Related papers: Magic squares: Latin, Semiclassical and Quantum
Matrix configurations define noncommutative spaces endowed with extra structure including a generalized Laplace operator, and hence a metric structure. Made dynamical via matrix models, they describe rich physical systems including…
A quantum Latin square of order $n$ (denoted as QLS$(n)$) is an $n\times n$ array whose entries are unit column vectors from the $n$-dimensional Hilbert space $\mathcal{H}_n$, such that each row and column forms an orthonormal basis. Two…
Stochastic matrices and positive maps in matrix algebras proved to be very important tools for analysing classical and quantum systems. In particular they represent a natural set of transformations for classical and quantum states,…
We consider classical and quantum algorithms which have a duality property: roughly, either the algorithm provides some nontrivial improvement over random or there exist many solutions which are significantly worse than random. This enables…
In order to use quantum devices for computations, it is necessary to understand the intricacies of the theoretical description. To this end, we provide several novel constructions useful for the comprehension of quantum mechanics from the…
This paper is a review of our recent work on three notorious problems of non-relativistic quantum mechanics: realist interpretation, quantum theory of classical properties and the problem of quantum measurement. A considerable progress has…
A genuinely three-dimensional system, viz. the hyperbolic 4-sphere scattering system, is investigated with classical, semiclassical, and quantum mechanical methods at various center-to-center separations of the spheres. The efficiency and…
A Latin square has six conjugate Latin squares obtained by uniformly permuting its (row, column, symbol) triples. We say that a Latin square has conjugate symmetry if at least two of its six conjugates are equal. We enumerate Latin squares…
The rules of canonical quantization normally offer good results, but sometimes they fail, e.g., leading to quantum triviality ($=$ free) for certain examples that are classically nontrivial ($\ne$ free). A new procedure, called Enhanced…
It is known that semi-magic square matrices form a 2-graded algebra or superalgebra with the even and odd subspaces under centre-point reflection symmetry as the two components. We show that other symmetries which have been studied for…
We define a magic square to be a square matrix whose entries are nonnegative integers and whose rows, columns, and main diagonals sum up to the same number. We prove structural results for the number of such squares as a function of the…
This paper studies whether quantum proofs are more powerful than classical proofs, or in complexity terms, whether QMA=QCMA. We prove three results about this question. First, we give a "quantum oracle separation" between QMA and QCMA. More…
A quantum Latin square of order $n$ (denoted as QLS$(n)$) is an $n\times n$ array whose entries are unit column vectors from the $n$-dimensional Hilbert space $\mathcal{H}_n$, such that each row and column forms an orthonormal basis. Two…
In this paper, a characterization of maps between quantum states that preserve pure states and strict convex combinations is obtained. Based on this characterization, a structural theorem for maps between multipartite quantum states that…
Semiclassical methods provide important tools for approximating solutions in quantum mechanics. In several cases these methods are intriguingly exact rather than approximate, as has been shown by direct calculations on particular systems.…
In quantum mechanics, wave functions and density matrices represent our knowledge about a quantum system and give probabilities for the outcomes of measurements. If the combined dynamics and measurements on a system lead to a density matrix…
Alongside the development of quantum algorithms and quantum complexity theory in recent years, quantum techniques have also proved instrumental in obtaining results in classical (non-quantum) areas. In this paper we survey these results and…
Semiclassical methods are essential in analyzing quantum mechanical systems. Although they generally produce approximate results, relatively rare potentials exist for which these methods are exact. Such intriguing potentials serve as…
We discuss the performance of the Search and Fourier Transform algorithms on a hybrid computer constituted of classical and quantum processors working together. We show that this semi-quantum computer would be an improvement over a pure…
A system's apparent simplicity depends on whether it is represented classically or quantally. This is not so surprising, as classical and quantum physics are descriptive frameworks built on different assumptions that capture, emphasize, and…