Construction of efficient Schmidt number witnesses for high-dimensional quantum states

Abstract

Recent progress in quantum optics has led to setups that are able to prepare high-dimensional quantum states for quantum information processing tasks. As such, it is of importance to benchmark the states generated by these setups in terms of their quantum mechanical properties, such as their Schmidt numbers, i.e., the number of entangled degrees of freedom. In this paper, we develop an iterative algorithm that finds Schmidt number witnesses tailored to the measurements available in specific experimental setups. We then apply the algorithm to find a witness that requires the measurement of a number of density matrix elements that scales linearly with the local dimension of the system. As a concrete example, we apply our construction method to an implementation with photonic temporal modes.

arXiv comment7 pages, 4 figures

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• Tight bounds from multiple-observable entropic uncertainty relations
• Formulas for Mutually Orthogonal Quantum States in Two-Qubit Systems: Orthogonal Schmidt Decompositions
• Detecting high-dimensional entanglement by randomized product projections
• A note on Schmidt-number witnesses based on symmetric measurements
• Universal entanglement detection with geometrically optimal witnesses
• Semi-device-independent certification of high-dimensional quantum channels
• On the characterization of partially entanglement breaking and annihilating channels