breaking and annihilating channels