arXiv subjects

Nathan Cohen

Publications and source records attributed to Nathan Cohen.

4 recordsLinked to original sources

arXiv2026

Quantum incompatibility of Born probabilities

Quantum theory challenges the view that individual measurement outcomes are predefined and independent of the measurement context. Yet the quantum state itself -- the catalogue of probabilities for all possible measurements -- is usually assumed to be well defined. We argue that this assumption tacitly relies on measurements being performed relative to ideal, infinitely-resourceful reference frames. We show that, when measurements are made relative to non-ideal quantum reference frames, the probabilities themselves become indefinite: even in the limit of arbitrarily large number of runs, the relative frequencies may remain uncertain. The uncertainty is irreducible in a quantum-mechanical sense, as we show by proving a Bell-type theorem for relative frequencies. We further propose a quantum-optical implementation of these relational measurements based on pulsed homodyne detection. Our findings motivate an extension of the notion of the quantum state to regimes constrained by finite resources. We expect them to be especially relevant at the interface between quantum theory and general relativity, where the resources and information available in a bounded region of spacetime are fundamentally limited.

quant-ph↗

arXiv2026

(The) Wiggles going non-linear

The simplest models of slow-roll inflation predict a featureless, nearly scale-invariant power spectrum of primordial curvature perturbations, consistent with current observations. However, in many non-minimal realisations of inflation, one generically expects the primordial power spectrum (PPS) to be ''wiggly'' with features that strongly deviate from scale-invariance. Current and next generation large scale structure (LSS) surveys will probe the PPS with unprecedented accuracy and therefore also increase sensitivity to power spectrum wiggles. However, accessing the information contained in these data will require an understanding of the behaviour of wiggly power spectra beyond the linear regime of structure formation. In this work, we use high resolution $N$-body simulations to study the non-linear evolution of scenarios in which the PPS has superimposed oscillations, calibrate a one-parameter semi-analytic damping model to describe their signatures in the late-time matter power spectrum and test the relative improvement on constraints by implementing this modelling strategy in a likelihood analysis via Gaussian Process Regression (GPR) emulation. Paying special attention to identifying our approach's domain of validity and quantifying as well as propagating uncertainties, we demonstrate that as long as the frequency of the PPS modulation is large enough, we are able to predict the matter power spectrum with sub-percent accuracy -- thereby enabling us to search for inflationary wiggles in LSS data.

astro-ph.CO↗

arXiv2026

Bayesian optimisation for Bayesian evidence (BOBE) -- a fast and efficient likelihood emulator for model selection

The formalism of Bayesian model selection provides a very elegant way of ranking different physical models in terms of how compatible they are with a given set of observed data. However, its practical application is often hampered by the challenge of having to compute the Bayesian evidence - a multi-dimensional integral over the product of likelihood and prior probability. This usually necessitates a large number of function calls to the likelihood, which may become prohibitive in case of "slow", costly to evaluate likelihoods. A possible solution to this problem lies in approximating the slow full likelihood by a fast emulated likelihood. In this paper, we introduce BOBE (Bayesian Optimisation for Bayesian Evidence), a method to construct a Gaussian Process Regression (GPR)-based emulator. BOBE utilises a Bayesian Optimisation algorithm designed specifically to (i) provide a realistic estimate of the emulator's uncertainty and its impact on the evidence calculation, and (ii) minimise the number of likelihood evaluations required in order to meet a given evidence accuracy goal. We apply it to a number of toy examples as well as actual cosmological likelihoods, and demonstrate that training the emulator to a sufficient accuracy takes a factor of $O(10^3)$ fewer direct likelihood evaluations than would be needed if one were to directly compute the evidence integral via nested sampling. BOBE's overhead is independent of the likelihood computation time $t_L$, making it particularly useful for "expensive" likelihoods with $t_L \gtrsim 1$~s. BOBE is written in Python, supports MPI parallelisation, takes advantage of automatic differentiation and just-in-time-compilation provided by JAX, can straightforwardly be implemented with cosmological data analysis frameworks such as Cobaya, and is available for download from https://github.com/Ameek94/BOBE.

astro-ph.CO↗

arXiv2021

Rendezvous on the Line with Different Speeds and Markers that can be Dropped at Chosen Time

In this paper we introduce a Linear Program (LP) based formulation of a Rendezvous game with markers on the infinite line and solve it. In this game one player moves at unit speed while the second player moves at a speed bounded by vmax smaller than 1. We observe that in this setting a slow moving player may have interest to rest still instead of moving. This shows that in some conditions the wait-for-mummy strategy is optimal. We observe as well that the strategies are completely different if the player that holds the marker is the fast or slow one. Interestingly, the marker is not useful when the player without marker moves slowly, i.e. the fast moving player holds the marker.

cs.GT↗