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

• URL: http://arxiv.org/abs/2210.05272v1
• Date: Tue, 11 Oct 2022 09:12:38 GMT
• Title: Construction of efficient Schmidt number witnesses for high-dimensional quantum states
• Authors: Nikolai Wyderka, Giovanni Chesi, Hermann Kampermann, Chiara Macchiavello, Dagmar Bru{\ss}
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recent progress in quantum optics has lead 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 temporal modes.

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