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Register a new userFrobenius-norm-based measures of quantum coherence and asymmetry
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We formulate the Frobenius-norm-based measures for quantum coherence and asymmetry respectively. In contrast to the resource theory of coherence and asymmetry, we construct a natural measure of quantum coherence inspired from optical coherence theory while the group theoretical approach is employed to quantify the asymmetry of quantum states. Besides their simple structures and explicit physical meanings, we observe that these quantities are intimately related to the purity (or linear entropy) of the corresponding quantum states. Remarkably, we demonstrate that the proposed coherence quantifier is not only a measure of mixedness, but also an intrinsic (basis-independent) quantification of quantum coherence contained in quantum states, which can also be viewed as a normalized version of Brukner-Zeilinger invariant information. In our context, the asymmetry of N-qubit quantum systems is considered under local independent and collective SU(2) transformations. Intriguingly, it is illustrated that the collective effect has a significant impact on the asymmetry measure, and quantum correlation between subsystems plays a non-negligible role in this circumstance.
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It has been asked by different authors whether the two classes of Schatten-$p$-norm-based functionals $C_p(rho)=min_{sigmainmathcal{I}}||rho-sigma||_p$ and $ tilde{C}_p(rho)= |rho-Deltarho|_{p}$ with $pgeq 1$ are valid coherence measures under incoherent operations, strictly incoherent operations, and genuinely incoherent operations, respectively, where $mathcal{I}$ is the set of incoherent states and $Deltarho$ is the diagonal part of density operator $rho$. Of these questions, all we know is that $C_p(rho)$ is not a valid coherence measure under incoherent operations and strictly incoherent operations, but all other aspects remain open. In this paper, we prove that (1) $tilde{C}_1(rho)$ is a valid coherence measure under both strictly incoherent operations and genuinely incoherent operations but not a valid coherence measure under incoherent operations, (2) $C_1(rho)$ is not a valid coherence measure even under genuinely incoherent operations, and (3) neither ${C}_{p>1}(rho)$ nor $tilde{C}_{p>1}(rho)$ is a valid coherence measure under any of the three sets of operations. This paper not only provides a thorough examination on the validity of taking $C_p(rho)$ and $tilde{C}_p(rho)$ as coherence measures, but also finds an example that fulfills the monotonicity under strictly incoherent operations but violates it under incoherent operations.
Coherence and correlation are key features of the quantum system. Quantifying these quantities are astounding task in the framework of resource theory of quantum information processing. In this article, we identify an affinity-based metric to quantify closeness between two states. Using this metric, we introduce a valid quantum coherence measure. It is shown that the affinity based coherence measure is bounded by that based on fidelity and trace distance. Further, we propose a bipartite quantum correlation measure based on the affinity metric. The connection between the quantum correlation of states and its local coherence is established. The measure of quantumness in terms of difference of bipartite coherence and corresponding product state coherence is also identified. Finally, we interpret the operational meaning of the affinity based coherence as an upper bound of interferometric power of the quantum state.
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We introduce and study the l1 norm of coherence of assistance both theoretically and operationally. We first provide an upper bound for the l1 norm of coherence of assistance and show a necessary and sufficient condition for the saturation of the upper bound. For two and three dimensional quantum states, the analytical expression of the l1 norm of coherence of assistance is given. Operationally, the mixed quantum coherence can always be increased with the help of another party s local measurement and one way classical communication since the l1 norm of coherence of assistance, as well as the relative entropy of coherence of assistance, is shown to be strictly larger than the original coherence. The relation between the l1 norm of coherence of assistance and entanglement is revealed. Finally, a comparison between the l1 norm of coherence of assistance and the relative entropy of coherence of assistance is made.
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