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We study the geometric measure of quantum coherence recently proposed in [Phys. Rev. Lett. 115, 020403 (2015)]. Both lower and upper bounds of this measure are provided. These bounds are shown to be tight for a class of important coherent states -- maximally coherent mixed states. The trade-off relation between quantum coherence and mixedness for this measure is also discussed.
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Quantum coherence is a key resource in quantum information processing scenarios, and quantifying coherence is an important task for both quantum foundation and quantum technology. However, until now, all most of coherence measures are basis-dependent that does not accord with physical reality, since the physical properties of the physical system should not be changed with the different choice of coordinate systems. Here, we propose an textit{intrinsic basis-independent quantum coherence measure} which satisfies all conditions for quantifying coherence. This measurement not only reveals physical essence of quantum coherence of the quantum state itself clearly, but also simplifies the measurement procedure by avoiding the optimization procedure of distance measure.
Quantum metrology holds the promise of an early practical application of quantum technologies, in which measurements of physical quantities can be made with much greater precision than what is achievable with classical technologies. In this review, we collect some of the key theoretical results in quantum parameter estimation by presenting the theory for the quantum estimation of a single parameter, multiple parameters, and optical estimation using Gaussian states. We give an overview of results in areas of current research interest, such as Bayesian quantum estimation, noisy quantum metrology, and distributed quantum sensing. We address the question how minimum measurement errors can be achieved using entanglement as well as more general quantum states. This review is presented from a geometric perspective. This has the advantage that it unifies a wide variety of estimation procedures and strategies, thus providing a more intuitive big picture of quantum parameter estimation.
We discuss some properties of the quantum discord based on the geometric distance advanced by Dakic, Vedral, and Brukner [Phys. Rev. Lett. {bf 105}, 190502 (2010)], with emphasis on Werner- and MEM-states. We ascertain just how good the measure is in representing quantum discord. We explore the dependence of quantum discord on the degree of mixedness of the bipartite states, and also its connection with non-locality as measured by the maximum violation of a Bell inequality within the CHSH scenario.
A symmetric measure of quantum correlation based on the Hilbert-Schmidt distance is presented in this paper. For two-qubit states, we simplify considerably the optimization procedure so that numerical evaluation can be performed efficiently. Analytical expressions for the quantum correlation are attained for some special states. We further investigate the dynamics of quantum correlation of the system qubits in the presence of independent dissipative environments. Several nontrivial aspects are demonstrated. We find that the quantum correlation can increase even if the system state is suffering dissipative noise. Sudden changes occur, even twice, in the time evolution of quantum correlation. There is certain correspondence between the evolution of quantum correlation in the systems and that in the environments, and the quantum correlation in the systems will be transferred into the environments completely and asymptotically.
Quantification of coherence lies at the heart of quantum information processing and fundamental physics. Exact evaluation of coherence measures generally needs a full reconstruction of the density matrix, which becomes intractable for large-scale multipartite systems. Here, we propose a systematic theoretical approach to efficiently estimating lower and upper bounds of coherence in multipartite states. Under the stabilizer formalism, the lower bound is determined by the spectrum estimation method with a small number of measurements and the upper bound is determined by a single measurement. We verify our theory with a four-qubit optical quantum system.We experimentally implement various multi-qubit entangled states, including the Greenberger-Horne-Zeilinger state, the cluster state, and the W state, and show how their coherence are efficiently inferred from measuring few observables.
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