arXiv subjects

Nicolas G. Underwood

Publications and source records attributed to Nicolas G. Underwood.

7 recordsLinked to original sources

arXiv2026

The Quantum Plumber's Problem

Recent work quantified the notion of quantum counterfactual gain for an extended Elitzur-Vaidman bomb test style scenario, through a connection to the negativity of the Kirkwood-Dirac quasiprobability distribution. We here extend this work to identifying quantum advantage in a new scenario, which we term the ``Quantum Plumber's Problem''. In this scenario, we imagine a ``quantum plumber'', who knows that one path of an interferometer is blocked, and wants to find the optimal strategy for identifying with certainty which path this is. We discuss various strategies for a generalised path-encoded interferometer, as well as for the specific case of Hofmann's three-path interferometer, introduced in a recent analysis of the relationship between states in five measurement contexts of a three level system. We support our arguments on the relative merit of competing strategies with data collected over many simulated attempts at locating blockages. We also present results for a variant of the game in which the blockage is replaced by a non-demolition detector.

quant-ph↗

arXiv2026

Convex conservation of von Neumann entropy implies unitarity or antiunitarity

On the space of density matrices $D(H)$, Kadison's theorem establishes that all invertible convex transformations $K:D(H)\to D(H)$ are unitarity or antiunitary. For a finite Hilbert space, we propose a similar theorem which replaces the invertibility requirement with that of entropy conservation. Thus, we argue, the supposition of reversibility in quantum mechanics may be replaced with a principle of entropy conservation.

quant-ph↗

arXiv2024

One and two sample Dvoretzky-Kiefer-Wolfowitz-Massart type inequalities for differing underlying distributions

Kolmogorov-Smirnov (KS) tests rely on the convergence to zero of the KS-distance $d(F_n,G)$ in the one sample case, and of $d(F_n,G_m)$ in the two sample case. In each case the assumption (the null hypothesis) is that $F=G$, and so $d(F,G)=0$. In this paper we extend the Dvoretzky-Kiefer-Wolfowitz-Massart inequality to also apply to cases where $F \neq G$, i.e. when it is possible that $d(F,G) > 0$.

math.ST↗

arXiv2020

Anomalous spectral lines and relic quantum nonequilibrium

We describe features that could be observed in the line spectra of relic cosmological particles should quantum nonequilibrium be preserved in their statistics. According to our arguments, these features would represent a significant departure from those of a conventional origin. Among other features, we find a possible spectral broadening that is proportional to the energy resolution of the recording telescope (and so could be much larger than any conventional broadening). Notably, for a range of possible initial conditions we find the possibility of spectral line "narrowing", whereby a telescope could observe a line that is narrower than it is conventionally able to resolve. We discuss implications for the indirect search for dark matter, with particular reference to some recent controversial spectral lines.

quant-ph↗

arXiv2019

Signatures of relic quantum nonequilibrium

[Shortened Abstract:] This thesis explores the possibility that quantum probabilities arose thermodynamically. A chief concern is the detection of primordial `quantum nonequilibrium', since this is observably distinct from textbook quantum physics. Chapters 2, 3, 4, and 5 are adaptations of references [1,2,3], and [4] respectively. Chapter 2 proposes (information) entropy conservation as a minimal requirement for a theory to feature classical-style thermodynamic relaxation. The resulting structure is dubbed `the iRelax framework'. Both classical mechanics and de Broglie-Bohm quantum theory are shown to be special cases. Indications for a possible extension or unification of de Broglie-Bohm theory are briefly highlighted. Chapter 3 examines ways in which quantum relaxation may be prevented. The method of the drift-field is introduced. A systematic treatment of nodes is given. A category of quantum states is found for which relaxation is significantly impeded, and may not complete at all. Chapters 4 and 5 consider the possibility that primordial quantum nonequilibrium may be conserved in the statistics of a species of relic cosmological particle. Necessary factors for this to be the case are discussed and illustrative scenarios are given both in terms of nonequilibrium particles created by inflaton decay, as well as relic vacuum modes for species that decoupled close to the Planck temperature. The search for so-called `smoking-gun' spectral lines created by dark matter decay or annihilation is argued to be a particularly promising setting for the detection of quantum nonequilibrium. Unintuitive spectral effects relating to the contextuality of quantum measurements are described. If such a suspected source of quantum nonequilibrium were found, its subjection to a specifically quantum mechanical test would confirm or deny the presence of the quantum nonequilibrium conclusively.

quant-ph↗

arXiv2018

Extreme quantum nonequilibrium, nodes, vorticity, drift, and relaxation retarding states

Consideration is given to the behaviour of de Broglie trajectories that are separated from the bulk of the Born distribution with a view to describing the quantum relaxation properties of more `extreme' forms of quantum nonequilibrium. For the 2-dimensional isotropic harmonic oscillator, through the construction of what is termed the `drift field', a description is given of a general mechanism that causes the relaxation of `extreme' quantum nonequilibrium. Quantum states are found which do not feature this mechanism, so that relaxation may be severely delayed or possibly may not take place at all. A method by which these states may be identified, classified and calculated is given in terms of the properties of the nodes of the state. Properties of the nodes that enable this classification are described for the first time.

quant-ph↗

arXiv2015

Quantum field theory of relic nonequilibrium systems

In terms of the de Broglie-Bohm pilot-wave formulation of quantum theory, we develop field-theoretical models of quantum nonequilibrium systems which could exist today as relics from the very early universe. We consider relic excited states generated by inflaton decay, as well as relic vacuum modes, for particle species that decoupled close to the Planck temperature. Simple estimates suggest that, at least in principle, quantum nonequilibrium could survive to the present day for some relic systems. The main focus of this paper is to describe the behaviour of such systems in terms of field theory, with the aim of understanding how relic quantum nonequilibrium might manifest experimentally. We show by explicit calculation that simple perturbative couplings will transfer quantum nonequilibrium from one field to another (for example from the inflaton field to its decay products). We also show that fields in a state of quantum nonequilibrium will generate anomalous spectra for standard energy measurements. Possible connections to current astrophysical observations are briefly addressed.

hep-th↗