arXiv subjects

Xabier Oianguren-Asua

Publications and source records attributed to Xabier Oianguren-Asua.

4 recordsLinked to original sources

arXiv2026

Quantum Zeno-like Paradox for Position Measurements: A Particle Precisely Found in Space is Nowhere to be Found in Hilbert Space

On a quantum particle in the unit interval $[0,1]$, perform a position measurement with inaccuracy $1/n$ and then a quantum measurement of the projection $|ϕ\rangle\langleϕ|$ with some arbitrary but fixed normalized $ϕ$. Call the outcomes $X \in[0,1]$ and $Y \in\{0,1\}$. We show that in the limit $n\to\infty$ corresponding to perfect precision for $X$, the probability of $Y=1$ tends to 0 for every $ϕ$. Since there is no density matrix, pure or mixed, which upon measurement of any $|ϕ\rangle\langleϕ|$ yields outcome 1 with probability 0, our result suggests that a novel type of quantum state beyond Hilbert space is necessary to describe a quantum particle after a perfect position measurement.

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arXiv2026

Comment on "Association between quantum paradoxes based on weak values and a realistic interpretation of quantum measurements"

In their paper (arXiv:2402.09879), Aredes and Saldanha analyze several paradoxes related to weak values and present a "general argument" that aims to show that "realistic interpretations ...of weak values lead to inconsistencies". Although we agree with the identified inconsistencies for the specific weak values analyzed there, in this Comment we demonstrate that the origin of these inconsistencies is not their general argument, which is formally incorrect. We use Bohmian mechanics as a counterexample to confirm that their conclusions are not valid for all weak values and quantum theories. In particular, we show that weak values postselected in position can in fact be interpreted within Bohmian mechanics as properties of quantum systems, detached from any measuring devices, in a consistent and meaningful way.

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arXiv2024

Bohmian Mechanics as a Practical Tool

In this chapter, we will take a trip around several hot-spots where Bohmian mechanics and its capacity to describe the microscopic reality, even in the absence of measurements, can be harnessed as computational tools, in order to help in the prediction of phenomenologically accessible information (also useful for the followers of the Copenhagen theory). As a first example, we will see how a Stochastic Schrödinger Equation, when used to compute the reduced density matrix of a non-Markovian open quantum system, necessarily seems to employ the Bohmian concept of a conditional wavefunction. We will see that by dressing these conditional wavefunctions with an interpretation, the Bohmian theory can prove to be a useful tool to build general quantum frameworks, like a high-frequency electron transport model. As a second example, we will introduce how a Copenhagen "observable operator" can be derived from numerical properties of the Bohmian trajectories, which within Bohmian mechanics, are well-defined even for an "unmeasured" system. Most importantly in practice, even if these numbers are given no ontological meaning, not only we will be able to simulate (thus, predict and talk about) them, but we will see that they can be operationally determined in a weak value experiment. Therefore, they will be practical numbers to characterize a quantum system irrespective of the followed quantum theory.

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arXiv2023

How weak values illuminate the role of "hidden"-variables as predictive tools

In this chapter we offer an introduction to weak values from a three-fold perspective: first, outlining the protocols that enable their experimental determination; next, deriving their correlates in the quantum formalism and, finally, discussing their ontological significance according to different quantum theories or interpretations. We argue that weak values have predictive power and provide novel ways to characterise quantum systems. We show that this holds true regardless of ongoing ontological disputes. And, still, we contend that certain "hidden" variables theories like Bohmian mechanics constitute very valuable heuristic tools for identifying informative weak values or functions thereof. To illustrate these points, we present a case study concerning quantum thermalization. We show that certain weak values, singled out by Bohmian mechanics as physically relevant, play a crucial role in elucidating the thermalization time of certain systems, whereas standard expectation values are "blind" to the onset of thermalization.

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