In addition, we obtain that in the resource-theoretic framework of multilevel coherence, no resource state is isolated, that is, given a multilevel coherent pure state ∣ ψ〉, there exists another multilevel coherent pure state ∣ ϕ〉 and a k-coherence-preserving operation Λ k, such that Λ k(∣ϕ〉) = ∣ ψ〉. Meanwhile, we present the condition of the interconversions of two multilevel coherent resource pure states under k-coherence-preserving operations. We prove that any two multilevel coherent resource pure states can be interconverted with a nonzero probability via a completely positive and trace non-increasing k-coherence-preserving map. In this paper, we mainly study the transformations of resource pure states via free operations in the theoretical framework for multilevel coherence. Recently, the resource theory of multilevel quantum coherence is attracting substantial attention. A 92, 042101 (2015).Quantum coherence, emerging from the “superposition” of quantum states, is widely used in various information processing tasks. Hall, Complementarity relations for quantum coherence. Every Coherence X4 standard license can be activated on one machine. (Cambridge University Press, Cambridge, 2012) Peng, Experimental demonstration of observability and operability of robustness of coherence. Regula, General resource theories in quantum mechanics and beyond: operational characterization via discrimination tasks. Adesso, Operational advantage of quantum resources in subchannel discrimination. Adesso, Robustness of coherence: an operational and observable measure of quantum coherence. Wang, A generalized multipath delayed-choice experiment on a large-scale quantum nanophotonic chip. Qureshi, Measuring quantum coherence in multislit interference. Streltsov, Resource theory of imaginarity: quantification and state conversion. Streltsov, Operational resource theory of imaginarity. Gour, Quantifying the imaginarity of quantum mechanics. Fan, Testing real quantum theory in an optical quantum network. Pan, Ruling out real-valued standard formalism of quantum theory. Gisin, Simulating quantum systems using real Hilbert spaces. Pause, Save, Resume Keep your spot from screen to screen. Stream on Almost Any Device Download our free app to start. ![]() Vértesi, Efficiency of higher-dimensional Hilbert spaces for the violation of Bell inequalities. Watch Coherence (2014) free starring Emily Baldoni, Maury Sterling, Nicholas Brendon and directed by James Ward Byrkit. Algebraic structure of symmetry groups and ensembles in quantum mechanics. Flensberg, Many-Body Quantum Theory in Condensed Matter Physics (Oxford Univ. Niu, Berry phase effects on electronic properties. Berry, Quantal phase factors accompanying adiabatic changes. Spekkens, Resource theory of quantum states out of thermal equilibrium. Spekkens, Measuring the quality of a quantum reference frame: the relative entropy of frameness. Spekkens, The resource theory of quantum reference frames: manipulations and monotones. Tong, Superadditivity of convex roof coherence measures. Lu, Efficient estimation of multipartite quantum coherence. Liu, No-go theorems for deterministic purification and probabilistic enhancement of coherence. Brunner, Set coherence: basis-independent quantification of quantum coherence. ![]() Hsieh, Relating the resource theories of entanglement and quantum coherence.
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