Related papers: Quantum permutation puzzles with indistinguishable…
We develop a combinatorial approach to the quantum permutation algebras, as Hopf images of representations of type $\pi:A_s(n)\to B(H)$. We discuss several general problems, including the commutativity and cocommutativity ones, the…
We consider two different ways to encode quantum information, by parallel or anti-parallel pairs of spins. We find that there is more information in the anti-parallel ones. This purely quantum mechanical effect is due to entanglement, not…
Quantum bits can be isolated to perform useful information-theoretic tasks, even though physical systems are fundamentally described by very high-dimensional operator algebras. This is because qubits can be consistently embedded into…
We show that a qubit can be used to substitute for an arbitrarily large number of classical bits. We consider a physical system S interacting locally with a classical field phi(x) as it travels directly from point A to point B. The field…
This is an attempt to find a hidden virtue in Tolman's paradox by showing that it can give rise to quantum superposition. We consider tachyon exchange between two particles and show that it can generate superposition of eigenstates…
The Number Rotation Puzzle (NRP) is a combination puzzle in which the goal is to rearrange a scrambled rectangular grid of numbers back into order via moves that consist of rotating square blocks of numbers of fixed size. Over all possible…
In a topological quantum computer, universal quantum computation is performed by dragging quasiparticle excitations of certain two dimensional systems around each other to form braids of their world lines in 2+1 dimensional space-time. In…
In contrast with software-generated randomness (called pseudo-randomness), quantum randomness is provable incomputable, i.e.\ it is not exactly reproducible by any algorithm. We provide experimental evidence of incomputability --- an…
In combinatorial reconfiguration, the reconfiguration problems on a vertex subset (e.g., an independent set) are well investigated. In these problems, some tokens are placed on a subset of vertices of the graph, and there are three natural…
We propose a simple numerical experiment of two slits interference of particles. It disproves the popular belief that such an interference is incompatible with a knowledge which slit each particle came through or, more generally, ``quantum…
In this paper we make a step towards a time and space efficient algorithm for the hidden shift problem for groups of the form $\mathbb{Z}_k^n$. We give a solution to the case when $k$ is a power of 2, which has polynomial running time in…
In quantum mechanics, a classical particle is raised to a wave-function, thereby acquiring many more degrees of freedom. For instance, in the semi-classical regime, while the position and momentum expectation values follow the classical…
Gibbs paradox in the context of statistical mechanics addresses the issue of additivity of entropy of mixing gases. The usual discussion attributes the paradoxical situation to classical distinguishability of identical particles and credits…
Parrondo's Paradox arises when two losing games are combined to produce a winning one. A history dependent quantum Parrondo game is studied where the rotation operators that represent the toss of a classical biased coin are replaced by…
A simple mapping procedure is presented by which classical orbits and path integrals for the motion of a point particle in flat space can be transformed directly into those in curved space with torsion. Our procedure evolved from…
We extract the information of a quantum motion and decode it into a certain orbit via a single measurable quantity. Such that a quantum chaotic system can be reconstructed as a chaotic attractor. Two configurations for reconstructing this…
The theories of quantum mechanics and relativity dramatically altered our understanding of the universe ushering in the era of modern physics. Quantum theory deals with objects probabilistically at small scales, whereas relativity deals…
Exact solutions of several nonstationary problems of quantum mechanics are obtained. It is shown that if the initial conditions of the problem correspond to the localized-in-space particle, then it moves exactly along the classical…
In a quantum theory of cosmology spacetime behaves classically only in limited patches of the configuration space on which the wave function of the universe is defined. Quantum transitions can connect classical evolution in different…
Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating…