Symmetry rescues entanglement from thermal death ✛ ✎

Quantum entanglement is a fragile resource. Heat a system, and thermal fluctuations will tear the delicate threads of correlations: at a sufficiently high but finite temperature, the Gibbs state of a local Hamiltonian becomes separable, that is, representable as a probabilistic mixture of products of local states. This phenomenon has been dubbed 'sudden death of entanglement' — quantum entanglement disappears abruptly rather than gradually. It would seem that nature leaves no loopholes: heat is the universal destroyer of quantum wonders.

Yet nature has another universal principle: symmetry. Imagine a protective shield that prevents heat from reaching quantum correlations. That is precisely the role played by a global symmetry imposed on a thermal ensemble. The authors considered two ways of imposing it. The first is a canonical ensemble: the state is projected onto a sector with fixed symmetry charge, which corresponds to strong symmetry, where the entire state lies in a single charge sector. The second is a Gibbs ensemble with a superselection rule that forbids mixing states with different charges; here the definition of separability is modified to symmetric separability. It turns out that for abelian symmetries with local action on lattice sites and typical symmetric local Hamiltonians, the canonical ensemble has nonzero negativity at arbitrarily high temperatures, while the Gibbs ensemble is symmetrically entangled. The condition on the Hamiltonian is formulated as the noncommutativity of its part with the symmetry operator acting on the subsystem. For fermionic systems, it is proven that fermionic negativity does not vanish at high temperatures, confirming earlier conjectures.

This work changes our understanding of thermal states of symmetric systems. Previously, it was believed that high temperature inevitably destroys entanglement; now it is shown that global symmetry can act as a 'protective shield.' For the physics of mixed states, this means that symmetric thermal ensembles can serve as a resource for quantum protocols that are robust to heating. The results connect two previously independent directions: the study of strong symmetry in open quantum systems and the analysis of entanglement in fermionic systems with superselection. A natural next step is to generalize to non-abelian symmetries, higher-form and subsystem symmetries, and antiunitary symmetries. An open question is whether entanglement survives in the thermodynamic limit: the proofs apply to finite systems, and negativity may tend to zero as the size goes to infinity. Calculations on stabilizer models give hope for a positive answer, but a rigorous proof is lacking. It is also interesting to investigate whether other quantum resources, such as magic or Gaussianity, undergo 'sudden death.'