74 research outputs found
Geometric description of modular and weak values in discrete quantum systems using the Majorana representation
We express modular and weak values of observables of three- and higher-level
quantum systems in their polar form. The Majorana representation of N-level
systems in terms of symmetric states of N-1 qubits provides us with a
description on the Bloch sphere. With this geometric approach, we find that
modular and weak values of observables of N-level quantum systems can be
factored in N-1 contributions. Their modulus is determined by the product of
N-1 ratios involving projection probabilities between qubits, while their
argument is deduced from a sum of N-1 solid angles on the Bloch sphere. These
theoretical results allow us to study the geometric origin of the quantum phase
discontinuity around singularities of weak values in three-level systems. We
also analyze the three-box paradox [1] from the point of view of a bipartite
quantum system. In the Majorana representation of this paradox, an observer
comes to opposite conclusions about the entanglement state of the particles
that were successfully pre- and postselected
Interferences in quantum eraser reveal geometric phases in modular and weak values
In this letter, we present a new procedure to determine completely the
complex modular values of arbitrary observables of pre- and post-selected
ensembles, which works experimentally for all measurement strengths and all
post-selected states. This procedure allows us to discuss the physics of
modular and weak values in interferometric experiments involving a qubit meter.
We determine both the modulus and the argument of the modular value for any
measurement strength in a single step, by controlling simultaneously the
visibility and the phase in a quantum eraser interference experiment. Modular
and weak values are closely related. Using entangled qubits for the probed and
meter systems, we show that the phase of the modular and weak values has a
topological origin. This phase is completely defined by the intrinsic physical
properties of the probed system and its time evolution. The physical
significance of this phase can thus be used to evaluate the quantumness of weak
values
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
Molding Molecular and Material Properties by Strong Light-Matter Coupling
When atoms come together and bond, we call these new states molecules, and
their properties determine many aspects of our daily life. Strangely enough, it
is conceivable for light and molecules to bond, creating new hybrid
light-matter states with far-reaching consequences for these strongly coupled
materials. Even stranger, there is no `real' light needed to obtain the
effects, it simply appears from the vacuum, creating `something from nothing'.
Surprisingly, the setup required to create these materials has become
moderately straightforward. In its simplest form, one only needs to put a
strongly absorbing material at the appropriate place between two mirrors, and
quantum magic can appear. Only recently has it been discovered that strong
coupling can affect a host of significant effects at a material and molecular
level, which were thought to be independent of the `light' environment: phase
transitions, conductivity, chemical reactions, etc. This review addresses the
fundamentals of this opportunity: the quantum mechanical foundations, the
relevant plasmonic and photonic structures, and a description of the various
applications, connecting materials chemistry with quantum information,
nonlinear optics and chemical reactivity. Ultimately, revealing the interplay
between light and matter in this new regime opens attractive avenues for many
applications in the material, chemical, quantum mechanical and biological
realms
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