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Optimal superdense coding capacity in the non-Markovian regime 非马尔可夫机制中的最优超密集编码能力
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-04-19 DOI: 10.1088/1751-8121/ad40e0
Y. Aiache, S. Al-Kuwari, K. El Anouz, A. El Allati
{"title":"Optimal superdense coding capacity in the non-Markovian regime","authors":"Y. Aiache, S. Al-Kuwari, K. El Anouz, A. El Allati","doi":"10.1088/1751-8121/ad40e0","DOIUrl":"https://doi.org/10.1088/1751-8121/ad40e0","url":null,"abstract":"\u0000 Superdense coding is a significant technique widely used in quantum information processing. Indeed, it consists of sending two bits of classical information using a single qubit, leading to faster and more efficient quantum communication. In this paper, we propose a model to evaluate the effect of backflow information in a superdense coding protocol through a non-Markovian dynamics. The model considers a qubit interacting with a structured Markovian environment. In order to generate a non-Markovian dynamic, an auxiliary qubit contacts a Markovian reservoir in such a way that the non-Markovian regime can be induced. By varying the coupling strength between the central qubit and the auxiliary qubit, the two dynamical regimes can be switched interchangeably. An enhancement in non-Markovian effects corresponds to an increase in this coupling strength. Furthermore, we conduct an examination of various parameters, namely temperature weight, and decoherence parameters in order to explore the behaviors of superdense coding, quantum Fisher information, and local quantum uncertainty using an exact calculation. The obtained results show a significant relationship between non-classical correlations and quantum Fisher information since they behave similarly, allowing them to detect what is beyond entanglement. In addition, the presence of non-classical correlations enables us to detect the optimal superdense coding capacity in a non-Markovian regime.","PeriodicalId":502730,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":" 17","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140684559","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The overlap of Generalized Coherent States of any rank one simple Lie algebra and its classical limit 任何一级简单李代数的广义相干态的重叠及其经典极限
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-04-19 DOI: 10.1088/1751-8121/ad40e2
Nicola Pranzini
{"title":"The overlap of Generalized Coherent States of any rank one simple Lie algebra and its classical limit","authors":"Nicola Pranzini","doi":"10.1088/1751-8121/ad40e2","DOIUrl":"https://doi.org/10.1088/1751-8121/ad40e2","url":null,"abstract":"\u0000 We provide a formula for computing the overlap between two Generalized Coherent States of any rank one simple Lie algebra. Then, we apply our formula to spin coherent states (i.e. su(2) algebra), pseudo-spin coherent states (i.e. su(1,1) algebra), and the sl(2,R) subalgebras of Virasoro. In all these examples, we show the emergence of a semi-classical behaviour from the set of coherent states and verify that it always happens when some parameter, depending on the algebra and its representation, becomes large.","PeriodicalId":502730,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":" August","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140682566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Moments based entanglement criteria and measures 基于矩的纠缠标准和测量方法
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-04-19 DOI: 10.1088/1751-8121/ad40e3
Yiding Wang, Tinggui Zhang, Xiaofen Huang, Shao-Ming Fei
{"title":"Moments based entanglement criteria and measures","authors":"Yiding Wang, Tinggui Zhang, Xiaofen Huang, Shao-Ming Fei","doi":"10.1088/1751-8121/ad40e3","DOIUrl":"https://doi.org/10.1088/1751-8121/ad40e3","url":null,"abstract":"\u0000 Quantum entanglement plays a key role in quantum computation and quantum information processing. It is of great signiffcance to ffnd efffcient and experimentally friend separability criteria to detect entanglement. In this paper, we ffrstly propose two easily used entanglement criteria based on matrix moments. The ffrst entanglement criterion only uses the ffrst two realignment moments of a density matrix. The second entanglement criterion is based on the moments related to the partially transposed matrix. By detailed examples we illustrate the effectiveness of these criteria in detecting entanglement. Moreover, we provide an experimentally measurable lower bound of concurrence based on these moments. Finally, we present both bipartite and genuine tripartite entanglement measures based on the moments of the reduced states. By detailed examples, we show that our entanglement measures characterize the quantum entanglement in a more ffne ways than the existing measures.","PeriodicalId":502730,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":" 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140683773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stability analysis of uncertain simple pendulum equation 不确定简摆方程的稳定性分析
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-04-18 DOI: 10.1088/1751-8121/ad4076
Xiaoyue Qiu, Liying Liu
{"title":"Stability analysis of uncertain simple pendulum equation","authors":"Xiaoyue Qiu, Liying Liu","doi":"10.1088/1751-8121/ad4076","DOIUrl":"https://doi.org/10.1088/1751-8121/ad4076","url":null,"abstract":"\u0000 The law of motion of a simple pendulum system is described by an uncertain simple pendulum equation which is a second-order uncertain differential equation driven by Liu process. The stability of a simple pendulum system refers to whether the system tends to the equilibrium state under small perturbation. In order to discuss the sensitivity of the uncertain simple pendulum equation to the perturbation in the initial state, we give the concept of many kinds of stability of the uncertain simple pendulum equation, including almost deterministic stability, distributional stability and exponential stability. And, the sufficient conditions of almost deterministic stability, distributional stability and exponential stability of the uncertain simple pendulum equation are proved respectively.","PeriodicalId":502730,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":" 29","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140687889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quantized Weyl algebras, the double centralizer property, and a new first fundamental theorem for Uq (gl n ) 量子化韦尔代数、双中心化性质以及 Uq (gl n ) 的新第一基本定理
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-04-15 DOI: 10.1088/1751-8121/ad3ef1
G. Letzter, S. Sahi, Hadi Salmasian
{"title":"Quantized Weyl algebras, the double centralizer property, and a new first fundamental theorem for Uq\u0000 (gl\u0000 n\u0000 )","authors":"G. Letzter, S. Sahi, Hadi Salmasian","doi":"10.1088/1751-8121/ad3ef1","DOIUrl":"https://doi.org/10.1088/1751-8121/ad3ef1","url":null,"abstract":"\u0000 Let P := Pm×n denote the quantized coordinate ring of the space of m × n matrices. We introduce a q-analog PD of the algebra of polynomial coefficient differential operators inside End(P) and we prove that PD is an integral form of the algebra Pol(Matm×n)q introduced earlier by Shklyarov-Sinel'shchikov-Vaksman [SSV04]. Let L and R denote the images in End(P) of the natural actions of the quantized enveloping algebras Uq(glm) and Uq(gln), respectively, and let Lh and Rh denote the images of their Cartan subalgebras. Our main result is that L ∩ PD and R ∩ PD are mutual centralizers in PD, and using this, we establish a new First Fundamental Theorem of invariant theory for Uq(gln). We also determine explicit generators of the subalgebras Lh ∩ PD and Rh ∩ PD in terms of q-determinants.","PeriodicalId":502730,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"48 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140701811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Half-blind quantum computation with operation teleportation 带操作远传的半盲量子计算
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-04-12 DOI: 10.1088/1751-8121/ad3e45
Zhenquan Yang, Guangyang Wu, Ming-qiang Bai
{"title":"Half-blind quantum computation with operation teleportation","authors":"Zhenquan Yang, Guangyang Wu, Ming-qiang Bai","doi":"10.1088/1751-8121/ad3e45","DOIUrl":"https://doi.org/10.1088/1751-8121/ad3e45","url":null,"abstract":"\u0000 Blind quantum computation allows that a client who only possesses a little quantum capability can delegate a powerful quantum computer to realize a secret quantum computation. In this paper, we find a security loophole in the first universal half-blind quantum computation protocol, and repair it via a method of operation teleportation. Simultaneously, in order to reduce quantum consumption of both the client and the server, proposed protocol is established based on the universal set of gates {H,T,CX}, and only needs the client to possess capability of preparing qubit in eigenstates of Pauli gate X and Y or measuring qubit in the basis of these gates. Finally, a sample example is given to demonstrate proposed protocol clearly. All these extensions enrich the application scene of half-blind quantum computation.","PeriodicalId":502730,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"70 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140709642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
SO(2,2) representations in polar coordinates and Pöschl-Teller potentials 极坐标中的 SO(2,2) 表示和 Pöschl-Teller 势
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-04-10 DOI: 10.1088/1751-8121/ad3d45
M. C. Blazquez, Javier Negro
{"title":"SO(2,2) representations in polar coordinates and Pöschl-Teller potentials","authors":"M. C. Blazquez, Javier Negro","doi":"10.1088/1751-8121/ad3d45","DOIUrl":"https://doi.org/10.1088/1751-8121/ad3d45","url":null,"abstract":"\u0000 This work is devoted to show the interest of polar coordinates in the description of some unitary irreducible representations (or uir’s) of the SO(2, 2) group where the support space are functions on the three dimensional pseudosphere H2,2R . We will show that the differential equations associated to such uir’s can be interpreted as quantum systems including centrifugal terms; in our case these equations lead to one-dimensional Pöschl-Teller systems. The solutions to these equations are computed and the uir’s are characterized in terms of polar coordinates. We will also discuss briefly the more standard pseudospherical coordinates on H2,2R in order to appreciate some of the differences. We will consider as well the (maximally superintegrable) free classical systems defined on the real pseudosphere H2,2R symmetric under SO(2, 2). The constans of motion are found and they are applied to find some bounded (therefore periodic) and unbounded orbits also in terms of polar coordinates.","PeriodicalId":502730,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140716833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quantum soft waveguides with resonances induced by broken symmetry 破对称性诱发共振的量子软波导
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-04-09 DOI: 10.1088/1751-8121/ad3c83
S. Kondej
{"title":"Quantum soft waveguides with resonances induced by broken symmetry","authors":"S. Kondej","doi":"10.1088/1751-8121/ad3c83","DOIUrl":"https://doi.org/10.1088/1751-8121/ad3c83","url":null,"abstract":"\u0000 We consider two-dimensional, non-relativistic quantum system with asymptotically straight soft waveguide. We show that the local deformation of the symmetric waveguide can lead to the emerging of the embedded eigenvalues living in the continuous spectrum. The main problem of this paper is devoted to the analysis of weak perturbation of the symmetric system. We show that the original embedded eigenvalues turn to the second sheet of the resolvent analytic continuation and constitute resonances. We describe the asymptotics of the real and imaginary components of the complex resonant pole depending on deformation. Finally, we generalize the problem to three dimensional system equipped with a soft layer.","PeriodicalId":502730,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"87 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140725802","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Non-inertial interpretation of the Dirac oscillator 狄拉克振荡器的非惯性解释
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-04-09 DOI: 10.1088/1751-8121/ad3c81
Michele Marrocco
{"title":"Non-inertial interpretation of the Dirac oscillator","authors":"Michele Marrocco","doi":"10.1088/1751-8121/ad3c81","DOIUrl":"https://doi.org/10.1088/1751-8121/ad3c81","url":null,"abstract":"\u0000 Non-inertial physics is seldom considered in quantum mechanics and this contrasts with the ubiquity of non-inertial reference frames. Here, we show an application to the Dirac oscillator which provides a fundamental model of relativistic quantum mechanics. The model emerges from a term linearly dependent on spatial coordinates added to the momentum of the free-particle Dirac Hamiltonian. The definition generates peculiar features (mutating vacuum energy, non-Hermitian momentum, accidental degeneracies of the spectrum, etc.). We interpret these anomalies in terms of inertial effects. The demonstration is based on the decoupling of the Dirac equation from the stereographic projection that maps the 3D geometry of the dynamical problem to the complex plane. The decoupling shows that the fundamental mechanical model underpinning the Dirac oscillator reduces to the representation of the oscillator in the rotating reference frame attached to the orbital angular momentum. The resulting Coriolis-like contribution to the Hamiltonian accounts for the peculiarities of the model (mutating vacuum energy, form of the non-minimal correction to the momentum, classical intrinsic spin and gain of its quantum value, accidental degeneracies of the energy spectrum, supersymmetric potential). The suggested interpretation has an interdisciplinary character where stereographic geometry, classical physics of the Coriolis effect and quantum physics of Dirac particles contribute to the definition of one of the few exactly soluble models of relativistic quantum mechanics.","PeriodicalId":502730,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"60 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140722741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Replica symmetry breaking in supervised and unsupervised Hebbian networks 有监督和无监督海比网络中的复制对称性破坏
Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-03-28 DOI: 10.1088/1751-8121/ad38b4
L. Albanese, Andrea Alessandrelli, A. Annibale, Adriano Barra
{"title":"Replica symmetry breaking in supervised and unsupervised Hebbian networks","authors":"L. Albanese, Andrea Alessandrelli, A. Annibale, Adriano Barra","doi":"10.1088/1751-8121/ad38b4","DOIUrl":"https://doi.org/10.1088/1751-8121/ad38b4","url":null,"abstract":"\u0000 Hebbian neural networks with multi-node interactions, often called Dense Associative Memories, have recently attracted considerable interest in the statistical mechanics community, as they have been shown to outperform their pairwise counterparts in a number of features, including resilience against adversarial attacks, pattern retrieval with extremely weak signals and supra-linear storage capacities. However, their analysis has so far been carried out within a replica-symmetric theory. In this manuscript, we relax the assumption of replica symmetry and analyse these systems at one step of replica-symmetry breaking, focusing on two different prescriptions for the interactions that we will refer to as supervised and unsupervised learning. We derive the phase diagram of the model using two different approaches, namely Parisi's hierarchical ansatz for the relationship between different replicas within the replica approach, and the so-called telescope ansatz within Guerra's interpolation method: our results show that replica-symmetry breaking does not alter the threshold for learning and slightly increases the maximal storage capacity. Further, we also derive analytically the instability line of the replica-symmetric theory, using a generalization of the De Almeida and Thouless approach.","PeriodicalId":502730,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"31 31","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140372853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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