We investigate the von Neumann entanglement entropy as function of the size of a subsystem for permutation invariant ground states in models with finite number of states per site, e.g., in quantum spin models. We demonstrate that the entanglement entropy of $n$ sites in a system of length $L$ generically grows as $\ensuremath{\sigma}\phantom{\rule{0.2em}{0ex}}{\mathrm{log}}_{2}[2\ensuremath{\pi}en(L\ensuremath{-}n)∕L]+C$, where $\ensuremath{\sigma}$ is the on-site spin and $C$ is a function depending only on magnetization.We investigate the von Neumann entanglement entropy as function of the size of a subsystem for permutation invariant ground states in models with finite number of states per site, e.g., in quantum spin models. We demonstrate that the entanglement entropy of $n$ sites in a system of length $L$ generically grows as $\ensuremath{\sigma}\phantom{\rule{0.2em}{0ex}}{\mathrm{log}}_{2}[2\ensuremath{\pi}en(L\ensuremath{-}n)∕L]+C$, where $\ensuremath{\sigma}$ is the on-site spin and $C$ is a function depending only on magnetization.

arXiv:quant-ph/0506209Physical Review ASep 22, 200538 citations

Growing Schrödinger's cat states by local unitary time evolution of product states

Saverio Bocini, Maurizio Fagotti

We envisage many-body systems described by quantum spin-chain Hamiltonians featuring a trivial separable eigenstate. For generic Hamiltonians, such a state represents a quantum scar. We show that, typically, a macroscopically entangled state naturally grows after a single projective measurement of just one spin in the quantum scar. Moreover, we identify a condition under which what is growing is a “Schrödinger's cat state.” Our analysis does not reveal any particular requirement for the entangled state to develop, provided that the quantum scar does not minimize/maximize a local conservation law. We study two explicit examples: systems described by generic Hamiltonians where spins interact in pairs, and models that exhibit a U ( 1 ) hidden symmetry. The latter can be reinterpreted as a two-leg ladder in which the interactions along the legs are controlled by the local state on the other leg through transistorlike building blocks. Published by the American Physical Society 2024We envisage many-body systems described by quantum spin-chain Hamiltonians featuring a trivial separable eigenstate. For generic Hamiltonians, such a state represents a quantum scar. We show that, typically, a macroscopically entangled state naturally grows after a single projective measurement of just one spin in the quantum scar. Moreover, we identify a condition under which what is growing is a “Schrödinger's cat state.” Our analysis does not reveal any particular requirement for the entangled state to develop, provided that the quantum scar does not minimize/maximize a local conservation law. We study two explicit examples: systems described by generic Hamiltonians where spins interact in pairs, and models that exhibit a U ( 1 ) hidden symmetry. The latter can be reinterpreted as a two-leg ladder in which the interactions along the legs are controlled by the local state on the other leg through transistorlike building blocks. Published by the American Physical Society 2024

arXiv:2210.15585Physical Review ResearchJul 25, 20249 citations

Entanglement in quantum spin systems

Jeffrey Scott Pratt

Jan 1, 20050 citations

Fate of Quantum Magic

Liuke Lyu, Erik S. Sørensen, William Witczak-Krempa

Magic, a quantum resource distinct from entanglement, measures departure from states stabilized by products of Pauli operators. Such stabilizer states can be maximally entangled yet admit efficient classical description: quantum advantage requires magic. We develop a powerful framework to evaluate the degree of magic in generic many-body states. We use it to study the fate of magic under thermal and dynamical evolution. In the transverse field Ising model, we find a thermal sudden death of magic that saturates with system size, and occurs after the death of entanglement. We reach similar conclusions in generic spin chains, and in the Kitaev quantum spin liquid on the honeycomb lattice, where the threshold shows an intricate dependence on subregion shape. We then study how magic equilibrates after a quantum quench. In quenches of generic spin chains, the magic of a subregion typically dies before entanglement, contrary to thermal trajectories. An explanation is given in terms of the geometry of non-magical states. As a third type of trajectory, we examine the fate of magic with separation with an appropriate notion of non-local magic and establish a sudden death. Finally, we show how to experimentally witness a volume law of frame-robust magic in quantum materials by using neutron scattering.Magic, a quantum resource distinct from entanglement, measures departure from states stabilized by products of Pauli operators. Such stabilizer states can be maximally entangled yet admit efficient classical description: quantum advantage requires magic. We develop a powerful framework to evaluate the degree of magic in generic many-body states. We use it to study the fate of magic under thermal and dynamical evolution. In the transverse field Ising model, we find a thermal sudden death of magic that saturates with system size, and occurs after the death of entanglement. We reach similar conclusions in generic spin chains, and in the Kitaev quantum spin liquid on the honeycomb lattice, where the threshold shows an intricate dependence on subregion shape. We then study how magic equilibrates after a quantum quench. In quenches of generic spin chains, the magic of a subregion typically dies before entanglement, contrary to thermal trajectories. An explanation is given in terms of the geometry of non-magical states. As a third type of trajectory, we examine the fate of magic with separation with an appropriate notion of non-local magic and establish a sudden death. Finally, we show how to experimentally witness a volume law of frame-robust magic in quantum materials by using neutron scattering.

quant-pharXiv:2610.39059Oct 30, 20260 citations

Single-spin entanglement

G. B. Furman, V. Meerovich, Vladimir Sokolovsky

arXiv:1707.02407Quantum Information ProcessingJul 18, 20176 citations

n

sites in a system of length

L

generically grows as $\ensuremath{\sigma}\phantom{\rule{0.2em}{0ex}}{\mathrm{log}}_{2}[2\ensuremath{\pi}en(L\ensuremath{-}n)∕L]+C$, where $\ensuremath{\sigma}$ is the on-site spin and

C

is a function depending only on magnetization.