49,659 research outputs found
Exact dimension estimation of interacting qubit systems assisted by a single quantum probe
Estimating the dimension of an Hilbert space is an important component of
quantum system identification. In quantum technologies, the dimension of a
quantum system (or its corresponding accessible Hilbert space) is an important
resource, as larger dimensions determine e.g. the performance of quantum
computation protocols or the sensitivity of quantum sensors. Despite being a
critical task in quantum system identification, estimating the Hilbert space
dimension is experimentally challenging. While there have been proposals for
various dimension witnesses capable of putting a lower bound on the dimension
from measuring collective observables that encode correlations, in many
practical scenarios, especially for multiqubit systems, the experimental
control might not be able to engineer the required initialization, dynamics and
observables.
Here we propose a more practical strategy, that relies not on directly
measuring an unknown multiqubit target system, but on the indirect interaction
with a local quantum probe under the experimenter's control. Assuming only that
the interaction model is given and the evolution correlates all the qubits with
the probe, we combine a graph-theoretical approach and realization theory to
demonstrate that the dimension of the Hilbert space can be exactly estimated
from the model order of the system. We further analyze the robustness in the
presence of background noise of the proposed estimation method based on
realization theory, finding that despite stringent constrains on the allowed
noise level, exact dimension estimation can still be achieved.Comment: v3: accepted version. We would like to offer our gratitudes to the
editors and referees for their helpful and insightful opinions and feedback
Measurement Theory in Lax-Phillips Formalism
It is shown that the application of Lax-Phillips scattering theory to quantum
mechanics provides a natural framework for the realization of the ideas of the
Many-Hilbert-Space theory of Machida and Namiki to describe the development of
decoherence in the process of measurement. We show that if the quantum
mechanical evolution is pointwise in time, then decoherence occurs only if the
Hamiltonian is time-dependent. If the evolution is not pointwise in time (as in
Liouville space), then the decoherence may occur even for closed systems. These
conclusions apply as well to the general problem of mixing of states.Comment: 14 pages, IASSNS-HEP 93/6
Ground States of S-duality Twisted N=4 Super Yang-Mills Theory
We study the low-energy limit of a compactification of N=4 U(n) super
Yang-Mills theory on with boundary conditions modified by an S-duality
and R-symmetry twist. This theory has N=6 supersymmetry in 2+1D. We analyze the
compactification of this 2+1D theory by identifying a dual weakly coupled
type-IIA background. The Hilbert space of normalizable ground states is
finite-dimensional and appears to exhibit a rich structure of sectors. We
identify most of them with Hilbert spaces of Chern-Simons theory (with
appropriate gauge groups and levels). We also discuss a realization of a
related twisted compactification in terms of the (2,0)-theory, where the recent
solution by Gaiotto and Witten of the boundary conditions describing D3-branes
ending on a (p,q) 5-brane plays a crucial role.Comment: 104 pages, 5 figures. Revisions to subsection (6.6) and other minor
corrections included in version
Finite dimensional Markovian realizations for stochastic volatility forward rate models
We consider forward rate rate models of HJM type, as well as more general infinite dimensional SDEs, where the volatility/diffusion term is stochastic in the sense of being driven by a separate hidden Markov process. Within this framework we use the previously developed Hilbert space realization theory in order provide general necessary and sufficent conditions for the existence of a finite dimensional Markovian realizations for the stochastic volatility models. We illustrate the theory by analyzing a number of concrete examples.HJM models; stochastic volatility; factor models; forward rates; state space models; Markovian realizations; infinite dimensional SDEs
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