23 research outputs found
Fundamental study of weak values and post-selected measurements:from geometry and quantum foundations to quantum information and open systems
On the relevance of weak measurements in dissipative quantum systems
We investigate the impact of dissipation on weak measurements. While weak
measurements have been successful in signal amplification, dissipation can
compromise their usefulness. More precisely, we show that in systems with
non-degenerate eigenstates, weak values always converge to the expectation
value of the measured observable as dissipation time tends to infinity, in
contrast to systems with degenerate eigenstates, where the weak values can
remain anomalous, i.e., outside the range of eigenvalues of the observable,
even in the limit of an infinite dissipation time. In addition, we propose a
method for extracting information about the dissipative dynamics of a system
using weak values at short dissipation times. Specifically, we explore the
amplification of the dissipation rate in a two-level system and the use of weak
values to differentiate between Markovian and non-Markovian dissipative
dynamics. We also find that weak measurements operating around a weak
atom-cavity coupling can probe the atom dissipation through the weak value of
non-Hermitian operators within the rotating-wave approximation of the weak
interaction
Geometrical interpretation of the argument of weak values of general observables in N-level quantum systems
Observations in quantum weak measurements are determined by complex numbers
called weak values. We present a geometrical interpretation of the argument of
weak values of general Hermitian observables in -dimensional quantum systems
in terms of geometric phases. We formulate an arbitrary weak value in function
of three real vectors on the unit sphere in dimensions, .
These vectors are linked to the initial and final states, and to the weakly
measured observable, respectively. We express pure states in the complex
projective space of dimensions, , which has a
non-trivial representation as a dimensional submanifold of
(a generalization of the Bloch sphere for qudits). The argument of the weak
value of a projector on a pure state of an -level quantum system describes a
geometric phase associated to the symplectic area of the geodesic triangle
spanned by the vectors representing the pre-selected state, the projector and
the post-selected state in . We then proceed to
show that the argument of the weak value of a general observable is equivalent
to the argument of an effective Bargmann invariant. Hence, we extend the
geometrical interpretation of projector weak values to weak values of general
observables. In particular, we consider the generators of SU() given by the
generalized Gell-Mann matrices. Finally, we study in detail the case of the
argument of weak values of general observables in two-level systems and we
illustrate weak measurements in larger dimensional systems by considering
projectors on degenerate subspaces, as well as Hermitian quantum gates.Comment: 29 pages, 3 figure
Revisiting weak values through non-normality
Quantum measurement is one of the most fascinating and discussed phenomena in
quantum physics, due to the impact on the system of the measurement action and
the resulting interpretation issues. Scholars proposed weak measurements to
amplify measured signals by exploiting a quantity called a weak value, but also
to overcome philosophical difficulties related to the system perturbation
induced by the measurement process. The method finds many applications and
raises many philosophical questions as well, especially about the proper
interpretation of the observations. In this paper, we show that any weak value
can be expressed as the expectation value of a suitable non-normal operator. We
propose a preliminary explanation of their anomalous and amplification behavior
based on the theory of non-normal matrices and their link with non-normality:
the weak value is different from an eigenvalue when the operator involved in
the expectation value is non-normal. Our study paves the way for a deeper
understanding of the measurement phenomenon, helps the design of experiments,
and it is a call for collaboration to researchers in both fields to unravel new
quantum phenomena induced by non-normality
Weak measurements under dissipation
peer reviewedWe study weak measurements under the influence of dissipation. Even though dissipation harms the anomalous properties of the weak value, we found specific setups in which extracting information from the weak value is feasible
State transfer in Open Quantum Systems
[eng] This master thesis is focused on the study of quantum state transfer in open
quantum systems. While the presence of losses generally damages the state transfer quality, it is important to find the conditions under which such degradation
can be minimized. We analyze a chain of four spins in multiple scenarios, different types of baths, different coupling constants, and a wide range of oscillatory
frequencies. Dissipation in general hinders the fidelity of the information transfer
but some configurations are found to be more resilient. The time under which
the transfer is maximum is also analyzed, being not strongly altered by dissipation when state transfer is successful. Preliminary results about spontaneous
quantum synchronization are also presente