arXiv subjects

C. L. Liu

Publications and source records attributed to C. L. Liu.

At least 19 recordsLinked to original sources

arXiv2026

Incoherent Operations Enable State Transformations Impossible under Dephasing-covariant Incoherent Operations

We show that incoherent operations (IOs) can achieve the state transformations that are forbidden under dephasing-covariant incoherent operations (DIOs), thereby resolving the open problem posed by Chitambar and Gour [Phys. Rev. Lett. 117, 030401 (2016)]. We further demonstrate that no set of IO monotones suffices to characterize state convertibility under strictly incoherent operations (SIOs), and that monotones common to IOs and DIOs are insufficient to characterize convertibility under DIOs.

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arXiv2025

Insufficiency of Pure-State Ensembles in Characterizing Transformations of Entangled States under LOCC

The conditions for transforming pure entangled states under local operations and classical communication (LOCC) are well understood. A natural question then arises: Can we determine the transformation conditions for mixed entangled states under LOCC based on the properties of their pure-state ensembles? While much effort has been devoted to this issue, in this paper, we rule out this possibility. Our findings address several open questions, including: (i) The conditions $ E_f^{cr}(ρ) \geq E_f^{cr}(σ) $ for all convex roof entanglement measures $E_f^{cr}$ is insufficient to guarantee the existence of an LOCC transformation $Λ^L(\cdot)$ from $ρ$ to $σ$; and (ii) The inequalities $\sum_j p_j E(φ_j) \geq \sum_l q_l E(ψ_l)$ for all entanglement monotones $E$ are not sufficient to ensure the existence of an LOCC transformation from $\{p_j, \ket{φ_j}\}$ to $\{q_l, \ket{ψ_l}\}$.

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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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arXiv2023

Coherence filtration under strictly incoherent operations

We study the task of coherence filtration under strictly incoherent operations in this paper. The aim of this task is to transform a given state $ρ$ into another one $ρ^\prime$ whose fidelity with the maximally coherent state is maximal by using stochastic strictly incoherent operations. We find that the maximal fidelity between $ρ^\prime$ and the maximally coherent state is given by a multiple of the $Δ$ robustness of coherence $R(ρ\|Δρ):=\min\{\uplambda|ρ\leq\uplambdaΔρ\}$, which provides $R(ρ\|Δρ)$ an operational interpretation. Finally, we provide a coherence measure based on the task of coherence filtration.

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arXiv2022

Approximate distillation of quantum coherence

Coherence distillation is a basic information-theoretic task in the resource theory of coherence. In this paper, we develop the framework of the approximate coherence distillation under strictly incoherent operations. This protocol considers the situation that we cannot transform an initial state $ρ$ into a target state $ψ$ with certainty; instead, we aim to deterministically transform the initial state $ρ$ into an intermediate state $ϕ$ that is most approximate to the target state $ψ$ in terms of fidelity. We also present the explicit conversion strategy of the approximate coherence distillation.

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arXiv2022

Criterion for a state to be distillable via stochastic incoherent operations

Coherence distillation is a basic information-theoretic task in the resource theory of coherence. In this paper, we present the necessary and sufficient conditions under which a mixed state can be distilled into a pure coherent state via stochastic incoherent operations (sIOs). With the help of this result, we further show the following: (i) Any $2$-dimensional coherent state is distillable via sIOs if and only if it is a pure coherent state; (ii) a state $ρ$ is n-distillable via sIOs if and only if it is 1-distillable; and (iii) the set of distillable states via stochastic maximally incoherent operations is identical to the set of distillable states via sIOs. Finally, we analyze the reason why sIO is stronger than stochastic strictly incoherent operations when we use them to distill a coherent state.

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arXiv2021

Optimal probabilistic distillation of quantum coherence

We complete the task of optimal probabilistic coherence distillation protocol, whose aim is to transform a general state into a set of n-level maximally coherent states via strictly incoherent operations (SIO). Specifically, we present the necessary and sufficient condition for the transformation from a mixed state into a pure-state ensemble via SIO. With the aid of this condition and the simplex algorithm, we can accomplish the probabilistic distillation protocol by presenting an analytical expression of the maximal average distillable coherence of a general state and constructing the corresponding operation achieving this bound. Our protocol is a universal protocol since it can be applied to any coherence measure.

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arXiv2021

Works with quantum resource of coherence

We study the modification of the second law of thermodynamics for a quantum system interacting with a reservoir regarding quantum coherence. The whole system is isolated so that neither energy nor information is lost. It is discovered that the coherence of the reservoir can serves as a useful resource allowing the system extract more energy from the reservoir; among the coherence measures, only is the relative entropy of coherence feasible to quantitatively characterize energy exchange. We demonstrate that a thermodynamic cycle between two coherent reservoirs can output more work than its classical counterpart. The efficiency of such cycle surpasses the Carnot efficiency, which is the upper bound of heat engine efficiency in classical regime.

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arXiv2020

Increasing the dimension of the maximal pure coherent subspace of a state via incoherent operations

Quantum states transformation under free operations plays a central role in the resource theory of coherence. In this paper, we investigate the transformation from a mixed coherent state into a pure one by using both incoherent operations and stochastic incoherent operations. We show that contrary to the strictly incoherent operations and the stochastic strictly incoherent operations, both the incoherent operations and the stochastic incoherent operations can increase the dimension of the maximal pure coherent subspace of a state. This means that the incoherent operations are generally stronger than the strictly incoherent operations when we want to transform a mixed coherent state into a pure coherent one. Our findings can also be interpreted as confirming the ability of incoherent operations to enhance the coherence of mixed states relative to certain coherence monotones under strictly incoherent operations.

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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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arXiv2020

Significant Contribution of Projectile Excited States to the Stopping of Slow Helium Ions in Hydrogen Plasma

The energy deposition and the atomic processes, such as the electron-capture, ionization, excitation and radiative-decays for slow heavy ions in plasma remains an unsolved fundamental problem. Here we investigate, both experimentally and theoretically, the stopping of 100 keV=u helium ions in a well-defined hydrogen plasma. Our precise measurements show a much higher energy loss than the predictions of the semi-classical approaches with the commonly used effective charge. By solving the Time Dependent Rate Equation (TDRE) with all the main projectile states and for all relevant atomic processes, our calculations are in remarkable agreement with the experimental data. We also demonstrated that, acting as a bridge for electron-capture and ionization, the projectile excited states and their radiative decays can remarkably influence the equilibrium charge states and consequently lead to a substantial increasing of the stopping of ions in plasma.

physics.plasm-ph↗

arXiv2020

Catalyst-Assisted Probabilistic Coherence Distillation for Mixed States

The remarkable phenomenon of catalyst tells us that adding a catalyst could help state transformation. In this paper, we consider the problem of catalyst-assisted probabilistic coherence distillation for mixed states under strictly incoherent operations. To this end, we first present the necessary and sufficient conditions for distilling a target pure coherent state from an initial mixed state via stochastic strictly incoherent operations and the maximal probability of obtaining the target pure state from the initial state. With the help of these results, we present the necessary and sufficient conditions for the existence of a catalyst that increases the maximal transformation probability.

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arXiv2019

Deterministic Coherence Distillation

Coherence distillation is one of the central problems in the resource theory of coherence. In this Letter, we complete the deterministic distillation of quantum coherence for a finite number of coherent states under strictly incoherent operations. Specifically, we find the necessary and sufficient condition for the transformation from a mixed coherent state into a pure state via strictly incoherent operations, which recovers a connection between the resource theory of coherence and the algebraic theory of majorization lattice. With the help of this condition, we present the deterministic coherence distillation scheme and derive the maximum number of maximally coherent states obtained via this scheme.

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arXiv2019

Flag Additivity in Quantum Resource Theories

Quantum resource theories offer a powerful framework for studying various phenomena in quantum physics. Despite considerable effort has been devoted to developing a unified framework of resource theories, there are few common properties that hold for all quantum resources. In this paper, we fill this gap by introducing the flag additivity based on the tensor product structure and the flag basis for the general quantum resources. To illustrate the usefulness of flag additivity, we show that flag additivity can be used to derive other nontrivial properties in quantum resource theories, e.g., strong monotonicity, convexity, and full additivity.

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arXiv2018

Superadditivity of convex roof coherence measures

In this paper, we examine the superadditivity of convex roof coherence measures. We put forward a theorem on the superadditivity of convex roof coherence measures, which provides a sufficient condition to identify the convex roof coherence measures fulfilling the superadditivity. By applying the theorem to each of the known convex roof coherence measures, we prove that the coherence of formation and the coherence concurrence are superadditive, while the geometric measure of coherence, the convex roof coherence measure based on linear entropy, the convex roof coherence measure based on fidelity, and convex roof coherence measure based on $\frac{1}{2}$-entropy are non-superadditive.

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arXiv2018

Estimating coherence measures from limited experimental data available

Quantifying coherence has received increasing attention, and considerable work has been directed towards finding coherence measures. While various coherence measures have been proposed in theory, an important issue following is how to estimate these coherence measures in experiments. This is a challenging task, since the state of a system is often unknown in practical applications and the accessible measurements in a real experiment are typically limited. In this Letter, we put forward an approach to estimate coherence measures of an unknown state from any limited experimental data available. Our approach is not only applicable to coherence measures but can be extended to other resource measures.

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arXiv2017

Enhancing coherence of a state by stochastic strictly incoherent operations

In this paper, we address the issue of enhancing coherence of a state under stochastic strictly incoherent operations. Based on the $l_1$ norm of coherence, we obtain the maximal value of coherence that can be achieved for a state undergoing a stochastic strictly incoherent operation and the maximal probability of obtaining the maximal coherence. Our findings indicate that a pure state can be transformed into a maximally coherent state under a stochastic strictly incoherent operation if and only if all the components of the pure state are nonzero while a mixed state can never be transformed into a maximally coherent state under a stochastic strictly incoherent operation.

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arXiv2017

A new coherence measure based on fidelity

Quantifying coherence is an essential endeavor for both quantum foundations and quantum technologies. In this paper, we put forward a quantitative measure of coherence by following the axiomatic definition of coherence measures introduced in [T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett. 113, 140401 (2014)]. Our measure is based on fidelity and analytically computable for arbitrary states of a qubit. As one of its applications, we show that our measure can be used to examine whether a pure qubit state can be transformed into another pure or mixed qubit state only by incoherent operations.

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