Phase estimation Under energy conservation

Antonio Russo, Kenneth Rudinger, Benjamin Morrison +1 more

Qu-Cheng Gao, Xiao Chen

We investigate one-dimensional systems with both energy conservation and a continuous symmetry, focusing on the impact of a boundary perturbation that breaks the continuous symmetry. Our study reveals two distinct dynamical phases: one in which the corresponding charge exhibits extensive fluctuations, and another where the charge remains conserved. These phases appear in both free and interacting models. We interpret this behavior through a boundary-induced pumping mechanism, which estimates the amplitude connecting two degenerate states from different charge sectors via a local charge-non-conserving operator. In the Floquet setting, we show that the frozen phase can survive at high driving frequencies but vanishes at low frequencies. This phenomenon is exact in free-fermion systems in the thermodynamic limit, but in interacting systems it appears only at finite system size. The emergence of the charge-frozen phase is attributed to effective energy conservation, and we demonstrate that this phase disappears when effective energy conservation is broken or replaced by other symmetries.

Weng-Long Chang, Athanasios V. Vasilakos

Tomasz Wasak, Augusto Smerzi, Luca Pezzè +1 more

Tommaso Favalli, Žan Kokalj, Andrea Trombettoni

We investigate the phase sensitivity of a linear two-mode atom interferometer subject to environmental noise, modeled within the framework of open quantum systems with both number-conserving and non-conserving Lindblad operators. Considering several input states, we first study the cases N=1,2 (N number of particles) and perform numerical simulations for N>2. The sensitivity as a function of the holding time can display divergence points where phase estimation becomes impossible, to which we refer as insensitivity points. We characterize their behavior as the input state, particle number, and noise operator are varied, and we find that their positions are independent of the noise intensity. Moreover, while our fixed measurement scheme may favor number-conserving noise at small N (i.e., having better sensitivity), the Cramér-Rao bound reveals that particle non-conserving noise yields strictly lower achievable sensitivity for all particle numbers.

Naoto Shiraishi

The resource theory with covariant Gibbs-preserving operations, also called enhanced thermal operations, is investigated. We prove that with the help of a correlated catalyst, the state convertibility for any coherent state is fully characterized by the free energy defined with the quantum relative entropy. We can extend this result to general resource theories in the form that imposing the covariant condition to a general resource theory does not change the state convertibility, as long as the initial state is coherent and distillable and this resource theory admits the phase estimation and the phase shift. This means that adding a constraint from the law of energy conservation is irrelevant in the correlated-catalytic framework.