Speaker
Description
We investigate multipartite entanglement in a specific class of pure n-qubit quantum states, the uniform real-phased states referred to as Hadamard states, through a statistical mechanics framework, where the average bipartite purity maps onto an effective Hamiltonian of $2^n$ binary classical spins. In this correspondence, each Hadamard state uniquely corresponds to a classical spin configuration, while temperature emerges as a control parameter that continuously interpolates between randomly sampled states at high temperature and maximally multipartite entangled states (MMES) in the zero-temperature limit. Remarkably, the zero-temperature entropy directly counts the MMES within the class of Hadamard states. For small system sizes (n < 6), we perform exact enumeration, fully characterizing the energy landscape and associated thermodynamic observables, and validating known MMES counts. For larger systems (n = 6 and 7), where exact methods become computationally infeasible, we employ simulated annealing and tempering to efficiently sample the high-dimensional state space. Our analysis yields quantitative predictions of MMES counts and reveals how entanglement is statistically distributed across the Hadamard state manifolds. The results establish this family of states as an ideal platform for exploring multipartite entanglement through thermodynamic methods, offering both computational advances and physical insights into the structure of quantum entanglement in constrained Hilbert spaces.
References
This talk will be based on a work that is currently unpubblished.
| Sessions | Foundational studies |
|---|---|
| Invited | No |