arXiv subjects

Xiao-Dan Cui

Publications and source records attributed to Xiao-Dan Cui.

3 recordsLinked to original sources

arXiv2023

Closed expressions for one-qubit states of convex roof coherence measures

We study the closed expressions of the convex roof coherence measures for one-qubit states in this paper. We present the analytical expressions for the convex roof coherence measures, $C_f(ρ)$, of one-qubit states with $C_f(φ):=f(\abs{c_0}^2,\abs{c_1}^2)$ (where $\ketφ=c_0\ket{0}+c_1\ket{1}$) being convex with respect to the $l_1$ norm of coherence of $φ$ (i.e., $C_{l_1}(φ)$), such coherence measures including the coherence of formation, the geometric measure of coherence, the coherence concurrence, and the coherence rank. We further present the operational interpretations of these measures. Finally, we present the usefulness of the convex roof coherence measures $C_f(φ)$ being non-convex with respect to $C_{l_1}(φ)$ by giving the necessary and sufficient conditions for the transformations $pφ_1\oplus(1-p)φ_2\to qϕ_1\oplus(1-q)ϕ_2$ via incoherent operations, where $φ_i$, $ϕ_j$ $(i, j=1, 2)$ are one-qubit pure states and $0\leq p, q\leq 1$.

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arXiv2020

Examining the validity of Schatten-$p$-norm-based functionals as coherence measures

It has been asked by different authors whether the two classes of Schatten-$p$-norm-based functionals $C_p(ρ)=\min_{σ\in\mathcal{I}}||ρ-σ||_p$ and $ \tilde{C}_p(ρ)= \|ρ-Δρ\|_{p}$ with $p\geq 1$ 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 $Δρ$ is the diagonal part of density operator $ρ$. Of these questions, all we know is that $C_p(ρ)$ 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) $\tilde{C}_1(ρ)$ is a valid coherence measure under both strictly incoherent operations and genuinely incoherent operations but not a valid coherence measure under incoherent operations, (2) $C_1(ρ)$ is not a valid coherence measure even under genuinely incoherent operations, and (3) neither ${C}_{p>1}(ρ)$ nor $\tilde{C}_{p>1}(ρ)$ 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 $C_p(ρ)$ and $\tilde{C}_p(ρ)$ as coherence measures, but also finds an example that fulfills the monotonicity under strictly incoherent operations but violates it under incoherent operations.

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arXiv2017

Rydberg-atom-based scheme of nonadiabatic geometric quantum computation

Nonadiabatic geometric quantum computation provides a means to perform fast and robust quantum gates. It has been implemented in various physical systems, such as trapped ions, nuclear magnetic resonance and superconducting circuits. Another system being adequate for implementation of nonadiabatic geometric quantum computation may be Rydberg atoms, since their internal states have very long coherence time and the Rydberg-mediated interaction facilitates the implementation of a two-qubit gate. Here, we propose a scheme of nonadiabatic geometric quantum computation based on Rydberg atoms, which combines the robustness of nonadiabatic geometric gates with the merits of Rydberg atoms.

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