Fundamental Limits in Bayesian Thermometry and Attainability via Adaptive Strategies.

We investigate the limits of thermometry using quantum probes at thermal equilibrium within the Bayesian approach. We consider the possibility of engineering interactions between the probes in order to enhance their sensitivity, as well as feedback during the measurement process, i.e., adaptive protocols. On the one hand, we obtain an ultimate bound on thermometry precision in the Bayesian setting, valid for arbitrary interactions and measurement schemes, which lower bounds the error with a quadratic (Heisenberg-like) scaling with the number of probes. We develop a simple adaptive strategy that can saturate this limit. On the other hand, we derive a no-go theorem for nonadaptive protocols that does not allow for better than linear (shot-noise-like) scaling even if one has unlimited control over the probes, namely, access to arbitrary many-body interactions.

Exploiting the Causal Tensor Network Structure of Quantum Processes to Efficiently Simulate Non-Markovian Path Integrals.

In the path integral formulation of the evolution of an open quantum system coupled to a Gaussian, noninteracting environment, the dynamical contribution of the latter is encoded in an object called the influence functional. Here, we relate the influence functional to the process tensor-a more general representation of a quantum stochastic process-describing the evolution. Then, we use this connection to motivate a tensor network algorithm for the simulation of multitime correlations in open systems, building on recent work where the influence functional is represented in terms of time evolving matrix product operators. By exploiting the symmetries of the influence functional, we are able to use our algorithm to achieve orders-of-magnitude improvement in the efficiency of the resulting numerical simulation. Our improved algorithm is then applied to compute exact phonon emission spectra for the spin-boson model with strong coupling, demonstrating a significant divergence from spectra derived under commonly used assumptions of memorylessness.