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 $entanglement$ $entropy$ 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 $complex$ $positivity$ that guarantees in a least-squares type fit that a local minimum of a $\chi^{2}$ 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