Soutenance publique de thèse de doctorat en Sciences physiques - Lorena BALLESTEROS FERRAZ
Fundamental study of weak values and post-selected measurements: from geometry and quantum foundations, to quantum information and open systems
Date : 13/09/2023 14:00 - 13/09/2023 17:00
Lieu : Rosalind Franklin Auditorium
Orateur(s) : Lorena BALLESTEROS FERRAZ
Organisateur(s) : Yves Caudano
Jury
- Prof. MAYER Alexandre (département de physique, UNamur), président
- Prof. CAUDANO Yves (département de physique, UNamur), promoteur et secrétaire
- Prof. CARLETTI Timoteo (département de mathématique, UNamur)
- Dr MATZKIN Alexandre (laboratoire de physique théorique et modélisation, CY Cergy Paris Université)
- Prof. MARTIN John (département de physique, ULiège)
- Prof. LAMBERT Dominique (département sciences, philosophies, sociétés, UNamur)
- Dr MILMAN Pérola (laboratoire matériaux et phénomènes quantiques, Université Paris Cité)
Abstract
The focus of this thesis is on weak measurements – a type of quantum measurement where the interaction strength between the measuring device and the system being studied is very small. After the weak interaction, post-selection takes place, requiring a projective measurement and filtering on the desired final state. Ultimately, the shift in the ancilla's wavefunction is proportional to the weak value – a complex and unbounded number.
In this study, we focus on the polar description of weak values. Initially, we delve into the geometrical properties of weak values. Our analysis shows then that the argument of the weak value is related to the sum of two solid angles on the Bloch sphere. Next, we examine the modulus of weak values. We demonstrate that weak values can be expressed as the expectation value of a non-normal operator. We prove that weak values can differ from the observable's eigenvalues only if the operator is non-normal.
Looking at the weak value from a different angle, we can express it as the expectation value of the observable using a pseudo-Hermitian projector. We further demonstrate that, by modifying the Hilbert space standard metric, weak values can be described as expectation values in an indefinite metric space. We establish a link between this space and non-classical logics and find that the emerging logic is para-consistent and para-complete.
In quantum mechanics, a state can never be truly isolated and constantly interacts with its environment. We explore the effects of weak measurements with dissipation between the weak interaction and post-selection. We observe anomalous weak values, even at infinite dissipation time, in cases where the ground state is degenerate. By examining the system at short dissipation times with weak measurements in the amplification regime, we can extract valuable information about the dissipative dynamics, including the dissipation rate and whether the system is Markovian or non-Markovian.
Quantum computing is among the most sought-after applications of quantum physics. In this study, we explore a protocol for implementing quantum algorithms using modular values.
In summary, weak measurements hold great promise for both their amplification properties and their potential to deepen our understanding of fundamental quantum properties.
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