arXiv subjects

Long Huang

Publications and source records attributed to Long Huang.

45 records · Page 3Linked to original sources

arXiv2018

Certifying quantumness with the classical fidelity threshold

For a given ensemble of input and target states, the classical fidelity threshold (CFT) is the maximum valve of the averaged fidelity, and it can be achieved with a measure-and-prepare operation. This quantity can be employed to verify whether the channel is in the quantum domain or not. In a recent work by Chiribella and Xie [Phys. Rev. Lett. {\bf 110}, 213601 (2013)], it was showed that all the information about the input and target states can be equivalently described by an entangled state and an effective entanglement-braking (EB) channel, and the CFTs can be defined with the Choi matrix of the effective EB channel. Following this idea, the protocol proposed by Fuchs and Sasaki [Quantum. Inf. Comput, {\bf 3}, 377 (2003)] are reformulated in terms of the effective EB channel, and ss applications, the deterministic and probabilistic CFTs for qubit states and the coherent states are derived in this paper.

quant-ph↗

arXiv2018

Dual Spaces of Anisotropic Mixed-Norm Hardy Spaces

Let $\vec{a}:=(a_1,\ldots,a_n)\in[1,\infty)^n$, $\vec{p}:=(p_1,\ldots,p_n)\in(0,\infty)^n$ and $H_{\vec{a}}^{\vec{p}}(\mathbb{R}^n)$ be the anisotropic mixed-norm Hardy space associated with $\vec{a}$ defined via the non-tangential grand maximal function. In this article, the authors give the dual space of $H_{\vec{a}}^{\vec{p}}(\mathbb{R}^n)$, which was asked by Cleanthous et al. in [J. Geom. Anal. 27 (2017), 2758-2787]. More precisely, via first introducing the anisotropic mixed-norm Campanato space $\mathcal{L}_{\vec{p},\,q,\,s}^{\vec{a}}(\mathbb{R}^n)$ with $q\in[1,\infty]$ and $s\in\mathbb{Z}_+:=\{0,1,\ldots\}$, and applying the known atomic and finite atomic characterizations of $H_{\vec{a}}^{\vec{p}}(\mathbb{R}^n)$, the authors prove that the dual space of $H_{\vec{a}}^{\vec{p}}(\mathbb{R}^n)$ is the space $\mathcal{L}_{\vec{p},\,r',\,s}^{\vec{a}}(\mathbb{R}^n)$ with $\vec{p}\in(0,1]^n$, $r\in(1,\infty]$, $1/r+1/r'=1$ and $s\in[\lfloor\fracν{a_-}(\frac{1}{p_-}-1) \rfloor,\infty)\cap\mathbb{Z}_+$, where $ν:=a_1+\cdots+a_n$, $a_-:=\min\{a_1,\ldots,a_n\}$, $p_-:=\min\{p_1,\ldots,p_n\}$ and, for any $t\in \mathbb{R}$, $\lfloor t\rfloor$ denotes the largest integer not greater than $t$. This duality result is new even for the isotropic mixed-norm Hardy spaces on $\mathbb{R}^n$.

math.CA↗

arXiv2018

Atomic and Littlewood-Paley Characterizations of Anisotropic Mixed-Norm Hardy Spaces and Their Applications

Let $\vec{a}:=(a_1,\ldots,a_n)\in[1,\infty)^n$, $\vec{p}:=(p_1,\ldots,p_n)\in(0,\infty)^n$ and $H_{\vec{a}}^{\vec{p}}(\mathbb{R}^n)$ be the anisotropic mixed-norm Hardy space associated with $\vec{a}$ defined via the non-tangential grand maximal function. In this article, via first establishing a Calderón-Zygmund decomposition and a discrete Calderón reproducing formula, the authors then characterize $H_{\vec{a}}^{\vec{p}}(\mathbb{R}^n)$, respectively, by means of atoms, the Lusin area function, the Littlewood-Paley $g$-function or $g_λ^\ast$-function. The obtained Littlewood-Paley $g$-function characterization of $H_{\vec{a}}^{\vec{p}}(\mathbb{R}^n)$ coincidentally confirms a conjecture proposed by Hart et al. [Trans. Amer. Math. Soc. (2017), DOI: 10.1090/tran/7312]. Applying the aforementioned Calderón-Zygmund decomposition as well as the atomic characterization of $H_{\vec{a}}^{\vec{p}}(\mathbb{R}^n)$, the authors establish a finite atomic characterization of $H_{\vec{a}}^{\vec{p}}(\mathbb{R}^n)$, which further induces a criterion on the boundedness of sublinear operators from $H_{\vec{a}}^{\vec{p}}(\mathbb{R}^n)$ into a quasi-Banach space. Then, applying this criterion, the authors obtain the boundedness of anisotropic Calderón-Zygmund operators from $H_{\vec{a}}^{\vec{p}}(\mathbb{R}^n)$ to itself [or to $L^{\vec{p}}(\mathbb{R}^n)$]. The obtained atomic characterizations of $H_{\vec{a}}^{\vec{p}}(\mathbb{R}^n)$ and boundedness of anisotropic Calderón-Zygmund operators on these Hardy-type spaces positively answer two questions mentioned by Cleanthous et al. in [J. Geom. Anal. 27 (2017), 2758-2787]. All these results are new even for the isotropic mixed-norm Hardy spaces on $\mathbb{R}^n$.

math.CA↗

arXiv2017

Performance of five-qubit code for arbitrary error channels

In quantum error correction, it is an important assumption that errors on different qubits are independent. In our previous work [Phys. Rev. A {\bf 92}, 052320 (2015)], the generality of the concatenated five-qubit code has been investgated when noises of the principal system and the auxiliary environment are assumed to be the same. In the error correction with concatenated code, tiny differences (in fidelity or independent errors) between initial quantum channels may introduce different effective channels in the next level, and therefore, it is necessary to study a meaningful question: Does five-qubit code still work efficiently when errors on different qubits are different? In the present work, it is discovered that even errors for different qubits are arbitrary, the five-qubit code still works efficiently. Since it is much easier and more accurate to measure the fidelity, one can construct quantum error correction with five-qubit code according to the initial channel fidelity, and it is not necessary to know the complete information of the initial channel. Moreover, when the initial channel fidelity is below $0.992$, the fidelity threshold for five-qubit code is the fidelity of the effective channel after error correction in bit-flip channels.

quant-ph↗

arXiv2017

Pryce's mass-center operators and the anomalous velocity of a spinning electron

In the present work, we develop a method to calculate the anomalous velocity of a spinning electron. From Dirac equation, the relationships among the expectation values of the Pryce's mass-center operator, the position operator, the spin operator and the canonical momentum operator are investigated. By requiring that the center of mass for the classical spinning electron is related to the expectation value of the Pryce's mass-center operator, one can obtain a classical expression for the position of the electron. With the classical equations of motion, the anomalous velocity of a spinning electron can be easily calculated. It is shown that two factors contribute to the anomalous velocity: one is dependent on the selection of the Pryce's mass-center operators and the other is a type-independent velocity expressed by the rotational velocity and the Lorentz force.

quant-ph↗

arXiv2016

Study on the power scaling and mode instability property in an all-fiber narrow-linewidth tapered fiber amplifier

We develop a high-power narrow-linewidth fiber amplifier based on a tapered Yb-doped fiber. In the experiment, the narrow end of the tapered fiber is used as the input port of both pump source and signal light to form a robust all-fiber configuration. The stimulated Brillouin scattering (SBS) is effectively suppressed owing to its gradually increased mode area as well as continuously changed Brillouin frequency shift dependent on the core diameter. As a result, an output power of 260 W without SBS and mode instability (MI) is obtained, with a slope efficiency of 71.3 % and a narrow linewidth of ~2GHz. However, the MI rather than SBS is observed when output power reaches 260 W. The features of MI are experimentally studied in detail. It is pointed out that, the MI seems the primary and durative limitation factor of the tapered fiber amplifier for high-power narrow-linewidth output, although it has advantage to reduce other nonlinear effect. To the best of our knowledge, this is the first detailed experimental study on MI in a tapered fiber. At last, some worthwhile discussion about the optimization of the tapered fiber and the whole system for both SBS and MI suppression is conducted based on the present and previous results.

physics.optics↗

arXiv2015

Generality of the concatenated five-qubit code

In this work, a quantum error correction (QEC) procedure with the concatenated five-qubit code is used to construct a near-perfect effective qubit channel (with a error below $10^{-5}$) from arbitrary noise channels. The exact performance of the QEC is characterized by a Choi matrix, which can be obtained via a simple and explicit protocol. In a noise model with five free parameters, our numerical results indicate that the concatenated five-qubit code is general: To construct a near-perfect effective channel from the noise channels, the necessary size of the concatenated five-qubit code depends only on the entanglement fidelity of the initial noise channels.

quant-ph↗

arXiv2014

A protocol to estimate the average fidelity of the bipartite system

In present work, we shall develope a protocol to estimate the average fidelity for the bipartite system. We show that the average fidelity should be known if the three measurable quantities, the average survive probability of the product state and the the average survive probablity of each subsystem, have been decided. Our protocol can be also applied to decide the selected element of the quantum proess matrix.

quant-ph↗

arXiv2013

The Gravitational Deflection of Light in F(R)-gravity

The fact that the gravitation could deflect the light trajectory has been confirmed by a large number of observation data, that is consistent with the result calculated by Einstein's gravity. F(R)-gravity is the modification of Einstein's gravity. According to the field equations obtained by the action of the f(R) form, we get a similar Schwarzschild metric. According to the condition that four-dimension momenta of the photon return to zero and that of conservation of covariant momenta, we obtain the equation of motion of the photon in a specific form of f (R)-gravity. We solve the equation to get the gravitational deflection angle of light that grazes the surface of sun and the calculation result is consistent with the experimental observation data.

gr-qc↗