Pub Date : 2024-07-29DOI: 10.1088/1751-8121/ad6413
Sang-Jun Park, Yeong-Gwang Jung, Jeongeun Park, Sang-Gyun Youn
One of the fundamental questions in quantum information theory is determining entanglement of quantum states, which is generally an NP-hard problem. In this paper, we prove that all PPT <inline-formula> <tex-math><?CDATA $(overline{pi}_Aotimes pi_B)$?></tex-math> <mml:math overflow="scroll"><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mover><mml:mi>π</mml:mi><mml:mo accent="true">―</mml:mo></mml:mover><mml:mi>A</mml:mi></mml:msub><mml:mo>⊗</mml:mo><mml:msub><mml:mi>π</mml:mi><mml:mi>B</mml:mi></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> <inline-graphic xlink:href="aad6413ieqn1.gif" xlink:type="simple"></inline-graphic> </inline-formula>-invariant quantum states are separable if and only if all extremal unital positive <inline-formula> <tex-math><?CDATA $(pi_B,pi_A)$?></tex-math> <mml:math overflow="scroll"><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>π</mml:mi><mml:mi>B</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>π</mml:mi><mml:mi>A</mml:mi></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> <inline-graphic xlink:href="aad6413ieqn2.gif" xlink:type="simple"></inline-graphic> </inline-formula>-covariant maps are decomposable where <inline-formula> <tex-math><?CDATA $pi_A,pi_B$?></tex-math> <mml:math overflow="scroll"><mml:mrow><mml:msub><mml:mi>π</mml:mi><mml:mi>A</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>π</mml:mi><mml:mi>B</mml:mi></mml:msub></mml:mrow></mml:math> <inline-graphic xlink:href="aad6413ieqn3.gif" xlink:type="simple"></inline-graphic> </inline-formula> are unitary representations of a compact group and <italic toggle="yes">π</italic> <sub> <italic toggle="yes">A</italic> </sub> is irreducible. Moreover, an extremal unital positive <inline-formula> <tex-math><?CDATA $(pi_B,pi_A)$?></tex-math> <mml:math overflow="scroll"><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>π</mml:mi><mml:mi>B</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>π</mml:mi><mml:mi>A</mml:mi></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> <inline-graphic xlink:href="aad6413ieqn4.gif" xlink:type="simple"></inline-graphic> </inline-formula>-covariant map <inline-formula> <tex-math><?CDATA $mathcal{L}$?></tex-math> <mml:math overflow="scroll"><mml:mrow><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:mrow></mml:math> <inline-graphic xlink:href="aad6413ieqn5.gif" xlink:type="simple"></inline-graphic> </inline-formula> is decomposable if and only if <inline-formula> <tex-math><?CDATA $mathcal{L}$?></tex-math> <mml:math overflow="scroll"><mml:mrow><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:mrow></mml:math> <inline-graphic xlink:href="aad6413ieqn6.gif" xlink:type="simple"></inline-graphic> </inline-formula> is completely positive or completely copositive. We then apply these results to prove that all PPT quantum channels of the form <inline-formula> <tex-math><?CDATA $ Phileft(rhoright) = afrac{textrm{Tr}left(rhoright)}{d}textrm{Id}_d+
量子信息论的基本问题之一是确定量子态的纠缠，这通常是一个 NP 难问题。在本文中，我们证明了所有 PPT (π-A⊗πB)-invariant 量子态都是可分的，当且仅当所有极值单元正 (πB,πA)-covariant 映射都是可分解的，其中 πA,πB 是紧凑群的单元表示，且 πA 是不可还原的。此外，当且仅当 L 是完全正或完全共正时，极值单元正 (πB,πA)- 变映射 L 是可分解的。然后，我们应用这些结果证明所有形式为Φ(ρ)=aTr(ρ)dIdd+bρ+cρT+(1-a-b-c)diag(ρ)的 PPT 量子通道都是纠缠断裂的，并且不存在 A-BC PPT-entangled (U⊗U-⊗U)-invariant 三方量子态。前者加强了（Vollbrecht 和 Werner 2001 Phys. Rev. A 64 062307; Kopszak et al 2020 J. Phys.Theor.53 395306）中的一些结论，后者则解决了（Collins et al 2018 Linear Algebra Appl.555 398-411）中提出的一些悬而未决的问题。
{"title":"A universal framework for entanglement detection under group symmetry","authors":"Sang-Jun Park, Yeong-Gwang Jung, Jeongeun Park, Sang-Gyun Youn","doi":"10.1088/1751-8121/ad6413","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6413","url":null,"abstract":"One of the fundamental questions in quantum information theory is determining entanglement of quantum states, which is generally an NP-hard problem. In this paper, we prove that all PPT <inline-formula>\u0000<tex-math><?CDATA $(overline{pi}_Aotimes pi_B)$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mover><mml:mi>π</mml:mi><mml:mo accent=\"true\">―</mml:mo></mml:mover><mml:mi>A</mml:mi></mml:msub><mml:mo>⊗</mml:mo><mml:msub><mml:mi>π</mml:mi><mml:mi>B</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"aad6413ieqn1.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula>-invariant quantum states are separable if and only if all extremal unital positive <inline-formula>\u0000<tex-math><?CDATA $(pi_B,pi_A)$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>π</mml:mi><mml:mi>B</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>π</mml:mi><mml:mi>A</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"aad6413ieqn2.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula>-covariant maps are decomposable where <inline-formula>\u0000<tex-math><?CDATA $pi_A,pi_B$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:msub><mml:mi>π</mml:mi><mml:mi>A</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>π</mml:mi><mml:mi>B</mml:mi></mml:msub></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"aad6413ieqn3.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula> are unitary representations of a compact group and <italic toggle=\"yes\">π</italic>\u0000<sub>\u0000<italic toggle=\"yes\">A</italic>\u0000</sub> is irreducible. Moreover, an extremal unital positive <inline-formula>\u0000<tex-math><?CDATA $(pi_B,pi_A)$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>π</mml:mi><mml:mi>B</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>π</mml:mi><mml:mi>A</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"aad6413ieqn4.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula>-covariant map <inline-formula>\u0000<tex-math><?CDATA $mathcal{L}$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"aad6413ieqn5.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula> is decomposable if and only if <inline-formula>\u0000<tex-math><?CDATA $mathcal{L}$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"aad6413ieqn6.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula> is completely positive or completely copositive. We then apply these results to prove that all PPT quantum channels of the form <inline-formula>\u0000<tex-math><?CDATA $ Phileft(rhoright) = afrac{textrm{Tr}left(rhoright)}{d}textrm{Id}_d+ ","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"51 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141867967","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-29DOI: 10.1088/1751-8121/ad653c
Sébastien Bertrand, Ian Marquette, Willard Miller, Sarah Post
In this paper, we point out connections between certain types of indecomposable representations of sl(2) and generalizations of well-known orthogonal polynomials. Those representations take the form of infinite dimensional chains of weight or generalised weight spaces, for which the Cartan generator acts in a diagonal way or via Jordan blocks. The other generators of the Lie algebras sl(2) act as raising and lowering operators but are now allowed to relate the different chains as well. In addition, we construct generating functions, we calculate the action of the Casimir invariant and present relations to systems of non-homogeneous second-order coupled differential equations. We present different properties as higher-order linear differential equations for building blocks taking the form of one variable polynomials. We also present insight into the zeroes and recurrence relations.
{"title":"Special function models of indecomposable sl(2) representations: the Laguerre case","authors":"Sébastien Bertrand, Ian Marquette, Willard Miller, Sarah Post","doi":"10.1088/1751-8121/ad653c","DOIUrl":"https://doi.org/10.1088/1751-8121/ad653c","url":null,"abstract":"In this paper, we point out connections between certain types of indecomposable representations of <italic toggle=\"yes\">sl</italic>(2) and generalizations of well-known orthogonal polynomials. Those representations take the form of infinite dimensional chains of weight or generalised weight spaces, for which the Cartan generator acts in a diagonal way or via Jordan blocks. The other generators of the Lie algebras <italic toggle=\"yes\">sl</italic>(2) act as raising and lowering operators but are now allowed to relate the different chains as well. In addition, we construct generating functions, we calculate the action of the Casimir invariant and present relations to systems of non-homogeneous second-order coupled differential equations. We present different properties as higher-order linear differential equations for building blocks taking the form of one variable polynomials. We also present insight into the zeroes and recurrence relations.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"16 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141867914","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-29DOI: 10.1088/1751-8121/ad65a6
Shuang Wu
Extending the results of Wu (2022 J. Phys. A 55 415207), we study the double-scaling limit Sachdev–Ye–Kitaev model with an additional diagonal matrix with a fixed number c of nonzero constant entries θ. This constant diagonal term can be rewritten in terms of Majorana fermion products. Its specific formula depends on the value of c. We find exact expressions for the moments of this model. More importantly, by proposing a moment-cumulant relation, we reinterpret the effect of introducing a constant term in the context of non-commutative probability theory. This gives rise to a q~ dependent mixture of independences within the moment formula. The parameter q~, derived from the q-Ornstein–Uhlenbeck (q-OU) process, controls this transformation. It interpolates between classical independence (q~=1) and Boolean independence (q~=0). The underlying combinatorial structures of this model provide the non-commutative probability connections. Additionally, we explore the potential relation between these connections and their gravitational path integral counterparts.
我们扩展了吴文俊（2022 J. Phys. A 55 415207）的研究成果，研究了双尺度极限萨奇德夫-叶-基塔耶夫模型，其中有一个额外的对角矩阵，具有固定数量的非零常数项θ。我们找到了该模型矩的精确表达式。更重要的是，通过提出矩积关系，我们在非交换概率论的背景下重新解释了引入常数项的效果。这就在矩公式中产生了一个与 q~ 相关的独立混合物。参数 q~ 源自 q-Ornstein-Uhlenbeck (q-OU)过程，它控制着这一转变。它介于经典独立性（q~=1）和布尔独立性（q~=0）之间。该模型的基本组合结构提供了非交换概率联系。此外，我们还探索了这些联系与其引力路径积分对应物之间的潜在关系。
{"title":"Non-commutative probability insights into the double-scaling limit SYK model with constant perturbations: moments, cumulants and q-independence","authors":"Shuang Wu","doi":"10.1088/1751-8121/ad65a6","DOIUrl":"https://doi.org/10.1088/1751-8121/ad65a6","url":null,"abstract":"Extending the results of Wu (2022 <italic toggle=\"yes\">J. Phys.</italic> A <bold>55</bold> 415207), we study the double-scaling limit Sachdev–Ye–Kitaev model with an additional diagonal matrix with a fixed number <italic toggle=\"yes\">c</italic> of nonzero constant entries <italic toggle=\"yes\">θ</italic>. This constant diagonal term can be rewritten in terms of Majorana fermion products. Its specific formula depends on the value of <italic toggle=\"yes\">c</italic>. We find exact expressions for the moments of this model. More importantly, by proposing a moment-cumulant relation, we reinterpret the effect of introducing a constant term in the context of non-commutative probability theory. This gives rise to a <inline-formula>\u0000<tex-math><?CDATA $tilde{q}$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:mrow><mml:mover><mml:mi>q</mml:mi><mml:mo stretchy=\"true\">~</mml:mo></mml:mover></mml:mrow></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"aad65a6ieqn1.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula> dependent mixture of independences within the moment formula. The parameter <inline-formula>\u0000<tex-math><?CDATA $tilde{q}$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:mrow><mml:mover><mml:mi>q</mml:mi><mml:mo stretchy=\"true\">~</mml:mo></mml:mover></mml:mrow></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"aad65a6ieqn2.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula>, derived from the <italic toggle=\"yes\">q</italic>-Ornstein–Uhlenbeck (<italic toggle=\"yes\">q</italic>-OU) process, controls this transformation. It interpolates between classical independence (<inline-formula>\u0000<tex-math><?CDATA $tilde{q} = 1$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:mrow><mml:mover><mml:mi>q</mml:mi><mml:mo stretchy=\"true\">~</mml:mo></mml:mover></mml:mrow><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"aad65a6ieqn3.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula>) and Boolean independence (<inline-formula>\u0000<tex-math><?CDATA $tilde{q} = 0$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:mrow><mml:mover><mml:mi>q</mml:mi><mml:mo stretchy=\"true\">~</mml:mo></mml:mover></mml:mrow><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"aad65a6ieqn4.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula>). The underlying combinatorial structures of this model provide the non-commutative probability connections. Additionally, we explore the potential relation between these connections and their gravitational path integral counterparts.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"30 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141867916","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-25DOI: 10.1088/1751-8121/ad6538
Ali Yacine Sahnoun, Mustapha Djebbar, Tounsi Benmessabih and Benaoumeur Bakhti
We present an exact derivation of the free energy functional of a fluid mixture of hard rods with arbitrary sizes on a one-dimensional lattice. Our approach is based on the Wertheim cluster theory which consists of mapping a system with finite range interactions to the system with pure hard-core interaction but with modified activities. We show that the free energy functional has the same form as the fundamental measure functional. The interactions part of the free energy has two contributions, one from the one-particle cavity restricted to the hard rod or hard-sphere diameter and a second from the two-particle cavity which includes the finite range of the interaction. In the limit of a one-component system, our results reduce to the one derived using the Markov chain approach. For vanishing interactions, the density functionals coincide exactly with the previously derived for the mixture of hard rods with pure hard-core interaction.
{"title":"One dimensional lattice fluid mixture with nearest neighbour interactions","authors":"Ali Yacine Sahnoun, Mustapha Djebbar, Tounsi Benmessabih and Benaoumeur Bakhti","doi":"10.1088/1751-8121/ad6538","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6538","url":null,"abstract":"We present an exact derivation of the free energy functional of a fluid mixture of hard rods with arbitrary sizes on a one-dimensional lattice. Our approach is based on the Wertheim cluster theory which consists of mapping a system with finite range interactions to the system with pure hard-core interaction but with modified activities. We show that the free energy functional has the same form as the fundamental measure functional. The interactions part of the free energy has two contributions, one from the one-particle cavity restricted to the hard rod or hard-sphere diameter and a second from the two-particle cavity which includes the finite range of the interaction. In the limit of a one-component system, our results reduce to the one derived using the Markov chain approach. For vanishing interactions, the density functionals coincide exactly with the previously derived for the mixture of hard rods with pure hard-core interaction.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"67 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141777070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-25DOI: 10.1088/1751-8121/ad6226
Julien Barré and Ouassim Feliachi
Starting from a microscopic particle model whose hydrodynamic limit under hyperbolic space-time scaling is a 1D conservation law, we derive the large deviation rate function encoding the probability to observe a density profile which is a non entropic shock, and compare this large deviation rate function with the classical Jensen-Varadhan functional, valid for the totally asymmetric exclusion process and the weakly asymmetric exclusion process in the strong asymmetry limit. We find that these two functionals have no reason to coincide, and in this sense Jensen-Varadhan functional is not universal. However, they do coincide in a small Mach number limit, suggesting that universality is restored in this regime. We then compute the leading order correction to the Jensen-Varadhan functional.
{"title":"How general is the Jensen–Varadhan large deviation functional for 1D conservation laws?","authors":"Julien Barré and Ouassim Feliachi","doi":"10.1088/1751-8121/ad6226","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6226","url":null,"abstract":"Starting from a microscopic particle model whose hydrodynamic limit under hyperbolic space-time scaling is a 1D conservation law, we derive the large deviation rate function encoding the probability to observe a density profile which is a non entropic shock, and compare this large deviation rate function with the classical Jensen-Varadhan functional, valid for the totally asymmetric exclusion process and the weakly asymmetric exclusion process in the strong asymmetry limit. We find that these two functionals have no reason to coincide, and in this sense Jensen-Varadhan functional is not universal. However, they do coincide in a small Mach number limit, suggesting that universality is restored in this regime. We then compute the leading order correction to the Jensen-Varadhan functional.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"43 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141785630","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-25DOI: 10.1088/1751-8121/ad6539
Pauli Jokinen, Sophie Egelhaaf, Juha-Pekka Pellonpää and Roope Uola
We generalize the notion of joint measurability to continuous variable systems by extending a recently introduced compression algorithm of quantum measurements to this realm. The extension results in a property that asks for the minimal dimensional quantum system required for representing a given set of quantum measurements. To illustrate the concept, we show that the canonical pair of position and momentum is completely incompressible. We translate the concept of measurement compression to the realm of quantum correlations, where it results in a generalization of continuous variable quantum steering. In contrast to the steering scenario, which detects entanglement, the generalization detects the dimensionality of entanglement. We illustrate the bridge between the concepts by showing that an analogue of the original EPR argument is genuinely infinite-dimensional with respect to our figure of merit, and that a fundamental discrete variable result on preparability of unsteerable state assemblages with separable states does not directly carry over to the continuous variable setting. We further prove a representation result for partially entanglement breaking channels that can be of independent interest.
{"title":"Compressing continuous variable quantum measurements","authors":"Pauli Jokinen, Sophie Egelhaaf, Juha-Pekka Pellonpää and Roope Uola","doi":"10.1088/1751-8121/ad6539","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6539","url":null,"abstract":"We generalize the notion of joint measurability to continuous variable systems by extending a recently introduced compression algorithm of quantum measurements to this realm. The extension results in a property that asks for the minimal dimensional quantum system required for representing a given set of quantum measurements. To illustrate the concept, we show that the canonical pair of position and momentum is completely incompressible. We translate the concept of measurement compression to the realm of quantum correlations, where it results in a generalization of continuous variable quantum steering. In contrast to the steering scenario, which detects entanglement, the generalization detects the dimensionality of entanglement. We illustrate the bridge between the concepts by showing that an analogue of the original EPR argument is genuinely infinite-dimensional with respect to our figure of merit, and that a fundamental discrete variable result on preparability of unsteerable state assemblages with separable states does not directly carry over to the continuous variable setting. We further prove a representation result for partially entanglement breaking channels that can be of independent interest.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"37 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141776905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-24DOI: 10.1088/1751-8121/ad649a
Wolfgang Rudolf Bauer
We show that a set of thermally weakly coupled geometrically frustrated systems (GFSs), each of which is constraint to reside at negative Boltzmann temperatures, is in equilibrium cooler than its constituents. It may even exhibit positive temperatures at low energies. The challenge for the second law of thermodynamics arising from potential heat flow related to the gradient of temperatures between a GFS and its environment is resolved by considering the energy fluctuations above the ground state. They are comprised in the canonical temperature, derived from information theory. Whereas the gradient of Boltzmann temperatures gives the direction of the stochastic drift of the most probable state of a GFS within its environment, the canonical temperature gradient defines that of heat flow.
{"title":"Geometrically frustrated systems which are as singles hotter than in company","authors":"Wolfgang Rudolf Bauer","doi":"10.1088/1751-8121/ad649a","DOIUrl":"https://doi.org/10.1088/1751-8121/ad649a","url":null,"abstract":"We show that a set of thermally weakly coupled geometrically frustrated systems (GFSs), each of which is constraint to reside at negative Boltzmann temperatures, is in equilibrium cooler than its constituents. It may even exhibit positive temperatures at low energies. The challenge for the second law of thermodynamics arising from potential heat flow related to the gradient of temperatures between a GFS and its environment is resolved by considering the energy fluctuations above the ground state. They are comprised in the canonical temperature, derived from information theory. Whereas the gradient of Boltzmann temperatures gives the direction of the stochastic drift of the most probable state of a GFS within its environment, the canonical temperature gradient defines that of heat flow.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"13 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141777065","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-24DOI: 10.1088/1751-8121/ad6411
Alberto Brollo and Herbert Spohn
The Ablowitz–Ladik (AL) chain is an integrable discretized version of the nonlinear Schrödinger equation. We report on a novel underlying Hamiltonian particle system with properties similar to the ones known for the classical Toda chain and Calogero fluid with pair interaction. Boundary conditions are imposed such that, both in the distant past and future, particles have a constant velocity. We establish the many-particle scattering for the AL chain and obtain properties known for generic integrable many-body systems. For a specific choice of the chain, real initial data remain real in the course of time. Then, asymptotically, particles move in pairs with a velocity-dependent size and scattering shifts are governed by the fusion rule.
阿布罗维茨-拉迪克（AL）链是非线性薛定谔方程的可积分离散化版本。我们报告了一个新颖的底层哈密顿粒子系统，其性质类似于已知的经典托达链和具有成对相互作用的卡洛吉罗流体。施加的边界条件使得粒子在遥远的过去和未来都具有恒定的速度。我们建立了 AL 链的多粒子散射，并获得了一般可积分多体系统的已知性质。对于链的特定选择，真实的初始数据在时间过程中保持真实。然后，渐进地，粒子成对运动，其大小与速度有关，散射位移受融合规则支配。
{"title":"Particle scattering and fusion for the Ablowitz–Ladik chain","authors":"Alberto Brollo and Herbert Spohn","doi":"10.1088/1751-8121/ad6411","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6411","url":null,"abstract":"The Ablowitz–Ladik (AL) chain is an integrable discretized version of the nonlinear Schrödinger equation. We report on a novel underlying Hamiltonian particle system with properties similar to the ones known for the classical Toda chain and Calogero fluid with pair interaction. Boundary conditions are imposed such that, both in the distant past and future, particles have a constant velocity. We establish the many-particle scattering for the AL chain and obtain properties known for generic integrable many-body systems. For a specific choice of the chain, real initial data remain real in the course of time. Then, asymptotically, particles move in pairs with a velocity-dependent size and scattering shifts are governed by the fusion rule.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"17 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141777064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-24DOI: 10.1088/1751-8121/ad6068
N Zagli, V Lucarini and G A Pavliotis
We consider a class of nonequilibrium systems of interacting agents with pairwise interactions and quenched disorder in the dynamics featuring, in the thermodynamic limit, phase transitions. We identify mathematical conditions on the microscopic interaction structure, namely the separability of the interaction kernel, that lead to a dimension reduction of the system in terms of a finite number of reaction coordinates (RCs). Such RCs prove to be proper nonequilibrium thermodynamic variables as they carry information on correlation, memory and resilience properties of the system. Phase transitions can be identified and quantitatively characterised as singularities of the complex valued susceptibility functions associated to the RCs. We provide analytical and numerical evidence of how the singularities affect the physical properties of finite size systems.
{"title":"Response theory identifies reaction coordinates and explains critical phenomena in noisy interacting systems","authors":"N Zagli, V Lucarini and G A Pavliotis","doi":"10.1088/1751-8121/ad6068","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6068","url":null,"abstract":"We consider a class of nonequilibrium systems of interacting agents with pairwise interactions and quenched disorder in the dynamics featuring, in the thermodynamic limit, phase transitions. We identify mathematical conditions on the microscopic interaction structure, namely the separability of the interaction kernel, that lead to a dimension reduction of the system in terms of a finite number of reaction coordinates (RCs). Such RCs prove to be proper nonequilibrium thermodynamic variables as they carry information on correlation, memory and resilience properties of the system. Phase transitions can be identified and quantitatively characterised as singularities of the complex valued susceptibility functions associated to the RCs. We provide analytical and numerical evidence of how the singularities affect the physical properties of finite size systems.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"3 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141777074","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-24DOI: 10.1088/1751-8121/ad6363
Eliana Fiorelli
We consider a class of open quantum many-body systems that evolves in a Markovian fashion, the dynamical generator being in GKS-Lindblad form. Here, the Hamiltonian contribution is characterized by an all-to-all coupling, and the dissipation features local transitions that depend on collective, operator-valued rates, encoding average properties of the system. These types of generators can be formally obtained by generalizing, to the quantum realm, classical (mean-field) stochastic Markov dynamics, with state-dependent transitions. Focusing on the dynamics emerging in the limit of infinitely large systems, we build on the exactness of the mean-field equations for the dynamics of average operators. In this framework, we derive the dynamics of quantum fluctuation operators, that can be used in turn to understand the fate of quantum correlations in the system. We then apply our results to quantum generalized Hopfield associative memories. Here we show that, asymptotically and at the description level of quantum fluctuations, only a very weak amount of quantum correlations, in the form of quantum discord, emerges beyond classical correlations.
{"title":"Quantum fluctuation dynamics of open quantum systems with collective operator-valued rates, and applications to Hopfield-like networks","authors":"Eliana Fiorelli","doi":"10.1088/1751-8121/ad6363","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6363","url":null,"abstract":"We consider a class of open quantum many-body systems that evolves in a Markovian fashion, the dynamical generator being in GKS-Lindblad form. Here, the Hamiltonian contribution is characterized by an all-to-all coupling, and the dissipation features local transitions that depend on collective, operator-valued rates, encoding average properties of the system. These types of generators can be formally obtained by generalizing, to the quantum realm, classical (mean-field) stochastic Markov dynamics, with state-dependent transitions. Focusing on the dynamics emerging in the limit of infinitely large systems, we build on the exactness of the mean-field equations for the dynamics of average operators. In this framework, we derive the dynamics of quantum fluctuation operators, that can be used in turn to understand the fate of quantum correlations in the system. We then apply our results to quantum generalized Hopfield associative memories. Here we show that, asymptotically and at the description level of quantum fluctuations, only a very weak amount of quantum correlations, in the form of quantum discord, emerges beyond classical correlations.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"48 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141777063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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