Shenzhen-Nagoya Workshop on Quantum Science 2025

Dates and Place

• Dates: September 24 (Wed) - 27 (Sat), 2025
• Style: Hybrid (onsite and Zoom)
• Venue: Room 509, Graduate School of Mathematics, Nagoya Univeristy (accsess)
  Room 203 of Conference complex II, CHHK-SZ
• Organizing committee: Masahito Hayashi (Chair; CUHK-SZ, IQA, and Nagoya), Kun Fang (CUHK-SZ),
  Hiroaki Kanno (Nagoya), Kohtaro Kato (Nagoya), Shintarou Yanagida (Nagoya)
• Contact: shenzhennagoya2025 [at] gmail [dot] com

Registration

For online participation, please register from Microsoft Forms.

YouTube live streaming

Talks will be streamed by YouTube.
9/24 (Wed) AM, PM; 9/25 (Thu) AM, PM; 9/26 (Fri) AM PM; 9/27 (Sat) AM, PM.

Time table

Program

• 9/24 (Wed)
  • 09:30-10:10 (CST) 10:30-11:10 (JST)
    Hiroaki Kanno (Graduate School of Mathematics, Nagoya University)
    On the Pieri formula of the super Macdonald polynomials slides
    The super Macdonald polynomials generalize the Macdonald polynomials to the super space with Grassmann coordinates. They are indexed by the set of super partitions and give a basis of a level zero representation of the quantum toroidal algebra of type gl_1|1. We derive the Pieri formula of the super Macdonald polynomials from the action of the raising and the lowering operators of the algebra. We also present a conjecture on the Pieri formula, from which we can compute the commuting Hamiltonians. The super Macdonald polynomials are characterized as simultaneous eigenfunctions of these Hamiltonians.
  • 10:20-10:40 (CST) 11:20-11:40 (JST)
    Xianghang Zhang (Graduate School of Mathematics, Nagoya University)
    Open N=2 String Field Theory
    We formulate a string field theory for open N=2 strings with an homotopy algebra structure. Starting from the BRST cohomology relative to the U(1) anti-ghost zero-mode, we generalize [arXiv:1312.2948] and constructed all interacting vertices recursively and without singularity. This talk is based on [arXiv:2506.21247].
  • 10:50-11:30 (CST) 11:50-12:30 (JST)
    Daniel Wong (School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen)
    Unitarity of Minimal Principal Series Representations slides
    A major unsolved problem in representation theory of real reductive Lie groups is to classify their unitary representations. In this talk, we study the case when G is a split classical group, and give a classification of all unitary irreducible representations of G whose lowest K-types are fine (in the sense of Vogan).
  • 13:30-14:10 (CST) 14:30-15:10 (JST)
    Francois Le Gall (Graduate School of Mathematics, Nagoya University)
    Classical Algorithms for Constant Approximation of the Ground State Energy of Local Hamiltonians slides
    In this talk I will explain how to construct classical algorithms computing an approximation of the ground state energy of an arbitrary k-local Hamiltonian acting on n qubits.
    I will first consider the setting where a good guiding state is available, which is the main setting where quantum algorithms are expected to achieve an exponential speedup over classical methods. I will explain how to significant improve the recent classical algorithm by Gharibian and Le Gall (SICOMP 2023) and match (up a to polynomial overhead) both the time and space complexities of quantum algorithms for constant approximation of the ground state energy.
    For the setting where no guided state is given (i.e., the standard version of the local Hamiltonian problem), I will present a classical algorithm computing a constant approximation of the ground state energy in 2^O(n) time and poly(n) space. Before this work it was unknown how to classically achieve these bounds simultaneously, even for constant approximation.
    This talk is based on arXiv:2410.21833.
  • 14:20-14:40 (CST) 15:20-15:40 (JST)
    Dhara Thakkar (Graduate School of Mathematics, Nagoya University)
    Group Order is in QCMA slides
    In this talk, we will show that verifying the order of a finite group given as a black-box is in the complexity class QCMA. This solves an open problem asked by Watrous in 2000 in his seminal paper on quantum proofs and directly implies that the Group Non-Membership problem is also in the class QCMA, which further proves a conjecture proposed by Aaronson and Kuperberg in 2006. This talk is based on the joint work with François Le Gall, Harumichi Nishimura. Please find the paper at arXiv:2504.05547.
  • 14:50-15:30 (CST) 15:50-16:30 (JST)
    Jun Qi (Hong Kong Baptist University, Hong Kong)
    Tensor Networks and Hybrid Architectures for Scalable and Robust-Resilient Quantum Machine Learning
    Variational Quantum Circuits (VQCs) hold promise as building blocks for quantum machine learning, but their deployment in the Noisy Intermediate-Scale Quantum (NISQ) era is hindered by limited expressivity, trainability issues (e.g., barren plateaus), and sensitivity to noise. In a series of recent works, we develop hybrid quantum-classical architectures that systematically address these limitations via tensor-train (TT) parameterizations and hybridisation with classical neural networks. I will present three interlinked models: TTN-VQC, TensoMeta-VQC, and VQC-MLPNet, emphasizing their theoretical foundations, empirical performance, and practical implications for scalable and noise-resilient quantum machine learning.
  • 15:40-16:20 (CST) 16:40-17:20 (JST)
    Chen Hongzhen (Shenzhen University)
    Quantum Metrology Enhanced by Leveraging Informative Noise with Error Correction
    Noise is a central obstacle to practical quantum technologies, typically inducing decoherence that erodes quantum advantage. Yet certain noise processes are informative about the parameters of interest and, when properly harnessed, can improve metrological performance. While such effects have been noted for specific channels, their scope under general dynamics remains unclear. In this work, we show that informative noise, combined with quantum error correction, can be converted into a resource for precision enhancement. We derive necessary and sufficient conditions under which metrological precision in the presence of informative noise attains Heisenberg scaling. These results provide a unified criterion for when noise can be beneficial and offer a constructive route to designing error-corrected sensing protocols that approach fundamental limits.
• 9/25 (Thu)
  • 09:30-10:10 (CST) 10:30-11:10 (JST)
    Jingsong Huang (Mathematics Research Center, School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen)
    Principal Elements and fermion-boson harmonic oscillator
    Let g be a complex simple Lie algebra and G the adjoint group of g. The principal element of G corresponds to the Coxeter element and the Fourier element corresponds to the longest element of the Weyl group. We define the Fourier operators for either a split or compact real form G(R) and show that they act on unitary representations of G(R) in a way similar to the bosonic Fourier transform on the oscillator representation of symplectic group or the fermionic Fourier transforms on the spin representation of orthogonal group. This framework fits into framework of superspace analysis and reveals the spectral decomposition of the hybrid Fourier transform corresponding to the hybrid fermion-boson Hamiltonian.
  • 10:20-10:40 (CST) 11:20-11:40 (JST)
    Takumi Iwane (Graduate School of Mathematics, Nagoya University)
    Vertex Lie bialgebras slides
    Vertex algebras (VAs) are fundamental objects in mathematical physics, particularly in the study of two-dimensional conformal field theory. As their classical counterparts, vertex Poisson algebras (VPAs) arise naturally. A typical example is that the jet algebra of an ordinary Poisson algebra.
    In this talk, we investigate the jets of Poisson Hopf algebras, which corrponds to Poisson–Lie groups. This leads us to the notion of vertex Poisson Hopf algebras, and, at the level of tangent spaces, to that of vertex Lie bialgebras. Finally, I will introduce the quantization problem for vertex Lie bialgebras, which serves as a natural extension of the quantization theory for Lie bialgebras.
  • 10:50-11:30 (CST) 11:50-12:30 (JST)
    Qin Li (Shenzhen Institute for Quantum Science and Engineering, SUSTech)
    Geometric and Deformation quantization of Kähler manifolds
    
  • 11:40-12:00 (CST) 12:40-13:00 (JST)
    Yusuke Nishinaka (Graduate School of Mathematics, Nagoya University)
    Factorization envelopes and enveloping vertex algebras
    Costello-Gwilliam factorization algebras are mathematical objects that encode the algebraic structure of observables in quantum field theories. On the other hand, vertex algebras provide an algebraic framework for two-dimensional chiral conformal field theories. Costello and Gwilliam developed a general method for constructing vertex algebras from factorization algebras on the complex plane. They also constructed factorization algebras via factorization envelopes, corresponding to the affine vertex algebras and the beta-gamma vertex algebra. Since these vertex algebras are particular instances of enveloping vertex algebras of vertex Lie algebras, it is natural to seek a generalization of their construction to arbitrary vertex Lie algebras. In this talk, after a brief introduction to factorization algebras and vertex algebras, I will explain this generalization, namely the construction of factorization algebras starting from vertex Lie algebras.
  • 13:30-14:10 (CST) 14:30-15:10 (JST)
    Francesco Buscemi (Graduate School of Informatics, Nagoya University)
    Fully quantum Bayes' rule from the minimum change principle slides
    Bayes' rule, which is routinely used to update beliefs based on new evidence, can be derived from a principle of minimum change. This principle states that updated beliefs must be consistent with new data, while deviating minimally from the prior belief. Here, we introduce a quantum analog of the minimum change principle and use it to derive a quantum Bayes' rule by minimizing the change between two quantum input-output processes, not just their marginals. This is analogous to the classical case, where Bayes' rule is obtained by minimizing several distances between the joint input-output distributions. When the change maximizes the fidelity, the quantum minimum change principle has a unique solution, and the resulting quantum Bayes' rule recovers the Petz transpose map in many cases. This is work done in collaboration with Ge Bai and Valerio Scarani.
    Reference: Physical Review Letters 135, 090203 (2025); arXiv:2410.00319
  • 14:20-14:40 (CST) 15:20-15:40 (JST)
    Jinpei Zhao (Department of Information Engineering, The Chinese University of Hong Kong)
    Search for an analogue of the sub-additive--doubling--rotation proof of Gaussian optimality in quantum systems
    In this talk, I will demonstrate the sub-additive--doubling--rotation proof and its application on proving the entropy power inequality. I will also discuss the potential analogue of this proof technique in quantum systems.
  • 14:50-15:30 (CST) 15:50-16:30 (JST)
    Qisheng Wang (University of Edinburgh)
    Bridging Quantum Query and Sample Complexities: Theory and Applications
    Quantum query complexity measures the difficulty of testing quantum oracles while quantum sample complexity measures the difficulty of testing quantum states. The two quantum complexities have attracted much attention in their respective fields. In this talk, we present a novel connection between them via a quantum lifting method, yielding new results for the both complexities. First, we present a quantum sample-to-query lifting theorem [SIAM J. Comput. 2025, arXiv:2308.01794] and use it as the key tool to prove new quantum query lower bounds from quantum sample lower bounds. Second, we present a quantum samplizer [ESA 2024, IEEE Trans. Inf. Theory 2025, arXiv:2401.09947], a generalization of the lifting theorem, and use it to design new quantum sample-based algorithms based on techniques for quantum query algorithms. We also present representative applications, including (i) the quantum query lower bounds for quantum Gibbs sampling and the entanglement entropy problem and (ii) the quantum sample upper bound for entropy estimation and closeness estimation.
  • 15:40-16:00 (CST) 16:40-17:00 (JST)
    Wusheng Wang (Graduate School of Mathematics, Nagoya University)
    Quantum digital signature based on single-qubit without a trusted third-party slides
    Digital signatures are a significant cryptographic primitive that provide reliable ways for message authentication. Although quantum digital signatures have been extensively studied, the existing quantum digital signature protocols still require a trusted third-party to ensure security. We propose a specific bounded-copy quantum digital signature protocol, where the trusted third-party is not needed. A malicious party intending to forge a signature may measure the public keys. We also prove that the maximum probability that the malicious party succeeds in a forging attack is negligible as long as we properly select the security parameter.
    This talk is mainly based on the joint work with Masahito Hayashi, arXiv:2410.13397.
  • 16:00-16:20 (CST) 17:00-17:20 (JST)
    Mingrui Jing (Hong Kong University of ST, Guangzhou)
    Quantum Recurrent Embedding Neural Networks slides
    Quantum neural networks have emerged as promising quantum machine learning models, leveraging the properties of quantum systems and classical optimization to solve complex problems in physics and beyond. However, the pursuit of quantum advantage in this field faces a paradoxical tradeoff: where the QNN architectures with proven trainability can possess bounded dimensional Lie algebraic structures, potentially losing quantum advantage, even they can resist the most susceptible gradient vanishing. In this work, we propose a quantum recurrent embedding neural network (QRENN), a versatile framework that tightly integrates tunable QNN components with quantum data embedding, inspired by fast-track information pathways in ResNet, and grounded in quantum circuit architecture theory. Through rigorous theoretical analysis using the dynamical Lie algebra formalism, we provide a rigorous proof of the trainability of QRENN circuits, demonstrating that this deep quantum neural network can avoid barren plateaus. Notably, the general QRENN architecture resists classical simulation as it encompasses powerful quantum circuits such as QSP, QSVT, and DQC1, which are widely believed to be classically intractable. Building on this theoretical foundation, we apply our QRENN to accurately classify quantum Hamiltonians and detect symmetry-protected topological phases, demonstrating its applicability in quantum supervised learning. Our results highlight the power of recurrent data embedding in quantum neural networks and the potential for scalable quantum supervised learning in predicting physical properties and solving complex problems.
• 9/26 (Fri)
  • 09:30-10:10 (CST) 10:30-11:10 (JST)
    Harumichi Nishimura (Graduate School of Informatics, Nagoya University)
    Multiparty quantum simultaneous message passing communication complexity
    Quantum simultaneous message passing (SMP) model is a basic one in quantum communication complexity: two parties Alice on input x and Bob on input y send their quantum messages to the third party Referee, and the aim is that Referee computes f(x,y) for a function f. However, its multiparty version has not been well-studied in the literature. In this talk, I will report known results and open problems on this version. The talk will be mainly based on arXiv:2412.08091.
  • 10:20-10:40 (CST) 11:20-11:40 (JST)
    Takeshi Kimura (Graduate School of Informatics, Nagoya University)
    An em algorithm for quantum Boltzmann machines
    We develop a quantum version of the em algorithm for training quantum Boltzmann machines. The em algorithm is an information-geometric extension of the well-known expectation-maximization (EM) algorithm, offering a structured alternative to gradient-based methods with potential advantages in stability and convergence. We implement the algorithm on a semi-quantum restricted Boltzmann machine, where quantum effects are confined to the hidden layer. This structure enables analytical update rules while preserving quantum expressivity. Numerical experiments on benchmark datasets show that the proposed method achieves stable learning and outperforms gradient-based training in several cases. These results demonstrate the potential of information-geometric optimization for quantum machine learning, particularly in settings where standard methods struggle due to non-commutativity or vanishing gradients.
  • 10:50-11:30 (CST) 11:50-12:30 (JST)
    Sanjib Ghosh (School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen)
    Quantum reservoir processing: a quantum neural network perspective
    A quantum reservoir processor is a framework for quantum information processing inspired by neural network architectures, where the reservoir is implemented in a quantum system. In this presentation, we introduce the concept of a quantum reservoir processor and discuss a realization based on quantum dots. We demonstrate that such a processor can efficiently perform tasks on quantum states, including the recognition of entanglement, quantum state tomography and the estimation of key quantum properties such as von Neumann entropy, purity, and negativity. Moreover, by training only part of the system, the processor can generate useful quantum states, such as Schrödinger cat states, entangled states, and single-photon Fock states. We further show that the same reservoir computing architecture can be adapted to implement quantum circuit algorithms, exemplified by Grover's search. Finally, we outline open questions and future directions arising from this work.
  • 13:30-14:10 (CST) 14:30-15:10 (JST)
    Shintarou Yanagida (Graduate School of Mathematics, Nagoya University)
    Zhu algebras of superconformal vertex algebras slides
    The purpose of this talk is the introduction of the Zhu algebra, which is an associative algebra associated to a vertex operator algebra (VOA). introduced by Y. Zhu (J. Amer. Math. Soc., 1996), and plays a fundamental role in understanding the representation theory of VOAs. I will also explain another formulation of the Zhu algebra for an arbitrary vertex algebra (not necessarily equipped with Hamiltonian operators or Virasoro elements) defined by Y.-Z. Huang (Comm. Contemp. Math., 2006), and the superiority of the latter formulation by achieving the following two goals: (1) description of the Zhu algebras of N=1,2,3,4 and big N=4 superconformal vertex algebras, (2) introducing the Zhu algebras of N_K=N supersymmetric vertex algebras.
    This talk is based on joint work with Ryo Sato (Aichi Institute of Technology), arXiv:2509.13124.
  • 14:20-14:40 (CST) 15:20-15:40 (JST)
    Renta Yagi (Graduate School of Mathematics, Nagoya University)
    The Hopf Superalgebra of Two‑Colored Graphs slides
    We investigate Hopf superalgebras and establish that the Hopf superalgebra of quasisymmetric functions in superspace, sQSym, is the terminal object in the category of all combinatorial Hopf superalgebras. Moreover, we show that the ring of symmetric functions in superspace is the terminal object in the category of all combinatorial cocommutative Hopf superalgebras. As an example of a combinatorial cocommutative Hopf superalgebra, we construct one from connected simple two‑colored graphs and demonstrate that it serves as a super-analogue of Stanley's chromatic symmetric functions.
    This talk is based on joint work with Masamune Hattori and Shintarou Yanagida, "On the Hopf superalgebra of symmetric functions in superspace", published online in the Bull. Lond. Math. Soc., 2025; arXiv:2412.17670.
  • 14:50-15:30 (CST) 15:50-16:30 (JST)
    Liang Kong (International Quantum Academy, Shenzhen)
    Topological Wick Rotation and SymTFT
    In this talk, I will show that this idea of SymTFT is a consequence of the mathematical theory of gapped/gapless boundaries of 2+1D topological orders developed in K.-Zheng: 1705.01087 (more details in 1905.04924, 1912.01760). This theory provides a precise meaning of above sandwich expansion and a powerful way to compute the sandwich.
  • 15:40-16:20 (CST) 16:40-17:20 (JST)
    Masashi Hamanaka (Graduate School of Mathematics, Nagoya University)
    ADHM Construction of Instantons slides
    Instantons are solutions of Anti-Self-Dual (ASD) Yang-Mills equations with finite-action boundary conditions and play important roles in quantum field theory and four-dimensional geometry. There is one-to-one correspondence between the moduli space of instantons and the moduli space of ADHM data. (ADHM=Atiyah-Drinfeld-Hitchin-Manin.) The former is defined by matrix-valued nonlinear partial differential equations and the latter by matrix equations. ADHM construction is based on this one-to-one correspondence (reciprocity). Instantons solutions are obtained just by solving problems of linear algebra. In this talk, we review ADHM construction/reciprocity of instantons from the viewpoint of Fourier-Mukai-Nahm transformation. If time allows, extension to noncommutative spaces is also discussed.
• 9/27 (Sat)
  • 09:30-10:10 (CST) 10:30-11:10 (JST)
    Kohtaro Kato (Graduate School of Informatics, Nagoya University)
    Bialgebraic structure and exact renormalization flow of mixed 1D tensor network states
    Generalized symmetries beyond onsite unitary actions are central to understanding exotic quantum phases of matter. In tensor network approaches, these symmetries are represented by matrix product operators (MPOs), but the conventional frameworks of fusion categories and weak Hopf algebras fail to capture many physically relevant cases. I will show that the algebraic structure underlying MPOs can be formulated as a non-counital pre-bialgebra, providing a natural generalization of existing descriptions. As a concrete example, I will discuss the mixed anomaly of the XX model and its lattice realization. I will also explain how a subclass of matrix product density operators (MPDOs) admits an exact renormalization group flow governed by such bialgebras, offering new insights into the classification of mixed-state quantum phases.
  • 10:20-10:40 (CST) 11:20-11:40 (JST)
    Jiaxi Kuang (Graduate School of Informatics, Nagoya University)
    The State-refocusing Square Root Instrument and Retrodictive Entropic Uncertainty Relations slides
    Abstract PDF
  • 10:50-11:30 (CST) 11:50-12:30 (JST)
    Masahito Hayashi (The Chinese University of Hong Kong, Shenzhen / International Quantum Academy, Shenzhen / Graduate School of Mathematics, Nagoya University)
    Heisenberg scaling based on population coding slides
    We study Heisenberg scaling of quantum metrology in the viewpoint of population coding. Although Fisher information has been used for a figure of merit to characterize Heisenberg scaling in quantum metrology, several studies pointed out it does not work as a figure of merit because it does not reflect the global structure. As an alternative figure of merit, we propose the mutual information, which connects the number of distinguishable elements of the parameter space in the viewpoint of population coding. We show that several unitary models achieve Heisenberg scaling in this context. The full paper version is available from doi.org/10.22331/q-2025-02-26-1648.
  • 13:30-14:10 (CST) 14:30-15:10 (JST)
    Kun Fang (School of Data Science, The Chinese University of Hong Kong, Shenzhen)
    An almost complete picture of quantum hypothesis testing with composite correlated hypotheses
    We study quantum hypothesis testing with composite correlated hypotheses, a general framework that encompasses scenarios where quantum states are not fully specified and may exhibit correlations beyond the i.i.d. setting. We characterize optimal performance in the error exponent, strong converse exponent, and Chernoff exponent regimes, complementing and refining existing results in the Stein exponent regime, thereby providing an almost complete picture of quantum hypothesis testing in this realistic yet challenging setting. Our results hold under minimal and broadly applicable assumptions—convexity, compactness, and stability under tensor product—conditions satisfied in most practical applications. The generality of these results makes them readily applicable across a wide range of tasks in quantum information theory.
  • 14:20-14:40 (CST) 15:20-15:40 (JST)
    Atsuya Hasegawa (Graduate School of Mathematics, Nagoya University)
    Does there exist a quantum fingerprinting protocol without coherent measurements?
    Buhrman, Cleve, Watrous, and de Wolf (PRL 2001) discovered the quantum fingerprinting protocol, which is the quantum SMP protocol with S(log n) qubits communication for the equality problem. In the protocol, Alice and Bob create some quantum fingerprints of their inputs, and the referee conducts the SWAP tests for the quantum fingerprints. Since Ω(√n) bits communication is required with the classical SMP scheme for the equality problem first shown by Newman and Szegedy (STOC 1996), there exists an exponential quantum advantage in the amount of communication.
    In this talk, we consider a setting in which the referee can do only incoherent measurements rather than coherent measurements including the SWAP tests. We first show that, in the case of one-way LOCC measurements, Ω(√n) qubits communication is required. To prove the result, we derive a new method to replace quantum messages by classical messages and consider a reduction to the optimal lower bound in the hybrid SMP model where one message is quantum and the other is classical, which was first shown by Klauck and Podder (MFCS 2014). Our method uses the result of Oszmaniec, Guerini, Wittek, and Acín (PRL 2017), who showed that general POVM measurements can be simulated by randomized projective measurements with small ancilla qubits, and Newman's theorem. We further investigate the setting of quantum SMP protocols with two-way LOCC measurements, and derive a lower bound against some restricted two-way LOCC measurements. To prove it, we revisit the technique to replace quantum messages by classical deterministic messages introduced by Aaronson (ToC 2005) and generalized by Gavinsky, Regev, and de Wolf (CJTCS 2008), and show that, using the deterministic message, the referee can simulate the two-way LOCC measurements.
  • 14:50-15:10 (CST) 15:50-16:10 (JST)
    Zhaofeng Su (Research Institute for Quantum Technology, Hong Kong Polytechnic University)
    Optimal and Heuristic Strategies for Atom Movement Compilation in Zoned Neutral Atom Quantum Computing
    Neutral atom platforms have recently emerged as one of the most promising approaches to scalable quantum computing, thanks to their ability to dynamically reposition atoms and thereby achieve full qubit connectivity. However, this unique feature also brings a fundamental challenge: how to compile atom movements with minimal cost while respecting physical constraints. In this talk, I will present our recent work on fast compilation schemes for universal quantum circuits on zoned dynamical neutral atom arrays. We first establish a rigorous mathematical model of the problem, showing that finding the optimal movement scheme is exponentially hard. To address this, we design three algorithms: an optimal algorithm, a scalable heuristic with polynomial complexity O(LN³), and a hybrid algorithm balancing optimality and efficiency. Simulation results on benchmark quantum circuits demonstrate that both the optimal and hybrid algorithms consistently achieve the theoretical minimum number of moves, while the heuristic algorithm scales to very large atom arrays and deep circuits with only a modest overhead. These results provide a practical pathway toward efficient large-scale quantum circuit execution on neutral atom platforms.
  • 15:10-15:30 (CST) 16:10-16:30 (JST)
    Qian Chen (University of Hong Kong)
    Testing k-block-positivity: A hierarchical SDP approach and complexity analysis
    k-block-positivity is a central concept in quantum information theory, intrinsically linked to k-positive maps via the Choi isomorphism, and to fundamental problems like bound entanglement and distillability (e.g., the 2-copy distillability conjecture). However, determining k-block-positivity remains a formidable challenge. In this talk, we formulate this task as a hierarchical semidefinite program (SDP) based on the extendibility hierarchy. We then derive a formula for the size of the required SDP variables, which characterizes the complexity and explains the hierarchy collapse when k=d.

Links

• Shenzhen–Nagoya Workshop on Quantum Science 2024
• Shenzhen–Nagoya Workshop on Quantum Science 2023
• SUSTech-Nagoya workshop on Quantum Science 2022
• SUSTech-Nagoya workshop on Quantum Science 2021

Last update: 2025/09/28