Related papers: Magic squares: Latin, Semiclassical and Quantum
We introduce several classes of quantum combinatorial designs, namely quantum Latin squares, cubes, hypercubes and a notion of orthogonality between them. A further introduced notion, quantum orthogonal arrays, generalizes all previous…
Understanding how classical physics emerges from quantum mechanics remains a central problem in the foundations of physics. Here we derive a classical limit from finite-resolution measurements, modeled by continuous coarse-grained POVMs.…
Every Latin square of prime power order $q$ is uniquely described by a local permutation polynomial (LPP) in the polynomial ring $\mathbb{F}_q[x,y]$. Despite this equivalence, one may find in the literature only some preliminary results on…
In a metric variable based Hamiltonian quantization, we give a prescription for constructing semiclassical matter-geometry states for homogeneous and isotropic cosmological models. These "collective" states arise as infinite linear…
We present classical and quantum algorithms based on spectral methods for a problem in tensor principal component analysis. The quantum algorithm achieves a quartic speedup while using exponentially smaller space than the fastest classical…
In this work we initiate the question of whether quantum devices can provide us with an almost perfect source of classical randomness, and more generally, suffice for classical cryptographic tasks, such as encryption. Indeed, it is well…
The classical limit of quantum mechanics is discussed for closed quantum systems in terms of observational aspects. Initially, the failure of the limit h->0 is explicitly demonstrated in a model of two quantum mechanically interacting…
While it seems possible that quantum computers may allow for algorithms offering a computational speed-up over classical algorithms for some problems, the issue is poorly understood. We explore this computational speed-up by investigating…
When compared to quantum mechanics, classical mechanics is often depicted in a specific metaphysical flavour: spatio-temporal realism or a Newtonian "background" is presented as an intrinsic fundamental classical presumption. However, the…
Sums play a prominent role in the formalisms of quantum mechanics, be it for mixing and superposing states, or for composing state spaces. Surprisingly, a conceptual analysis of quantum measurement seems to suggest that quantum mechanics…
This is a translation of Leonhard Euler's ``De quadratis magicis'' . It is E795 in the Enestrom index. This paper studies how to construct magic squares with certain numbers of cells, in particular 9, 16, 25 and 36. It considers some…
Magic is a non-classical resource whose efficient manipulation is fundamental to advancing efficient and scalable fault-tolerant quantum computing. Quantum advantage is possible only if both magic and entanglement are present. Of particular…
Semiclassical gravity couples classical gravity to the quantized matter in meanfield approximation. The meanfield coupling is problematic for two reasons. First, it ignores the quantum fluctuation of matter distribution. Second, it violates…
Quantum coherence is a fundamental property of quantum systems, separating quantum from classical physics. Recently, there has been significant interest in the characterization of quantum coherence as a resource, investigating how coherence…
A phenomenon of classical quantization is discussed. This is revealed in the class of pseudoclassical gauge systems with nonlinear nilpotent constraints containing some free parameters. Variation of parameters does not change local (gauge)…
One of the crucial differences between mathematical models of classical and quantum mechanics is the use of the tensor product of the state spaces of subsystems as the state space of the corresponding composite system. (To describe an…
We describe a general procedure for associating a minimal informationally-complete quantum measurement (or MIC) and a set of linearly independent post-measurement quantum states with a purely probabilistic representation of the Born Rule.…
Given a quantum Hamiltonian, we explain how the dynamical properties of the underlying classical system affect the behaviour of quantum eigenstates in the semi-classical limit. We study this problem via the notion of semiclassical measures.…
Recently, increased computational power and data availability, as well as algorithmic advances, have led machine learning techniques to impressive results in regression, classification, data-generation and reinforcement learning tasks.…
The descriptions of the quantum realm and the macroscopic classical world differ significantly not only in their mathematical formulations but also in their foundational concepts and philosophical consequences. When and how physical systems…