Current-based metrology in a quantum thermal machine

Abstract

Quantum metrology is a rapidly growing field of quantum information science that aims to exploit the counter-intuitive properties of quantum systems to estimate physical quantities with better-than-classical precision. The field primarily deals with the problem of estimating system parameters, which may or may not directly be associated to an observable. A prominent result of quantum metrology is the quantum Cram ́er-Rao bound (QCRB), which establishes a fundamental lower bound on the attainable uncertainty in a parameter estimation problem. Nevertheless, this bound is in most cases unreachable by experiments. Hence, the study of estimation strategies that are simultaneously precise and experimentally feasible is essential for the development of quantum sensing devices.

In this work, the problem of parameter estimation is explored in a two-qubit autonomous thermal machine interacting weakly with two thermal reservoirs. The qubits are coupled to each other and their energy gaps are separated by a small detuning. The estimation precision is calculated from the particle currents that naturally arise between the system and the reservoirs. In addition, violations of classical thermodynamic inequalties, called thermodynamic uncertainty relations (TUR’s), are investigated and connected to a possible quantum advantage in parameter estimation. Finally, the current-based estimation precision is compared to the quantum Cramér-Rao bound.

A classical thermodynamic bound on the current precision is derived for the inter-qubit coupling and the detuning. It is found that TUR violations are possible in different regions of the parameter space, and that they can lead to an increase in current precision. Furthermore, it is observed that, for vanishing detuning, the current precision for the inter-qubit coupling can approximate the quantum Cramér-Rao bound to a high degree.

Popular Abstract

Our ability to reliably design and build objects, tools and devices is directly tied to how well we are able to measure physical quantities. After all, we all know how important it is to measure the right amounts of ingredients when baking a cake. Furthermore, all the technology that we use in our daily life, from smartphone to cars, would not be able to function properly without precise measurements during the production stage.

Metrology, as its Greek etymology suggests, is the scientific field that aims to ensure accuracy, precision, and reliability in quantitative measurements. Theoretical and experimental metrology go hand in hand, as the former deals with the development of precise measurement devices, whilst the latter studies optimal measurement strategies and their limitations.

Since its early days, quantum mechanics has radically changed our understanding of the world at its most fundamental scales. It all began at the beginning of the 20th centuries, when physicists gradually came to realise that very small things, such as atoms and molecules, behave rather differently than the macroscopic objects we see every day. One of the most prominent features of quantum mechanics is undoubtedly quantum entanglement: two or more particles, such as photons, after interacting with each other they can no longer be described by separate quantum states, and the new quantum state that describes all of them at the same time allows them to become statistically correlated. Quite surprisingly, this phenomenon can theoretically be used as a computational resource. In fact, quantum computers would be able to exploit the proprieties of quantum entanglement to easily solve certain sets of tasks and problems currently impossible to solve by classical computers. For example, a fully functional quantum chip would be able to completely simulate the dynamics of proteins and other organic molecules and thus be a fundamental instrument in the development of new medicines.

As it turns out, the bizarre properties of the quantum world, such as quantum entanglement, are not just useful for computational purposes. In fact, they can enable us to achieve levels of precision that classical physics does not allow for. The emerging field of quantum metrology aims to study theoretical and experimental methods to achieve such non-classical precision.

Most physical scenarios in quantum mechanics involve open systems, which can exchange energy and matter with an external environment. In particular, a certain class of open quantum systems called \emph{quantum thermal machines} are capable of exploiting the transfer of particles and heat to and from the environment in order to perform certain operations, such as the production of mechanical work. Such machines usually consist of several communicating parts and are dependent or certain parameters, such as the energies of the different part and the strength of the coupling between them. Therefore, in order to ensure that such a machine maintains a certain level of performance, one must be able to accurately estimate the aforementioned parameters.\\

By considering a simple quantum thermal machine consisting of two parts coupled to each other, this work aims to characterise the precision of parameter estimation that can be achieved by measuring the exchange of particles between the machine and the environment. It is found that such precision can exceed the highest one allowed by classical thermodynamics, and that in certain conditions, the precision can almost be as large as it is allowed by quantum mechanics.

• author: Gigante, Guglielmo Nicola
• supervisor: Shishir Khandelwal; Armin Tavakoli
• organization: Department of Physics; Mathematical Physics
• course: FYSK04 20241
• year: 2024
• type: M2 - Bachelor Degree
• subject: Physics and Astronomy
• keywords: Quantum metrology, open quantum systems, current fluctuations, quantum thermodynamics
• language: English
• id: 9164985
• date added to LUP: 2024-06-18 15:04:00
• date last changed: 2024-06-18 15:04:00