![]() We introduce a general method to directly measure quantum coherence of an unknown quantum state using two-copy collective measurement, focusing on two established coherence quantifiers: ℓ 1-norm coherence and relative entropy coherence. The errors in our experiment mainly come from the inaccuracy of angles of the wave plates and the imperfect interference visibility of the interferometer. The experimental data are in good agreement with the theoretical prediction. Thus, both coherence measures \(\) and C r are shown in Fig. In this way, we experimentally obtain two widely studied coherence measures, finding a good agreement between the numerical simulations and the experimental results. The collective measurements are performed on two identically prepared qubits, which are encoded in two degrees of freedom of a single photon. We also report an experimental demonstration of CMS for qubit states. The simulations show that in certain setups CMS outperforms all other schemes discussed in this work. We simulate the performance of this method for qubits and qutrits and compare the precision of CMS with other methods for coherence estimation, including tomography. ![]() In this paper, we put forward a general method to directly measure quantum coherence of an unknown quantum state using two-copy collective measurement scheme (CMS) 60, 61, 62, 63. However, estimation of coherence measures in general does not require the complete information about the state of the system, a fact which has been exploited in various approaches for detecting and estimating coherence of unknown quantum states 56, 57, 58, 59. ![]() Clearly, one possibility is to perform quantum state tomography 55 and then use the derived state density matrix to estimate the amount of coherence. While various coherence measures have been proposed 6, an important issue is how to efficiently estimate them in experiments. In the resource theory of coherence, the free operations are incoherent operations, corresponding to quantum measurements, which cannot create coherence for individual measurement outcomes 1. The common feature of all resource quantifiers is the postulate that they should not increase under free operations of the theory, which in entanglement theory are known as “local operations and classical communication”. First attempts for resource quantification were made in the resource theory of entanglement 53, 54, leading to various entanglement measures based on physical or mathematical considerations. Having identified quantum coherence as a valuable feature of quantum systems, it is important to develop methods for its rigorous quantification. Being a fundamental property of quantum systems, coherence plays an important role in quantum thermodynamics 34, 35, 36, 37, 38, 39, 40, nanoscale physics 41, transport theory 42, 43, biological systems 44, 45, 46, 47, 48, 49, and for the study of the wave-particle duality 50, 51, 52. Highly relevant from the experimental perspective is the recent progress on coherence theory in the finite copy regime, in particular regarding single-shot coherence distillation 28, 29, 30, 31, coherence dilution 32, and incoherent state conversion 33. Moreover, quantum coherence is closely related to other quantum resources, such as asymmetry 17, 18, entanglement 19, 20, and other quantum correlations 21 the manipulation of coherence and conversion between coherence and quantum correlations in bipartite and multipartite systems has been explored both theoretically 22, 23, 24, 25 and experimentally 26, 27. An operational resource theory of coherence has been established in the last years 1, 2, 3, 4, 5, 6, 7, allowing for a systematic study of quantum coherence in quantum technology 6, including quantum algorithms 8, 9, quantum computation 10, quantum key distribution 11, quantum channel discrimination 12, 13, and quantum metrology 14, 15, 16. Quantum coherence is the most distinguished feature of quantum mechanics, characterizing the superposition properties of quantum states.
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