Quantum Physics / Quantum Physics

All posts under category "Quantum Physics / Quantum Physics"

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Putting Probabilities First How Hilbert Space Generates and Constrains Them

Putting Probabilities First How Hilbert Space Generates and Constrains Them

We use Bub s (2016) correlation arrays and Pitowksy s (1989b) correlation polytopes to analyze an experimental setup due to Mermin (1981) for measurements on the singlet state of a pair of spin-$ frac12$ particles. The class of correlations allowed by quantum mechanics in this setup is represented by an elliptope inscribed in a non-signaling cube. The class of correlations allowed by local hidden-variable theories is represented by a tetrahedron inscribed in this elliptope. We extend this analysis to pairs of particles of arbitrary spin. The class of correlations allowed by quantum mechanics is still represented by the elliptope; the subclass of those allowed by local hidden-variable theories by polyhedra with increasing numbers of vertices and facets that get closer and closer to the elliptope. We use these results to advocate for an interpretation of quantum mechanics like Bub s. Probabilities and expectation values are primary in this interpretation. They are determined by inner products of vectors in Hilbert space. Such vectors do not themselves represent what is real in the quantum world. They encode families of probability distributions over values of different sets of observables. As in classical theory, these values ultimately represent what is real in the quantum world. Hilbert space puts constraints on possible combinations of such values, just as Minkowski space-time puts constraints on possible spatio-temporal constellations of events. Illustrating how generic such constraints are, the equation for the elliptope derived in this paper is a general constraint on correlation coefficients that can be found in older literature on statistics and probability theory. Yule (1896) already stated the constraint. De Finetti (1937) already gave it a geometrical interpretation.

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Lower Bounds for Function Inversion with Quantum Advice

Function inversion is the problem that given a random function $f [M] to [N]$, we want to find pre-image of any image $f^{-1}(y)$ in time $T$. In this work, we revisit this problem under the preprocessing model where we can compute some auxiliary information or advice of size $S$ that only depends on $f$ but not on $y$. It is a well-studied problem in the classical settings, however, it is not clear how quantum algorithms can solve this task any better besides invoking Grover s algorithm, which does not leverage the power of preprocessing. Nayebi et al. proved a lower bound $ST^2 ge tilde Omega(N)$ for quantum algorithms inverting permutations, however, they only consider algorithms with classical advice. Hhan et al. subsequently extended this lower bound to fully quantum algorithms for inverting permutations. In this work, we give the same asymptotic lower bound to fully quantum algorithms for inverting functions for fully quantum algorithms under the regime where $M = O(N)$. In order to prove these bounds, we generalize the notion of quantum random access code, originally introduced by Ambainis et al., to the setting where we are given a list of (not necessarily independent) random variables, and we wish to compress them into a variable-length encoding such that we can retrieve a random element just using the encoding with high probability. As our main technical contribution, we give a nearly tight lower bound (for a wide parameter range) for this generalized notion of quantum random access codes, which may be of independent interest.

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Bohr s Classical Echo in Quantum s Infinite Realm

In a recent preprint [1] Jeffrey Bub presents a discussion of neo-Bohrian interpretations of quantum mechanics, and also of von Neumann s work on infinite tensor products [2]. He rightfully writes that this work provides a theoretical framework that deflates the measurement problem and justifies Bohr s insistence on the primacy of classical concepts. But then he rejects these ideas, on the basis that the infinity limit is never reached for any real system composed of a finite number of elementary systems . In this note we present opposite views on two major points first, admitting mathematical infinities in a physical theory is not a problem, if properly done; second, the critics of [3,4,5] comes with a major misunderstanding of these papers they don t ask about the significance of the transition from classical to quantum mechanics , but they start from a physical ontology where classical and quantum physics need each other from the beginning. This is because they postulate that a microscopic physical object (or degree of freedom) always appears as a quantum system, within a classical context. Here we argue why this (neo-Bohrian) position makes sense.

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Quantum Checks Clarifying Bub’s No Quantum World

This note is a friendly technical check of Jeffrey Bub s There is No Quantum World (arXiv 2512.18400v2). I flag one unambiguous mathematical slip (a cardinality identity that implicitly assumes the Continuum Hypothesis) and then point out a few places where the discussion of infinite tensor products, ``sectorization, and measurement updates would benefit from sharper wording. Nothing here is meant as a critique of Bub s interpretive goals; the aim is simply to separate what is mathematically forced from what depends on choices of algebra, representation, or philosophical stance. I end with a short remark on Philippe Grangier s reply (arXiv 2512.22965v1).

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Quantum Geometry Trivial Bundles and Duality

We apply De Haro s Geometric View of Theories to one of the simplest quantum systems a spinless particle on a line and on a circle. The classical phase space M = T*Q is taken as the base of a trivial Hilbert bundle E ~ M x H, and the familiar position and momentum representations are realised as different global trivialisations of this bundle. The Fourier transform appears as a fibrewise unitary transition function, so that the standard position-momentum duality is made precise as a change of coordinates on a single geometric object. For the circle, we also discuss twisted boundary conditions and show how a twist parameter can be incorporated either as a fixed boundary condition or as a base coordinate, in which case it gives rise to a flat U(H)-connection with nontrivial holonomy. These examples provide a concrete illustration of how the Geometric View organises quantum-mechanical representations and dualities in geometric terms.

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< Category Statistics (Total: 566) >

Astrophysics
1
Computer Science
581
Condensed Matter
2
Economics
17
Electrical Engineering and Systems Science
38
Mathematics
19
Physics
10
Quantitative Biology
6
Quantitative Finance
4
Quantum Physics
5
Statistics
20

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