Abstract
We introduce a procedure based on quantum expectation values of measurement observables to characterize quantum coherence. Our measure allows one to quantify coherence without having to perform tomography of the quantum state, and can be directly calculated from measurement expectation values. This definition of coherence allows the decomposition into contributions corresponding to the non-classical correlations between the subsystems and localized on each subsystem. The method can also be applied to cases where the full set of measurement operators is unavailable. An estimator using the truncated measurement operators can be used to obtain lower bound to the genuine value of coherence. We illustrate the method for several bipartite systems, and show the singular behavior of the coherence measure in a spin-1 chain, characteristic of a quantum phase transition.
Highlights
Coherence is one of the fundamental concepts of quantum mechanics and has been studied extensively in the context of phase space distributions [1] and correlation functions [2,3]
We introduce a procedure based on quantum expectation values of measurement observables to characterize quantum coherence
We introduce a method of quantifying the quantum coherence and its distribution in a bipartite system using expectation values of physical observables
Summary
Coherence is one of the fundamental concepts of quantum mechanics and has been studied extensively in the context of phase space distributions [1] and correlation functions [2,3]. It was not quantified in a formal sense until recently using the tools of quantum information theory [4] These ideas have led to many new developments regarding quantum measurement [5,6,7,8], the distribution of coherence in multipartite systems [9], and its application for characterizing states [10,11,12,13,14,15,16,17,18,19]. [25,26] a resource theory of coherence based on quantum measurements was defined, where the set of incoherent states are defined by a coherence-destroying measurement The aims of these works are different to the results of this paper in the sense that one experimentally still requires tomographic reconstruction of the state to evaluate the coherence in these past works. The same set of measurements that are used to construct the coherence measure can be used to construct the covariance matrix, which has been used as an effective way of detecting entanglement [34,35,36,37,38,39,40,41,42,43]
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