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Register a new userEstimating coherence measures from limited experimental data available
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Quantifying coherence has received increasing attention, and considerable work has been directed towards finding coherence measures. While various coherence measures have been proposed in theory, an important issue following is how to estimate these coherence measures in experiments. This is a challenging task, since the state of a system is often unknown in practical applications and the accessible measurements in a real experiment are typically limited. In this Letter, we put forward an approach to estimate coherence measures of an unknown state from any limited experimental data available. Our approach is not only applicable to coherence measures but can be extended to other resource measures.
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Quantum coherence, like entanglement, is a fundamental resource in quantum information. In recent years, remarkable progress has been made in formulating resource theory of coherence from a broader perspective. The notions of block-coherence and POVM-based coherence have been established. Certain challenges, however, remain to be addressed. It is difficult to define incoherent operations directly, without requiring incoherent states, which proves a major obstacle in establishing the resource theory of dynamical coherence. In this paper, we overcome this limitation by introducing an alternate definition of incoherent operations, induced via coherence measures, and quantify dynamical coherence based on this definition. Finally, we apply our proposed definition to quantify POVM-based dynamical coherence.
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