We study mixed-state entanglement in Gibbs states with strong
SU(2) symmetry, focusing on locally interacting spin systems with ferromagnetic interactions. Our main result is to show that finite-temperature ordering transitions are associated with entanglement transitions, and therefore the steady state of strongly symmetric Lindbladians can exhibit entanglement transitions. While in the paramagnetic phase it is known that the distillable entanglement and logarithmic entanglement negativity between two halves of a large system grow logarithmically with the square root of the number of spins, we show that in ferromagnetic phases these quantities grow parametrically faster with system size. To arrive at this result we first establish relations between these mixed-state entanglement measures and spin correlations in states that are singlets under global
SU(2) symmetry transformations. We then introduce a semiclassical theory for
SU(2) singlet thermal states. While the global singlet constraint generally enters this theory as a complicated function of the full semiclassical spin configuration, we show that in large
S limit it simplifies drastically to a Gaussian suppression of total magnetization in disordered phases as well as in ordered phases in the vicinity of continuous thermal phase transitions. This leads us to a field theory describing spin correlations in the singlet sector. Using this we determine the behavior of various probes of mixed-state entanglement at low and at high temperatures, supporting our analytical results using numerical Monte Carlo simulations of a three-dimensional lattice realization of our semiclassical theory. We also use exact numerics in one-dimensional spin-
1/2 systems to confirm our predictions for the scaling of mixed-state entanglement with correlation length and system size in the paramagnetic phase.
The use of squeezing and entanglement allows advanced interferometers to detect signals that would otherwise be buried in quantum mechanical noise. High sensitivity instruments including magnetometers and gravitational wave detectors have shown enhanced signal-to-noise ratio (SNR) by injecting single-mode squeezed light into SU(2) interferometers, e.g. the Mach-Zehnder or Michelson topologies. The quantum enhancement in this approach is sensitive to losses, which break the fragile quantum correlations in the squeezed state. In contrast, SU(1,1) interferometers achieve quantum enhancement by noiseless amplification; they noiselessly increase the signal rather than reducing the quantum noise. Prior work on SU(1,1) interferometers has shown quantum-enhanced SNR11 and insensitivity to losses but to date has been limited to low powers and thus low SNR. Here we introduce a new interferometer topology, the SU(2)-in-SU(1,1) nested interferometer, that combines quantum enhancement, the high SNR possible with a SU(2) interferometer, and the loss tolerance of the SU(1,1) approach. We implement this interferometer using four-wave mixing in a hot atomic vapor and demonstrate 2:2(5) dB of quantum SNR enhancement, in a system with a phase variance nearly two orders of magnitude below that of any previous loss-tolerant enhancement scheme. The new interferometer enables new possibilities such as beyond-shot-noise sensing with wavelengths for which efficient detectors are not available.