arXiv subjects

Xiao-Gang Fan

Publications and source records attributed to Xiao-Gang Fan.

9 recordsLinked to original sources

arXiv2024

Einstein-Podolsky-Rosen Steering Criterion and Monogamy Relation via Correlation Matrices in Tripartite Systems

Quantum steering is considered as one of the most well-known nonlocal phenomena in quantum mechanics. Unlike entanglement and Bell non-locality, the asymmetry of quantum steering makes it vital for one-sided device-independent quantum information processing. Although there has been much progress on steering detection for bipartite systems, the criterion for EPR steering in tripartite systems remains challenging and inadequate. In this paper, we firstly derive a novel and promising steering criterion for any three-qubit states via correlation matrix. Furthermore, we propose the monogamy relation between the tripartite steering of system and the bipartite steering of subsystems based on the derived criterion. Finally, as illustrations, we demonstrate the performance of the steering criterion and the monogamy relation by means of several representative examples. We believe that the results and methods presented in this work could be beneficial to capture genuine multipartite steering in the near future.

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arXiv2024

Nonreciprocal Photon-Phonon Entanglement in Kerr-Modified Spinning Cavity Magnomechanics

Cavity magnomechanics has shown great potential in studying macroscopic quantum effects, especially for quantum entanglement, which is a key resource for quantum information science. Here we propose to realize magnon mediated nonreciprocal photon-phonon entanglement, which exhibits asymmetry when opposite magnetic or driving fields are respectively applied to the magnons with the Kerr effect or the photons with the Sagnac effect. We find that the mean magnon number can selectively exhibit nonreciprocal linear or nonlinear (bistable) behavior with the strength of the strong driving field on the cavity. Assisted by this driving field, the magnon-phonon coupling is greatly enhanced, leading to the nonreciprocal photon-phonon entanglement via the swapping interaction between the magnons and photons. This nonreciprocal entanglement can be significantly enhanced with the magnon Kerr and Sagnac effects. Given the available parameters, the nonreciprocal photon-phonon entanglement can be preserved at $\sim3$ K, showing remarkable resilience against the bath temperature. The result reveals that our paper holds promise in developing various nonreciprocal devices with both the magnon Kerr and Sagnac effects in cavity magnomechanics.

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arXiv2023

Nonreciprocal entanglement in cavity-magnon optomechanics

Cavity optomechanics, a promising platform to investigate macroscopic quantum effects, has been widely used to study nonreciprocal entanglement with Sagnec effect. Here we propose an alternative way to realize nonreciprocal entanglemment among magnons, photons, and phonons in a hybrid cavity-magnon optomechanics, where magnon Kerr effect is used. We show that the Kerr effect gives rise to a magnon frequency shift and an additional two-magnon effect. Both of them can be tuned from positive to negative via tuning the magectic field direction, leading to nonreciprocity. By tuning system parameters such as magnon frequency detuning or the coefficient of the two-magnon effect, bipartite and tripartite entanglements can be nonreciprocally enhanced. By further studying the defined bidirectional contrast ratio, we find that nonreciprocity in our system can be switch on and off, and can be engineered by the bath temperature. Our proposal not only provides a potential path to demonstrate nonreciprocal entanglement with the magnon Kerr effect, but also opens a direction to engineer and design diverse nonreciprocal devices in hybrid cavity-magnon optomechanics with nonlinear effects.

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arXiv2023

Complementary relations of entanglement, coherence, steering and Bell nonlocality inequality violation in three-qubit states

We put forward complementary relations of entanglement, coherence, steering inequality violation, and Bell nonlocality for arbitrary three-qubit states. We show that two families of genuinely entangled three-qubit pure states with single parameter exist, and they exhibit maximum coherence and steering inequality violation for a fixed amount of negativity, respectively. It is found that the negativity is exactly equal to the geometric mean of bipartite concurrences for the three-qubit pure states, although the negativity is always less than or equal to the latter for three-qubit mixed states. Moreover, the complementary relation between negativity and first-order coherence for tripartite entanglement states are established. Furthermore, we investigate the close relation between the negativity and the maximum steering inequality violation. In addition, the complementary relation between negativity and the maximum Bell-inequality violation for arbitrary three-qubit states is obtained. The results provide reliable evidence of fundamental connections among entanglement, coherence, steering inequality violation, and Bell nonlocality.

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arXiv2021

Necessary and sufficient criterion of steering for two-qubit T states

Einstein-Podolsky-Rosen (EPR) steering is the ability that an observer persuades a distant observer to share entanglement by making local measurements. Determining a quantum state is steerable or unsteerable remains an open problem. Here, we derive a new steering inequality with infinite measurements corresponding to an arbitrary two-qubit T state, from consideration of EPR steering inequalities with N projective measurement settings for each side. In fact, the steering inequality is also a sufficient criterion for guaranteering that the T state is unsteerable. Hence, the steering inequality can be viewed as a necessary and sufficient criterion to distinguish whether the T state is steerable or unsteerable. In order to reveal the fact that the set composed of steerable states is the strict subset of the set made up of entangled states, we prove theoretically that all separable T states can not violate the steering inequality. Moreover, we put forward a method to estimate the maximum violation from concurrence for arbitrary two-qubit T states, which indicates that the T state is steerable if its concurrence exceeds 1/4.

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arXiv2020

Constraint relation between steerability and concurrence for two-qubit states

Entanglement and steering are used to describe quantum inseparabilities. Steerable states form a strict subset of entangled states. A natural question arises concerning how much territory steerability occupies entanglement for a general two-qubit entangled state. In this work, we investigate the constraint relation between steerability and concurrence by using two kinds of evolutionary states and randomly generated two-qubit states. By combining the theoretical and numerical proofs, we obtain the upper and lower boundaries of steerability. And the lower boundary can be used as a sufficient criterion for steering detection. Futhermore, we consider a special kind of mixed state transformed by performing an arbitrary unitary operation on Werner-like state, and propose a sufficient steering criterion described by concurrence and purity.

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arXiv2020

Improved tripartite uncertainty relation with quantum memory

Uncertainty principle is a striking and fundamental feature in quantum mechanics distinguishing from classical mechanics. It offers an important lower bound to predict outcomes of two arbitrary incompatible observables measured on a particle. In quantum information theory, this uncertainty principle is popularly formulized in terms of entropy. Here, we present an improvement of tripartite quantum-memory-assisted entropic uncertainty relation. The uncertainty's lower bound is derived by considering mutual information and Holevo quantity. It shows that the bound derived by this method will be tighter than the lower bound in [Phys. Rev. Lett. 103, 020402 (2009)]. Furthermore, regarding a pair of mutual unbiased bases as the incompatibility, our bound will become extremely tight for the three-qubit $\emph{X}$-state system, completely coinciding with the entropy-based uncertainty, and can restore Renes ${\emph{et al.}}$'s bound with respect to arbitrary tripartite pure states. In addition, by applying our lower bound, one can attain the tighter bound of quantum secret key rate, which is of basic importance to enhance the security of quantum key distribution protocols.

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arXiv2019

Inequality relation between entanglement and Bell nonlocality for arbitrary two-qubit states

Entanglement and Bell nonlocality are used to describe quantum inseparabilities. Bell-nonlocal states form a strict subset of entangled states. A natural question arises concerning how much territory Bell nonlocality occupies entanglement for a general two-qubit entangled state. In this work, we investigate the relation between entanglement and Bell nonlocality by using lots of randomly generated two-qubit states, and give out a constraint inequality relation between the two quantum resources. For studying the upper or lower boundary of the inequality relation, we discover maximally (minimally) nonlocal entangled states, which maximize (minimize) the value of the Bell nonlocality for a given value of the entanglement. Futhermore, we consider a special kind of mixed state transformed by performing an arbitrary unitary operation on werner state. It is found that the special mixed state's entanglement and Bell nonlocality are related to ones of a pure state transformed by the unitary operation performed on the Bell state.

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arXiv2019

Universal trade-off relation between coherence and intrinsic concurrence for two-qubit states

Entanglement and coherence are two essential quantum resources for quantum information processing. A natural question arises of whether there are direct link between them. And by thinking about this question, we propose a new measure for quantum state that contains concurrence and is called intrinsic concurrence. Interestingly, we discover that the intrinsic concurrence is always complementary to coherence. Note that the intrinsic concurrence is related to the concurrence of a special pure state ensemble. In order to explain the trade-off relation more intuitively, we apply it in some composite systems composed by a single-qubit state coupling four typical noise channels with the aim at illustrating their mutual transformation relationship between their coherence and intrinsic concurrence. This unified trade-off relation will provide more flexibility in exploiting one resource to perform quantum tasks and also provide credible theoretical basis for the interconversion of the two important quantum resources.

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