Half a qubit: an algebraic fractionalization, Po-Yao Chang Room: Physics Building/3F--- - PRPC Multipurpose Room Fractionalizing a quantum two-level system is usually associated with encodings based on pairs of Majorana fermions---an operational fractionalization. We show an alternative algebraic fractionalization by embedding Székely's classical ``half-coin'' into a non-Hermitian Krein space. The coefficients of $(q+pz)^{1/2}$ define a signed sequence and a normalized, non-Hermitian biorthogonal operator describing a biorthogonal half-qubit. We prove that two such objects fuse into an arbitrary pure qubit through the signed Vandermonde convolution that the collective N≥2 vectors are null in Krein space. L1 norm of the half-qubit follows in closed form. Its L1 norm increases monotonically with the bias and attains its supremum $\sqrt{2}$ precisely at the unbiased point p=q=1/2. Interestingly, we identify two structural results as follows. First, number parity and the η-metric generate a distinguished commuting ℤ2×ℤ2 subgroup. Second, we find the η-metric obstructs any local η-self-adjoint partner of the parity, so a half-qubit carries a ℤ2 observable but no local SU(2). The full Pauli algebra emerges only upon fusion. We then show that the construction survives truncation of the Fock basis: the fused qubit is exact at every cutoff, and the Vandermonde cancellation is visible in sign-weighted photon-number statistics, and can be tested using existing cavity and trapped-ion state-synthesis methods. Finally, we generalize this algebraic fractionalization to a 1/n-qubit, which can be achieved by replacing the square root with an nth root.

Beyond Boson Sampling: From Higher Spins to Open Quantum Dynamics, En-Jui Kuo Room: Physics Building/3F--- - PRPC Multipurpose Room Boson sampling provides a promising route toward demonstrating quantum computational advantage, but its experimental implementation remains challenging due to demanding physical resource requirements. In this talk, I will discuss two approaches to extending boson sampling beyond idealized bosonic systems. First, I will introduce a higher-spin sampling framework in which finite-dimensional spin systems approximate Fock-state boson sampling. We establish a quasi-linear mode scaling relation, \(m\sim n^{1+3/(2S)}\), showing how increasing the spin quantum number reduces the required resources while preserving the relevant sampling complexity. Second, I will discuss computational complexity in open bosonic systems, focusing on the fixed points of Lindblad dynamics. Different dissipative mechanisms can produce classically tractable steady states or stabilize nonclassical states with potentially challenging sampling tasks. Together, these directions provide a framework for understanding how quantum computational complexity survives finite-dimensional approximations and environmental interactions.

Entanglement in $c=-2$ Logarithmic Conformal Field Theory, Kuang-Hung Chou Room: Physics Building/3F--- - PRPC Multipurpose Room The replica trick is widely used to calculate entanglement and R\'enyi entropies in conformal field theory, but its application to logarithmic and non-unitary theories is less understood. We study this problem in $c=-2$ logarithmic CFTs, using symplectic fermions and the continuum theory of the non-Hermitian SSH model as complementary realizations. We find an odd--even splitting of the R\'enyi moments arising from fermionic replica sewing, with odd and even replica numbers following distinct scaling sequences. On the odd branch connected to $n=1$, an infrared Grassmann zero mode produces an additional $\log(mL/v_F)$ contribution, accounting for the residual entropy observed in the lattice model. For two disjoint intervals, the twist-field four-point function contains an additional logarithmic contribution beyond the standard conformal dependence. Together, these results show that entanglement in c=-2 logarithmic critical theories contains universal information beyond the central charge.

Tensor network, renormalization group, and conformal field theory

• Pochung Chen (NTHU)

Room: Physics Building/3F--- - PRPC Multipurpose Room In this talk, I will discuss the deep connection between tensor network renormalization method and renormalization group concept. I will explain how to use this connection to extract the critical point and critical exponents. After that I will further extend the connection to conformal field theory. I will explain how to extract conformal data, including central charge, scaling dimension, conformal spin, operator product expansion coefficients. I will use 2D Ising model and 3-state clock model as examples. Finally, I will discuss the generalization to 3D models and to complex CFT.

Exact organization of density matrices and entanglement structure in the Kitaev spin liquid, Chen-Chih Wang Room: Physics Building/3F--- - PRPC Multipurpose Room We give an exact form of the density matrix for the spin-1/2 Kitaev spin liquid, expressed in terms of spin operators, and study the entanglement structure of the Kitaev spin liquid within the spin framework. We show that the density matrix is naturally organized by equivalence classes of string operators associated with the underlying gauge structure of the model. Using the explicit form of the density matrix, together with the exact Gauss law of the emergent gauge theory and the exact 1-form Wilson symmetry in the Kitaev model, we demonstrate the block-diagonal structure of the reduced density matrix, which gives rise to the extensive degeneracy in the entanglement spectrum. Furthermore, we explore subsystems with different numbers of lattice sites and topologies, revealing relationships between the entanglement spectrum and the subsystem fermion parity. Lastly, we briefly discuss the quantum magic of the Kitaev spin liquid and how the form of the density matrix implies its physical meaning. Reference: C.-C. Wang, Y.-P. Huang, and S. Yip, Phys. Rev. B 114, 305105