Analyzing quantum entanglement with the Schmidt decomposition in operator space

Abstract

Characterizing entanglement is central for quantum information science. Special observables which indicate entanglement, so-called entanglement witnesses, are a widely used tool for this task. The construction of these witnesses typically relies on the observation that quantum states with a high fidelity to some entangled target state are entangled, too. We introduce a general method to construct entanglement witnesses based on the Schmidt decomposition of observables. The method works for two- and, more importantly, many-body systems and is strictly stronger than fidelity-based constructions. The resulting witnesses can also be used to quantify entanglement as well as to characterize the dimensionality of it. Finally, we present experimentally relevant examples, where our approach improves entanglement detection significantly.

S. Denker and C. Zhang contributed equally; 17 pages, one figure

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• Higher-dimensional entanglement detection and quantum channel characterization using moments of generalized positive maps
• Schmidt number criterion via general symmetric informationally complete measurements
• Detecting high-dimensional entanglement by randomized product projections
• Measurement-device-independent Schmidt number certification of all entangled states
• Multipartite entanglement classes of a multiport beam-splitter
• Formulas for Mutually Orthogonal Quantum States in Two-Qubit Systems: Orthogonal Schmidt Decompositions
• On the characterization of partially entanglement breaking and annihilating channels