Past observable dynamics of a continuously monitored qubit

Monitoring a quantum observable continuously in time produces a stochastic measurement record that noisily tracks the observable. For a classical process such noise may be reduced to recover an average signal by minimizing the mean squared error between the noisy record and a smooth dynamical estimate. We show that for a monitored qubit this usual procedure returns unusual results. While the record seems centered on the expectation value of the observable during causal generation, examining the collected past record reveals that it better approximates a moving-mean Gaussian stochastic process centered at a distinct (smoothed) observable estimate. We show that this shifted mean converges to the real part of a generalized weak value in the time-continuous limit without additional postselection. We verify that this smoothed estimate minimizes the mean squared error even for individual measurement realizations. We go on to show that if a second observable is weakly monitored concurrently, then that second record is consistent with the smoothed estimate of the second observable based solely on the information contained in the first observable record. Moreover, we show that such a smoothed estimate made from incomplete information can still outperform estimates made using full knowledge of the causal quantum state.Comment: 11 pages, 4 figure

A single-world consistent interpretation of quantum mechanics from fundamental time and length uncertainties

Within ordinary ---unitary--- quantum mechanics there exist global protocols that allow to verify that no definite event ---an outcome to which a probability can be associated--- occurs. Instead, states that start in a coherent superposition over possible outcomes always remain as a superposition. We show that, when taking into account fundamental errors in measuring length and time intervals, that have been put forward as a consequence of a conjunction of quantum mechanical and general relativity arguments, there are instances in which such global protocols no longer allow to distinguish whether the state is in a superposition or not. All predictions become identical as if one of the outcomes occurs, with probability determined by the state. We use this as a criteria to define events, as put forward in the Montevideo Interpretation of Quantum Mechanics. We analyze in detail the occurrence of events in the paradigmatic case of a particle in a superposition of two different locations. We argue that our approach provides a consistent (C) single-world (S) picture of the universe, thus allowing an economical way out of the limitations imposed by a recent theorem by Frauchiger and Renner showing that having a self-consistent single-world description of the universe is incompatible with quantum theory. In fact, the main observation of this paper may be stated as follows: If quantum mechanics is extended to include gravitational effects to a QG theory, then QG, S, and C are satisfied.Comment: thoughts and comments more than welcom

M\"obius function of semigroup posets through Hilbert series

In this paper, we investigate the M{\"o}bius function $\mu\_{\mathcal{S}}$ associated to a (locally finite) poset arising from a semigroup $\mathcal{S}$ of $\mathbb{Z}^m$. We introduce and develop a new approach to study $\mu\_{\mathcal{S}}$ by using the Hilbert series of $\mathcal{S}$. The latter enables us to provide formulas for $\mu\_{\mathcal{S}}$ when $\mathcal{S}$ belongs to certain families of semigroups. Finally, a characterization for a locally finite poset to be isomorphic to a semigroup poset is given.Comment: 11 page

Extreme Decoherence and Quantum Chaos

We study the ultimate limits to the decoherence rate associated with dephasing processes. Fluctuating chaotic quantum systems are shown to exhibit extreme decoherence, with a rate that scales exponentially with the particle number, thus exceeding the polynomial dependence of systems with fluctuating $k$-body interactions. Our findings suggest the use of quantum chaotic systems as a natural test-bed for spontaneous wave function collapse models. We further discuss the implications on the decoherence of AdS/CFT black holes resulting from the unitarity loss associated with energy dephasing.Comment: 6+10 pp, 2+3 figures; published versio

Energy Storage and Green Hydrogen Systems in Electricity Markets: A Modelling and Optimization Framework with Degradation and Uncertainty Considerations

Mención Internacional en el título de doctorThe increasing penetration of renewable energy in electrical systems requires advances in increasing their controllability. Energy Storage Systems (ESSs) are one of the solutions, since they allow the management of generated energy. Green hydrogen production systems, on the other hand, can utilize electricity to produce hydrogen. This energy carrier which can be sold for revenue generation and can be produced using Alkaline Electrolyzers (AELs). To coordinate these systems in renewable energy plants, advanced control techniques are needed. Complex processes such as degradation, partial loading and the effect of uncertainties must be considered. These considerations add to the complexity, which can obstruct control process, hence a simplistic formulation is required. This dissertation addresses this issue by implementing the effect of both ESS and AEL degradation into short-term planning keeping a linear formulation. Moreover, electrolyzer partial loading effect and operational states are also considered. Novel approaches in their inclusion into short-term planning for electricity market participation are proposed, analyzing their long-term economical significance. Due to the nature of spot electricity markets, which require the commitment of energy delivery beforehand, the uncertainty of renewable source and electricity prices may affect the performance of the system. Various stochastic approaches for short-term optimization are evaluated, with the proposal of novel strategies. The long-term impact of including risk-aware strategies is also analyzed in a simulation framework, whose results indicate that conservative approaches do not necessarily yield better outcomes. The present study commences with the modelling and formulation of a standalone ESS participating in the day-ahead market. A renewable energy source is incorporated into this model, creating a Hybrid Farm (HF) for multi-market participation. Lastly, a green hydrogen production system is also integrated, allowing the involvement in the hydrogen market. A novel algorithm for operation under uncertainties is proposed, which has been found to outperform a classical Montecarlo approach. Throughout the research, Python was employed as the programming language of choice. The generated code has been uploaded to a public repository. Real historical data was used to validate the findings and provide a more realistic representation of the systems under study.Programa de Doctorado en Ingeniería Eléctrica, Electrónica y Automática por la Universidad Carlos III de MadridPresidenta: Mónica Chinchilla Sánchez.- Secretario: Joaquín Eloy-García Carrasco.- Vocal: Pedro Vicente Jover Rodrígue

Radioactive impact in sediments from an estuarine system affected by industrial wastes releases

A big fertilizer industrial complex and a vast extension of phosphogypsum piles (12 km2), sited in the estuary formed by the Odiel and Tinto river mouths (southwest of Spain), are producing an unambiguous radioactive impact in their surrounding aquatic environment through radionuclides from the U-series. The levels and distribution of radionuclides in sediments from this estuarine system have been determined. The analyses of radionuclide concentrations and activity ratios have provided us with an interesting information to evaluate the extension, degree and routes of the radioactive impact, as well as for the knowledge of the different pathways followed for the radioactive contamination to disturb this natural system. The obtained results indicate that the main pathway of radioactive contamination of the estuary is through the dissolution in its waters of the radionuclides released by the industrial activities and their later fixation on the particulate materials. Tidal activity also plays an important role in the transport and homogenization along the estuary of the radioactivity released from the fertilizer plants. D 2002 Elsevier Science Ltd. All rights reserved.Junta de Andalucia (España) project 1FD97-0900-C02-02 (AMB

Probing Quantumness with Joint Continuous Measurements of Non-Commuting Observables

We analyze the continuous measurement of two noncommuting observables for a qubit, and investigate whether the simultaneously observed noisy signals are consistent with the evolution of an equivalent classical system. Following the approach outlined by Leggett and Garg, we show that the readouts violate macrorealistic inequalities for arbitrarily short temporal correlations. Moreover, the derived inequalities are manifestly violated even in the absence of Hamiltonian evolution, unlike for Leggett-Garg inequalities that use a single continuous measurement. Such a violation should indicate the failure of at least one postulate of macrorealism: either physical quantities do not have well-defined values at all times or the measurement process itself disturbs what is being measured. Nevertheless, for measurements of equal strength we are able to construct a classical stochastic model for a spin that perfectly emulates both the qubit evolution and the observed noisy signals, thus emulating the violations; interestingly, this model also requires an unphysical noise to emulate the readouts, which effectively restricts the ability of an observer to learn information about the spin