2,514 research outputs found
Quantum tomography for collider physics: Illustrations with lepton pair production
Quantum tomography is a method to experimentally extract all that is
observable about a quantum mechanical system. We introduce quantum tomography
to collider physics with the illustration of the angular distribution of lepton
pairs. The tomographic method bypasses much of the field-theoretic formalism to
concentrate on what can be observed with experimental data, and how to
characterize the data. We provide a practical, experimentally-driven guide to
model-independent analysis using density matrices at every step. Comparison
with traditional methods of analyzing angular correlations of inclusive
reactions finds many advantages in the tomographic method, which include
manifest Lorentz covariance, direct incorporation of positivity constraints,
exhaustively complete polarization information, and new invariants free from
frame conventions. For example, experimental data can determine the
of the production process, which is a
model-independent invariant that measures the degree of coherence of the
subprocess. We give reproducible numerical examples and provide a supplemental
standalone computer code that implements the procedure. We also highlight a
property of that guarantees in a least-squares type fit
that a local minimum of a statistic will be a global minimum: There
are no isolated local minima. This property with an automated implementation of
positivity promises to mitigate issues relating to multiple minima and
convention-dependence that have been problematic in previous work on angular
distributions.Comment: 25 pages, 3 figure
Quantum change point
Sudden changes are ubiquitous in nature. Identifying them is of crucial
importance for a number of applications in medicine, biology, geophysics, and
social sciences. Here we investigate the problem in the quantum domain,
considering a source that emits particles in a default state, until a point
where it switches to another state. Given a sequence of particles emitted by
the source, the problem is to find out where the change occurred. For large
sequences, we obtain an analytical expression for the maximum probability of
correctly identifying the change point when joint measurements on the whole
sequence are allowed. We also construct strategies that measure the particles
individually and provide an online answer as soon as a new particle is emitted
by the source. We show that these strategies substantially underperform the
optimal strategy, indicating that quantum sudden changes, although happening
locally, are better detected globally.Comment: 4+8 pages, published version. New results added, including a theorem
applicable to general multihypothesis discrimination problem
Local discrimination of mixed states
We provide rigorous, efficiently computable and tight bounds on the average
error probability of multiple-copy discrimination between qubit mixed states by
Local Operations assisted with Classical Communication (LOCC). In contrast to
the pure-state case, these experimentally feasible protocols perform strictly
worse than the general collective ones. Our numerical results indicate that the
gap between LOCC and collective error rates persists in the asymptotic limit.
In order for LOCC and collective protocols to achieve the same accuracy, the
former requires up to twice the number of copies of the latter. Our techniques
can be used to bound the power of LOCC strategies in other similar settings,
which is still one of the most elusive questions in quantum communication.Comment: 4 pages, 2 figures+ supplementary materia
Beating noise with abstention in state estimation
We address the problem of estimating pure qubit states with non-ideal (noisy)
measurements in the multiple-copy scenario, where the data consists of a number
N of identically prepared qubits. We show that the average fidelity of the
estimates can increase significantly if the estimation protocol allows for
inconclusive answers, or abstentions. We present the optimal such protocol and
compute its fidelity for a given probability of abstention. The improvement
over standard estimation, without abstention, can be viewed as an effective
noise reduction. These and other results are exemplified for small values of N.
For asymptotically large N, we derive analytical expressions of the fidelity
and the probability of abstention, and show that for a fixed fidelity gain the
latter decreases with N at an exponential rate given by a Kulback-Leibler
(relative) entropy. As a byproduct, we obtain an asymptotic expression in terms
of this very entropy of the probability that a system of N qubits, all prepared
in the same state, has a given total angular momentum. We also discuss an
extreme situation where noise increases with N and where estimation with
abstention provides a most significant improvement as compared to the standard
approach
Formation of S0 galaxies through mergers. Bulge-disc structural coupling resulting from major mergers
Observations reveal a strong structural coupling between bulge and disc in S0
galaxies, which seems difficult to explain if they have formed from supposedly
catastrophic events such as major mergers. We face this question by quantifying
the bulge-disc coupling in dissipative simulations of major and minor mergers
that result in realistic S0s. We have studied the dissipative N-body binary
merger simulations from the GalMer database that give rise to realistic,
relaxed E/S0 and S0 remnants (67 major and 29 minor mergers). We simulate
surface brightness profiles of these S0-like remnants in the K-band, mimicking
typical observational conditions, to perform bulge-disc decompositions
analogous to those carried out in real S0s. The global bulge-disc structure of
these remnants has been compared with real data, and they distribute in the B/T
- r_e - h_d parameter space consistently with real bright S0s, where B/T is the
bulge-to-total luminosity ratio, r_e is the bulge effective radius, and h_d is
the disc scalelength. Major mergers can rebuild a bulge-disc coupling in the
remnants after having destroyed the structures of the progenitors, whereas
minor mergers directly preserve them. Remnants exhibit B/T and r_e/h_d spanning
a wide range of values, and their distribution is consistent with observations.
Many remnants have bulge Sersic indices ranging 1<n<2, flat appearance, and
contain residual star formation in embedded discs, a result which agrees with
the presence of pseudobulges in real S0s. Contrary to the popular view, mergers
(and in particular, major events) can result in S0 remnants with realistically
coupled bulge-disc structures in less than ~3 Gyr. In conclusion, the
bulge-disc coupling and the presence of pseudobulges in real S0s cannot be used
as an argument against the possible major-merger origin of these galaxies.Comment: 23 pages, accepted for publication in Astronomy and Astrophysics
(version after minor language corrections
Optimal signal states for quantum detectors
Quantum detectors provide information about quantum systems by establishing
correlations between certain properties of those systems and a set of
macroscopically distinct states of the corresponding measurement devices. A
natural question of fundamental significance is how much information a quantum
detector can extract from the quantum system it is applied to. In the present
paper we address this question within a precise framework: given a quantum
detector implementing a specific generalized quantum measurement, what is the
optimal performance achievable with it for a concrete information readout task,
and what is the optimal way to encode information in the quantum system in
order to achieve this performance? We consider some of the most common
information transmission tasks - the Bayes cost problem (of which minimal error
discrimination is a special case), unambiguous message discrimination, and the
maximal mutual information. We provide general solutions to the Bayesian and
unambiguous discrimination problems. We also show that the maximal mutual
information has an interpretation of a capacity of the measurement, and derive
various properties that it satisfies, including its relation to the accessible
information of an ensemble of states, and its form in the case of a
group-covariant measurement. We illustrate our results with the example of a
noisy two-level symmetric informationally complete measurement, for whose
capacity we give analytical proofs of optimality. The framework presented here
provides a natural way to characterize generalized quantum measurements in
terms of their information readout capabilities.Comment: 13 pages, 1 figure, example section extende
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