182 research outputs found
Measurement of damping and temperature: Precision bounds in Gaussian dissipative channels
We present a comprehensive analysis of the performance of different classes
of Gaussian states in the estimation of Gaussian phase-insensitive dissipative
channels. In particular, we investigate the optimal estimation of the damping
constant and reservoir temperature. We show that, for two-mode squeezed vacuum
probe states, the quantum-limited accuracy of both parameters can be achieved
simultaneously. Moreover, we show that for both parameters two-mode squeezed
vacuum states are more efficient than either coherent, thermal or single-mode
squeezed states. This suggests that at high energy regimes two-mode squeezed
vacuum states are optimal within the Gaussian setup. This optimality result
indicates a stronger form of compatibility for the estimation of the two
parameters. Indeed, not only the minimum variance can be achieved at fixed
probe states, but also the optimal state is common to both parameters.
Additionally, we explore numerically the performance of non-Gaussian states for
particular parameter values to find that maximally entangled states within
D-dimensional cutoff subspaces perform better than any randomly sampled states
with similar energy. However, we also find that states with very similar
performance and energy exist with much less entanglement than the maximally
entangled ones.Comment: 14 pages, 6 figure
Optimal quantum estimation of loss in bosonic channels
We address the estimation of the loss parameter of a bosonic channel probed
by Gaussian signals. We derive the ultimate quantum bound on precision and show
that no improvement may be obtained by having access to the environment degrees
of freedom. We found that, for small losses, the variance of the optimal
estimator is proportional to the loss parameter itself, a result that
represents a qualitative improvement over the shot noise limit. An observable
based on the symmetric logarithmic derivative is derived, which attains the
ultimate bound and may be implemented using Gaussian operations and photon
counting.Comment: 4 pages, 2 figures, replaced with published versio
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Low Skilled Local Labor Demand Shocks and Labor Market Outcomes: Evidence from the Mexican Tequila Crisis
How does immigration affect natives local wages? A vast literature considers this, much of it focused on Mexican immigration to the United States. Prior work emphasizes the importance of instrumenting for immigrant destinations, the key role of experience-skill cells, and the potential for spillovers to national markets. I build on these, using the Mexican ’Tequila Crisis’ of the mid-1990s as an exogenous shock to immigration. Instrumentation thus includes both a time dimension for the shock period, plus a destination dimension as in prior work. The 1.5% immigration shock of the Tequila Crisis lowered the wages of young low skilled US natives by 1 to 1.5 percent. It also prompted interstate labor reallocation. The share of low skilled workers is estimated to decrease by 2 percentage points as a result of the shock. This explains why within five years, national markets adjust, leaving no evidence of differential spatial impact
Characterizing and Quantifying Frustration in Quantum Many-Body Systems
We present a general scheme for the study of frustration in quantum systems.
We introduce a universal measure of frustration for arbitrary quantum systems
and we relate it to a class of entanglement monotones via an exact inequality.
If all the (pure) ground states of a given Hamiltonian saturate the inequality,
then the system is said to be inequality saturating. We introduce sufficient
conditions for a quantum spin system to be inequality saturating and confirm
them with extensive numerical tests. These conditions provide a generalization
to the quantum domain of the Toulouse criteria for classical frustration-free
systems. The models satisfying these conditions can be reasonably identified as
geometrically unfrustrated and subject to frustration of purely quantum origin.
Our results therefore establish a unified framework for studying the
intertwining of geometric and quantum contributions to frustration.Comment: 8 pages, 1 figur
Entanglement quantification by local unitaries
Invariance under local unitary operations is a fundamental property that must
be obeyed by every proper measure of quantum entanglement. However, this is not
the only aspect of entanglement theory where local unitaries play a relevant
role. In the present work we show that the application of suitable local
unitary operations defines a family of bipartite entanglement monotones,
collectively referred to as "mirror entanglement". They are constructed by
first considering the (squared) Hilbert-Schmidt distance of the state from the
set of states obtained by applying to it a given local unitary. To the action
of each different local unitary there corresponds a different distance. We then
minimize these distances over the sets of local unitaries with different
spectra, obtaining an entire family of different entanglement monotones. We
show that these mirror entanglement monotones are organized in a hierarchical
structure, and we establish the conditions that need to be imposed on the
spectrum of a local unitary for the associated mirror entanglement to be
faithful, i.e. to vanish on and only on separable pure states. We analyze in
detail the properties of one particularly relevant member of the family, the
"stellar mirror entanglement" associated to traceless local unitaries with
nondegenerate spectrum and equispaced eigenvalues in the complex plane. This
particular measure generalizes the original analysis of [Giampaolo and
Illuminati, Phys. Rev. A 76, 042301 (2007)], valid for qubits and qutrits. We
prove that the stellar entanglement is a faithful bipartite entanglement
monotone in any dimension, and that it is bounded from below by a function
proportional to the linear entropy and from above by the linear entropy itself,
coinciding with it in two- and three-dimensional spaces.Comment: 13 pages, 3 figures. Improved and generalized proof of monotonicity
of the mirror and stellar entanglemen
Optimal phase measurements with pure Gaussian states
We analyze the Heisenberg limit on phase estimation for Gaussian states. In
the analysis, no reference to a phase operator is made. We prove that the
squeezed vacuum state is the most sensitive for a given average photon number.
We provide two adaptive local measurement schemes that attain the Heisenberg
limit asymptotically. One of them is described by a positive operator-valued
measure and its efficiency is exhaustively explored. We also study Gaussian
measurement schemes based on phase quadrature measurements. We show that
homodyne tomography of the appropriate quadrature attains the Heisenberg limit
for large samples. This proves that this limit can be attained with local
projective Von Neuman measurements.Comment: 9 pages. Revised version: two new sections added, revised
conclusions. Corrected prose. Corrected reference
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