Coherence non-activating measurement
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Coherence non-activating measurement Xueyuan Hu1 Received: 21 January 2020 / Accepted: 5 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract We define the coherence non-activating measurement as the positive operator-valued measurement which gives the same result whether or not the coherence in a quantum state is destroyed. A connection is built between the coherence activating ability of a measurement and its ability to steer quantum states when coherence non-activating measurements are allowed. Then, we study the quantum discord based on coherence non-activating measurement and its behavior under local incoherent operations. Our results contribute to the study of resource non-activating condition, which is a complement to the well-studied resource non-generating condition. Keywords Quantum measurement · Quantum coherence · Resource theory · Quantum correlation
1 Introduction Quantum measurement, one of the fundamental elements in quantum theory, is an indispensable procedure in all the quantum information protocols. It underlies the phenomena such as the uncertainty principle [1,2] and the quantum steering [3,4] and provides the priority in tasks like quantum state discrimination [5]. Moreover, the reference basis of a quantum measurement plays an important role for the notion of non-classicality [6,7]. With the development of the quantum resource theory, quantifiers of quantumness for measurements are proposed [8,9], and remarkably, discrimination tasks are designed to give an operational characterization [5]. In this article, we ask two essential questions concerning the resource theory of quantum measurement : (Q1) what is the minimal constraint on free measurements (i.e., measurements which are not able to reveal quantum resource contained in any state to a
This work was supported by NSFC under Grant No. 11774205 and Young Scholars Program of Shandong University.
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Xueyuan Hu [email protected] School of Information Science and Engineering, Shandong University, Qingdao 266237, China 0123456789().: V,-vol
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classical observer), and (Q2) how to judge whether a given measurement is free in a device-independent way. The resource theory of quantum coherence [10–12] has attracted much recent interest because it has many promising aspects, such as the analytical expressions for various measures of coherence in states [13], the clear characterization of different sets of free operations [14–18], and most importantly, the existence of a natural coherence destroying map [19,20]. Therefore, it is of interest to study (Q1) and (Q2) in the regime of quantum coherence. If a measurement does not activate coherence, or in other words, gives the same result whether or not the quantum coherence in states is destroyed, then the measurement should not be considered “quantum.” Hence, this non-activating condition is natural for a free measurement, analogous to the nongenerating condition on free operations. The definition of quantum discord [21] relies on qu
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