Dark energy effects in the Schr\"odinger-Newton approach

The Schr\"odinger-Newton equation is a proposed model to explain the localization of macroscopic particles by suppressing quantum dispersion with the particle's own gravitational attraction. On cosmic scales, however, dark energy also acts repulsively, as witnessed by the accelerating rate of universal expansion. Here, we introduce the effects of dark energy in the form of a cosmological constant $\Lambda$, that drives the late-time acceleration of the Universe, into the Schr\"odinger-Newton approach. We then ask in which regime dark energy dominates both canonical quantum diffusion and gravitational self-attraction. It turns out that this happens for sufficiently delocalized objects with an arbitrary mass and that there exists a minimal delocalization width of about $67$ m. While extremely macroscopic from a quantum perspective, the value is in principle accessible to laboratories on Earth. Hence, we analyze, numerically, how the dynamics of an initially spherical Gaussian wave packet is modified in the presence of $\Lambda > 0$. A notable feature is the gravitational collapse of part of the wave packet, in the core region close to the center of mass, accompanied by the accelerated expansion of the more distant shell surrounding it. The order of magnitude of the distance separating collapse from expansion matches analytical estimates of the classical turnaround radius for a spherically symmetric body in the presence of dark energy. However, the time required to observe these modifications is astronomical. They can potentially be measured only in physical systems simulating a high effective cosmological constant, or, possibly, via their effects on the inflationary universe.Comment: 8 pages, 4 figures, 2 appendices. Published versio

Local Activation of Non-locality With Negative Bits

We show a purely local protocol to upgrade local realistic correlations to genuine non-local correlations if only one local party has access to a negative probabilistic bit (nebit), i.e., a bit taking $0$ with probability $1+\Delta$ and $1$ with probability $-\Delta$. The minimal amount of nebit's negativity $\Delta$ required for the upgrade can serve as a measure of non-locality. The upgrade protocol bears a striking resemblance to ordinary local unitary operations in quasi-stochastic formulations of quantum theory, mathematically equivalent to positive stochastic processes controlled by nebits. This suggests that nebits can be interpreted as units of quantum departure from classical physics as well.Comment: 7 pages, 1 figure, 3 appendice

Reexamination of the Kochen-Specker theorem: Relaxation of the completeness assumption

The Kochen-Specker theorem states that exclusive and complete deterministic outcome assignments are impossible for certain sets of measurements, called Kochen-Specker (KS) sets. A straightforward consequence is that KS sets do not have joint probability distributions because no set of joint outcomes over such a distribution can be constructed. However, we show it is possible to construct a joint quasiprobability distribution over any KS set by relaxing the completeness assumption. Interestingly, completeness is still observable at the level of measurable marginal probability distributions. This suggests the observable completeness might not be a fundamental feature, but a secondary property.Comment: 5 pages, 1 figur

Compression methods for approximate stochastic modelling

Understanding of the natural world can be accounted to effective information processing. Natural processes, however, are often riddled with enormous amount of information and high non-linearity. A need to simplify these problems becomes paramount for practical purposes. Computational mechanics has come up with a successful model --- known as $\epsilon$-machine --- to carry out statistically accurate prediction while assuming minimal representation. Reducing statistical complexity --- a fundamental measure of memory one needs to save to operate the $\epsilon$-machine --- has been a subject of interest as it provides operational advantages. In this final year project, we explore the problem of optimal construction of approximate $\epsilon$-machine that prioritize minimal complexity at the expense of prediction power. Several approaches are proposed to achieve this, namely the brute-force method and the information bottleneck method. Although requiring preliminary assumption on the approximate $\epsilon$-machine's structures, the brute-force method is fairly effective in finding the minimal model under some constraint. A more robust method is the information bottleneck method, which uses principle of rate-distortion theory to find a set of optimal predictive states to represent the process. We propose the use of two information bottleneck variations, specifically the deterministic information bottleneck and agglomerative clustering, to construct optimal predictive states that are unifilar. Through artificial reconstruction, the predictive states' probability law can be be used to inspire its corresponding approximate $\epsilon$-machine. Combination of these two techniques --- the information bottleneck followed by brute-force method --- can be proven to be useful in the problem of optimal model compression.Bachelor of Science in Physic

Qubit from the classical collision entropy

An orthodox formulation of quantum mechanics relies on a set of postulates in Hilbert space supplemented with rules to connect it with classical mechanics such as quantisation techniques, correspondence principle, etc. Here we deduce a qubit and its dynamics straightforwardly from a discrete deterministic dynamics and conservation of the classical collision entropy. No Hilbert space is required although it can be inferred from this approach if necessary.Comment: 7 page

Quantum Bayesian Inference in Quasiprobability Representations

Bayes’ rule plays a crucial role in logical inference in information and physical sciences alike. Its extension into the quantum regime has been the subject of several recent works. These quantum versions of Bayes’ rule have been expressed in the language of Hilbert spaces. In this paper, we derive the expression for the Petz recovery map within any quasiprobability representation, with explicit formulas for the two canonical choices of “normal quasiprobability representations” (which include discrete-Wigner representations) and of representations based on symmetric informationally complete positive operator-valued measures (SIC-POVMs). By using the same mathematical syntax of (quasi)stochastic matrices acting on (quasi)stochastic vectors, the core difference in logical inference between classical and quantum theory is found in the manipulation of the reference prior rather than in the representation of the channel