arXiv subjects

Xue-xiang Xu

Publications and source records attributed to Xue-xiang Xu.

At least 19 recordsLinked to original sources

arXiv2026

Information Geometry of Four-Parameter Single-Qutrit States: From Quantum to Semiclassical Geometric Tensors

The gap between the classical and quantum Fisher information matrices (CFIM and QFIM) separates what is operationally accessible through measurements from what is intrinsic to a quantum state. In the multiparameter setting, this quantum obstruction is generically not saturable. Motivated by the recently introduced semiclassical geometric tensor (SCGT), we perform an explicit information-geometric study for a class of pure four-parameter single-qutrit states (FPSQSs). These states are probed by a one-parameter family of measurements that interpolates between an uninformative POVM and a sharp projective measurement. We derive closed-form expressions for the CFIM, the quantum geometric tensor (QGT), and the SCGT. We show that the SCGT reproduces the QGT in the projective limit and vanishes in the trivial limit. The real part of the SCGT splits into two terms: the CFIM and an additional nonnegative measurement-transmitted metric in the phase sector. Its imaginary part provides a semiclassical Berry curvature. Its loss relative to the QGT is quantified by a measurement-dependent gap. Our results provide an exactly solvable four-parameter platform for the semiclassical geometric framework. They also clarify how realistic measurements read out the geometric content of quantum states, and how they partially degrade it.

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arXiv2025

Exploring entanglement, Wigner negativity and Bell nonlocality for anisotropic two-qutrit states

We introduce a family of anisotropic two-qutrit states (AITTSs). These AITTSs are expressed as $ρ_{aiso}=p\left\vert ψ_{\left( θ,ϕ\right) }\right\rangle \left\langle ψ_{\left( θ,ϕ\right)}\right\vert +(1-p)\frac{1_{9}}{9}$ with $\left\vert ψ_{\left( θ,ϕ\right) }\right\rangle =\sin θ\cos ϕ\left\vert00\right\rangle +\sin θ\sin ϕ\left\vert 11\right\rangle +\cosθ\left\vert 22\right\rangle $ and $1_{9}=\sum_{j,k=0}^{2}\left\vert jk\right\rangle \left\langle jk\right\vert $. For a given $p\in \lbrack 0,1]$, these states are adjustable in different ($θ,ϕ$) directions. In the case of ($θ,ϕ$) = ($\arccos (1/\sqrt{3}),π/4$), the AITTS will reduce to the isotropic two-qutrit state $ρ_{iso}$. In addition, the AITTSs are severely affected by the white noise ($ρ_{noise}=1_{9}/9$). Three properties of the AITTSs, including entanglement, Wigner negativity and Bell nonlocality, are explored detailedly in the analytical and numerical ways. Each property is witnessed by an appropriate existing criterion. Some of our results are summarized as follows: (i) Large entanglement does not necessarily mean high Wigner negativity and strong Bell nonlocality. (ii) A pure state with a large Schmidt number does not necessarily have a greater Wigner negativity. (iii) Only when $\left\vertψ_{\left( θ,ϕ\right) }\right\rangle $ has the Schmidt number 3, the AITTS has the possibility of exhibiting Bell nonlocality in proper parameter range.

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arXiv2024

Tripartite entanglement and tripartite steering in three-qubit pure states induced by vacuum--one-photon superpositions

Utilizing a tritter with variable parameter $T$ and induced by vacuum--one-photon superpositions $\left\vert 0\right\rangle +α\left\vert 1\right\rangle $ with $α=\left\vert α\right\vert e^{iϕ}$, we propose a scheme to prepare a class of three-qubit pure states. These states take the form of $\left\vert ψ\right\rangle _{123}=c_{0}\left\vert 000\right\rangle +c_{1}\left\vert 100\right\rangle +c_{2}\left\vert 010\right\rangle +c_{3}\left\vert 001\right\rangle $. The coefficients ($c_{0}$, $c_{1}$, $c_{2}$, and $c_{3}$) can be manipulated through interaction parameters ($\left\vert α\right\vert $, $ϕ$, and $T$). In line with Xie and Eberly's work[Phys. Rev. Lett. 127, 040403 (2021)], we investigate the genuine tripartite entanglement for $\left\vert ψ\right\rangle _{123}$ by using the measure of concurrence fill. Drawing on Hao \textit{et al.}'s research [Phys. Rev. Lett. 128, 120402 (2021)], we examine tripartite steering for $\left\vert ψ\right\rangle _{123}$ under certain measurements based on the uncertainty relations criterion. We identify nine potential configurations exhibiting varying steerability across different parameter spaces. It is important to highlight that, while the state $\left\vert ψ\right\rangle _{123}$ exhibits entanglement, steering remains unattainable in a substantial portion of the parameter space.

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arXiv2023

Noiselessly amplified thermal states and after multi-photon addition or subtraction

In this paper, we introduce a noiselessly amplified thermal state (ATS), by operating the noiseless amplification operator ($g^{\hat{n}}$) on the thermal state (TS) with corresponding mean photon number (MPN) $\bar{n}$. Actually, the ATS is an new TS with MPN $\bar{N}=g^{2}\bar{n}/[1-\bar{n}\left(g^{2}-1\right)]$. Furthermore, we introduce photon-added-ATS (PAATS) and photon-subtracted-ATS (PSATS) by operating $m$-photon addition ($\hat{a}^{†m}$) and $m$-photon subtraction ($\hat{a}^{m}$) on the ATS, respectively. We study photon number distributions (PNDs), purities, and Wigner functions (WFs) for all these states.

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arXiv2023

Coupled three-mode squeezed vacuum: Gaussian steering and remote generation of Wigner negativity

Multipartite Einstein-Podolsky-Rosen (EPR) steering and multimode quantum squeezing are essential resources for various quantum applications. The paper focuses on studying a coupled three-mode squeezed vacuum (C3MSV), which is a typical multimode squeezed Gaussian state and will exhibit peculiar steering property. Using the technique of integration within ordered products, we give the normal-ordering form for the coupled three-mode squeezing operator and derive the general analytical expressions of the statistical quantities for the C3MSV. Under Gaussian measurements, we analyze all bipartite Gaussian steerings (including no steering, one-way steering and two-way steering) in details and study the monogamy relations for the C3MSV. Then, we study the decoherence of all these steerings in noisy channels and find that sudden death will happen in a certain threshold time. Through the steerings shared in the C3MSV, we propose conceptual (and ideal) schemes of remotely generating Wigner negativity (WN) by performing appropriate photon subtraction(s) in the local position. Our obtained results may lay a solid theoretical foundation for a future practical study. We also believe that the C3MSV will be one of good candidate resources in future quantum protocols.

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arXiv2022

Multiphoton states engineering by heralded interference via six-port Mach-Zehnder interferometer

Based on heralded interference on a six-port Mach-Zehnder interferometer, we propose protocols to generate a series of multiphoton states in primary output port, by injecting a coherent state in primary input port and two Fock states in two ancillary input ports, and measuring two Fock states in two ancillary output ports. Only manipulating at the single-photon level (i.e, |0> or |1>) in all ancillary ports, we generate sixteen types (six categories) of multiphoton nonclassical states, whose state vectors are unified as superposition of a new coherent state, a single-photon added coherent state, and a two-photon added coherent state. Indeed, a wide range of nonclassical phenomena can be created by modulating the interaction parameters (including coherent field strength and shift phase). We mainly analyze quadrature-squeezing effects for all our considered states. Of particular interest is maximum squeezing of up to 2.57dB, with success probability 6.7%, at least in our present cases.

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arXiv2022

Two-mode light states before and after delocalized single-photon addition

We studied the effect of delocalized single-photon addition (DPA) on two input modes containing four cases: two independent coherent states (CSs), two independent thermal states (TSs), two independent single-mode squeezed vacuums (SVs), and an entangled two-mode squeezed vacuum (TMSV). In essence, four types of new non-Gaussian entangled light states are generated. We studied three different resources (including entanglement, discorrelation and Wigner negativity) for each two-mode light state. The output states after DPA are entangled, with more parameters and complex structures, characterizing more Wigner negativity or even discorrelation. In contrast, the CSs case is the most tunable protocol, because its negativity under partial transposition, discorrelation, and Wigner logarithmic negativity are more sensitive to superposition phase than those in TSs, SVs and TMSV cases.

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arXiv2022

Multi-photon-addition amplified coherent state

State $g^{\hat{n}}\hat{a}^{†m}\left\vert α\right\rangle $ and state $\hat{a}^{†m}g^{\hat{n}}\left\vert α\right\rangle $ are same to state $\hat{a}^{†m}\left\vert gα\right\rangle $, which is called as multi-photon-addition amplified coherent state (MPAACS) by us. Here, $\hat{n}$, $\hat{a}^{†}$, $\left\vert α\right\rangle $, $g$ ( $\geq 1$), and $m$ are photon number operator, creation operator, coherent state, gain facor, and an interger, respectively. We study mathematical and physical properties for these MPAACSs, including normalization, photon component analysis, Wigner function, effective gain, quadrature squeezing, and equivalent input noise. Actually, the MPAACS, which contains more nonclassicality, is an amplified version of photon-added coherent state (PACS) introduced by Agrwal and Tara [Phys. Rev. A 43, 492 (1991)]. Our work provides theoretical references for implementing amplifiers for light fields.

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arXiv2021

Multi-headed symmetrical superpositions of coherent states

Based on N different coherent states with equal weights and phase-space rotation symmetry, we introduce N-headed incoherent superposition states (NHICSSs) and N-headed coherent superposition states (NHCSSs). These N coherent states are associated with N-order roots of the same complex number. We study and compare properties of NHICSSs and NHCSSs, including average photon number, Mandel Q parameter, quadrature squeezing, Fock matrix elements and Wigner function. Among all these states, only 2HCSS (i.e., Schrodinger cat state) presents quadrature-squeezing effect. Our theoretical results can be used as a reference for researchers in this field.

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arXiv2020

Changing Fock matrix elements of two-mode squeezed vacuum state by employing three quantum operations in one-sided lossy channel

This paper focuses on changing Fock matrix elements of two-mode squeezed vacuum state (TMSVS) by employing three quantum operations in one-sided lossy channel. These three quantum operations include one-photon replacement (OPR), one-photon substraction (OPS) and one-photon addition (OPA). Indeed, three conditional quantum states have been generated from the original TMSVS. Using the characteristic function (CF) representation of quantum density operator, we derive the analytical expressions of their Fock matrix elements, which are dependent on the interaction parameters, including the squeezing parameter of the input TMSVS, the loss factor and the transmissivity of the variable beam splitter. For convenience of discussion, we only give the Fock matrices in the subspace span {|00>,|01>,|10>,|02>,|11>,|20>} for these two-mode states. Obviously, the TMSVS only has the populations in |00> and |11> in such subspace. By comparing the generated states with the TMSVS, we find that: (1) The generated state after OPR will remain the populations in |00> and |11>, and add the populations in |10> and |20>; (2) The generated state after OPS will lost the populations in |00> and |11>, but add the populations in |10> and |20>; (3) The generated state after OPA will remain the population only in |11> and add the population in |01>.

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arXiv2019

Conditional generation of multiphoton-subtracted squeezed vacuum states: loss consideration and operator description

In terms of the characteristic functions of the quantum states, we present a complete operator description of a lossy photon-subtraction scheme. Feeding a single-mode squeezed vacuum into a variable beam splitter and counting the photons in one of the output channels, a broad class of multiphoton-subtracted squeezed vacuum states (MSSVSs) can be generated in other channel. Here the losses are considered in the beginning and the end channels in the circuit. Indeed, this scheme has been discussed in Ref. [Phys. Rev. A 100, 022341 (2019)]. However, different from the above work, we give all the details of the optical fields in all stages. In addition, we present the analytical expressions and numerical simulations for the success probability, the quadrature squeezing effect, photon-number distribution and Wigner function of the MSSVSs. Some interesting results effected by the losses are obtained.

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arXiv2016

On the optical fields propagation in realistic environments

Evolution formulas of the density operator, the photon number distribution, and the Wigner function are derived for the problem on the optical fields propagation in realistic environments. The method of deriving these formulas is novel and the results are very useful for quantum optics and quantum statistics.

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arXiv2015

Generating single-photon catalyzed coherent states with quantum-optical catalysis

We generate single-photon catalyzed coherent states (SPCCSs) by means of quantum-optical catalysis based on the beam splitter (BS) or the parametric amplifier (PA). These states are obtained in one of the BS (or PA) output channels if a coherent state and a single-photon Fock state are present in two input ports and a single photon is registered in the other output port. The success probabilities of the detection (also the normalization factors) are discussed, which is different for BS and PA catalysis. In addition, we prove that the generated states catalyzed by BS and PA devices are actually the same quantum states after analyzing photon number distribution of the SPCCSs. The quantum properties of the SPCCSs, such as sub-Poissionian distribution, anti-bunching effect, quadrature squeezing effect, and the negativity of the Wigner function are investigated in detail. The results shows that the SPCCSs are non-Gaussian states with an abundance of nonclassicality, which can provide the quantum advantages for quantum technological tasks.

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arXiv2015

Measurement induced nonclassical states from coherent state heralded by Knill-Laflamme-Milburn-type SU(3) interference

We theoretically generate nonclassical states from coherent state heralded by Knill-Laflamme-Milburn (KLM)-type SU(3) interference. Injecting a coherent state in signal mode and two single-photon sources in other two auxiliary modes of SU(3) interferometry, a broad class of useful nonclassical states are obtained in the output signal port after making two single-photon-counting measurements in the two output auxiliary modes. The nonclassical properties, in terms of anti-bunching effect and squeezing effect as well as the negativity of the Wigner function, are studied in detail by adjusting the interaction parameters. The results show that the input coherent state can be transformed into non-Gaussian states with higher nonclassicality after measurement induction. The maximum squeezing of our generated states can be arrived at about 1.9 dB.

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arXiv2015

Enhancing quantum entanglement and quantum teleportation for two-mode squeezed vacuum state by local quantum-optical catalysis

I theoretically investigate how the entanglement properties of a two-mode squeezed vacuum state (TMSVS) can be enhanced by operating quantum-optical catalysis on each mode of the TMSVS. The quantum-optical catalysis is simply mixing one photon at the beam splitter and post-select the beam-splitter (BS) output based on detection of one photon, first proposed by Lvovsky and Mlynek [Phys. Rev. Lett. 88, 250401 (2002)]. I find that there exists some enhancement in the entanglement properties (namely, entanglement entropy, second-order Einstein-Podolsky-Rosen correlation, and the fidelity of quantum teleportation) in certain parameter ranges spanned by the low transmissivities of the BSs and the small squeezing parameter of the input TMSVS.

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arXiv2015

Generating Hermite polynomial excited squeezed states by means of conditional measurements on a beam splitter

A scheme for conditional generating a Hermite polynomial excited squeezed vacuum states (HESVS) is proposed. Injecting a two-mode squeezed vacuum state (TMSVS) into a beam splitter (BS) and counting the photons in one of the output channels, the conditional state in the other output channel is just a HESVS. To exhibit a number of nonclassical effects and non-Guassianity, we mainly investigate the photon number distribution, sub-Poissonian distribution, quadrature component distribution, and quasi-probability distribution of the HPESVS. We find that its nonclassicality closely relates to the control parameter of the BS, the squeezed parameter of the TMSVS, and the photon number of conditional measurement. These further demonstrate that performing the conditional measurement on a BS is an effective approach to generate non-Guassian state.

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arXiv2014

M Times Photon Subtraction-Addition Coherent Superposition Operated Odd-Schrődinger-cat State: Nonclassicality and Decoherence

We introduce a new non-Gaussian state, generated by m times coherent superposition operation $a\cos θ+a^{\dagger }e^{iφ}\sin θ$ (MCSO) on odd-Schrodinger-cat state (OSCS). Its normalized constant is turned out to be related with the Hermite polynomial. We further investigate the nonclassical properties of the MCSO-OSCS through Mandel's Q-parameter, quadrature squeezing, the photocount distribution and Wigner function (WF). It is shown that the nonclassicality of the MCSO-OSCS is influenced by the number of times (m) of coherent superpositon operation, the angle $θ$ and the amplitude of the coherent state (|$α_{0}$|). Especially the volume of negative region of WF increases with the increment of parameters m, $θ$ and $α_{0}$. We also investigate the decoherence of the MCSO-OSCS in terms of the fadeaway of the negativity of WF in a thermal environment.

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arXiv2010

Fractional Hadamard transform with continuous variables in the context of quantum optics

We introduce the quantum fractional Hadamard transform with continuous variables. It is found that the corresponding quantum fractional Hadamard operator can be decomposed into a single-mode fractional operator and two single-mode squeezing operators. This is extended to the entangled case by using the bipartite entangled state representation. The new transformation presents more flexibility to represent signals in the fractional Hadamard domain with extra freedom provided by an angle and two-squeezing parameters.

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