arXiv subjects

Mathias R. Jørgensen

Publications and source records attributed to Mathias R. Jørgensen.

6 recordsLinked to original sources

arXiv2022

Bayesian quantum thermometry based on thermodynamic length

In this work, we propose a theory of temperature estimation of quantum systems, which is applicable in the regime of non-negligible prior temperature uncertainty and limited measurement data. In this regime the problem of establishing a well-defined measure of estimation precision becomes non-trivial, and furthermore the construction of a suitable criterion for optimal measurement design must be re-examined to account for the prior uncertainty. We propose a fully Bayesian approach to temperature estimation based on the concept of thermodynamic length, which solves both these problems. As an illustration of this framework, we consider thermal spin-$1/2$ particles and investigate the fundamental difference between two cases; on the one hand, when the spins are probing the temperature of a heat reservoir and, on the other, when the spins themselves constitute the sample.

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arXiv2022

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 non-adaptive 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.

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arXiv2021

Optimal Quantum Thermometry with Coarse-grained Measurements

Precise thermometry for quantum systems is important to the development of new technology, and understanding the ultimate limits to precision presents a fundamental challenge. It is well known that optimal thermometry requires projective measurements of the total energy of the sample. However, this is infeasible in even moderately-sized systems, where realistic energy measurements will necessarily involve some coarse graining. Here, we explore the precision limits for temperature estimation when only coarse-grained measurements are available. Utilizing tools from signal processing, we derive the structure of optimal coarse-grained measurements and find that good temperature estimates can generally be attained even with a small number of outcomes. We apply our results to many-body systems and nonequilibrium thermometry. For the former, we focus on interacting spin lattices, both at and away from criticality, and find that the Fisher-information scaling with system size is unchanged after coarse-graining. For the latter, we consider a probe of given dimension interacting with the sample, followed by a measurement of the probe. We derive an upper bound on arbitrary, nonequilibrium strategies for such probe-based thermometry and illustrate it for thermometry on a Bose-Einstein condensate using an atomic quantum-dot probe.

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arXiv2020

A discrete memory-kernel for multi-time correlations in non-Markovian quantum processes

Efficient simulations of the dynamics of open systems is of wide importance for quantum science and tech-nology. Here, we introduce a generalization of the transfer-tensor, or discrete-time memory kernel, formalism to multi-time measurement scenarios. The transfer-tensor method sets out to compute the state of an open few-body quantum system at long times, given that only short-time system trajectories are available. Here, we showthat the transfer-tensor method can be extended to processes which include multiple interrogations (e.g. measurements) of the open system dynamics as it evolves, allowing us to propagate high order short-time correlation functions to later times, without further recourse to the underlying system-environment evolution. Our approach exploits the process-tensor description of open quantum processes to represent and propagate the dynamics in terms of an object from which any multi-time correlation can be extracted. As an illustration of the utility of the method, we study the build-up of system-environment correlations in the paradigmatic spin-boson model, and compute steady-state emission spectra, taking fully into account system-environment correlations present in the steady state.

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arXiv2020

Tight bound on finite-resolution quantum thermometry at low temperatures

Precise thermometry is of wide importance in science and technology in general and in quantum systems in particular. Here, we investigate fundamental precision limits for thermometry on cold quantum systems, taking into account constraints due to finite measurement resolution. We derive a tight bound on the optimal precision scaling with temperature, as the temperature approaches zero. The bound can be saturated by monitoring the non-equilibrium dynamics of a single-qubit probe. We support this finding by accurate numerical simulations of a spin-boson model. Our results are relevant both fundamentally, as they illuminate the ultimate limits to quantum thermometry, and practically, in guiding the development of sensitive thermometric techniques applicable at ultracold temperatures.

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arXiv2019

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, non-interacting 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. We then use this connection to motivate a tensor network algorithm for the simulation of multi-time 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.

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