相关论文: Quantum permutation puzzles with indistinguishable…

We develop an approach where the quantum system states and quantum observables are described as in classical statistical mechanics -- the states are identified with probability distributions and observables, with random variables. An…

We consider the puzzle of cosmic voids bounded by two dimensional structures of galactic clusters as also a puzzle pointed out by Weinberg: How can the mass of a typical elementary particle depend on a cosmic parameter like the Hubble…

We study the motion of two non-interacting quantum particles performing a random walk on a line and analyze the probability that the two particles are detected at a particular position after a certain number of steps (meeting problem). The…

We explore a particular way of reformulating quantum theory in classical terms, starting with phase space rather than Hilbert space, and with actual probability distributions rather than quasiprobabilities. The classical picture we start…

In this paper it is studied the cosmology of a homogeneous and isotropic spacetime endorsed with a conformally coupled massless scalar field. We find six different solutions of the Friedmann equation that represent six different types of…

In this paper I present a conjecture for a recursive algorithm that finds each permutation of combining two sets of objects (AKA the Shuffle Product). This algorithm provides an efficient way to navigate this problem, as each atomic…

The transition from classical to quantum mechanics rests on the recognition that the structure of information is not what we thought it was: there are operational, i.e., phenomenal, probabilistic correlations that lie outside the polytope…

The relativistic two-particle quantum mixtures are studied from the topological point of view. The mixture field variables can be transformed in such a way that a kinematical decoupling of both particle degrees of freedom takes place with a…

This work discusses simple examples how quantum systems are obtained as subsystems of classical statistical systems. For a single qubit with arbitrary Hamiltonian and for the quantum particle in a harmonic potential we provide explicitly…

Inspired by connections to two dimensional quantum theory, we define several models of computation based on permuting distinguishable particles (which we call balls), and characterize their computational complexity. In the quantum setting,…

We show that several problems that figure prominently in quantum computing, including Hidden Coset, Hidden Shift, and Orbit Coset, are equivalent or reducible to Hidden Subgroup for a large variety of groups. We also show that, over…

In this paper we give a mathematical model for a game that we call picture cube puzzle and investigate its properties. The central question is the number of moves required to solve the puzzle. A mathematical discussion is followed by the…

Classical reversible circuits, acting on $w$~bits, are represented by permutation matrices of size $2^w \times 2^w$. Those matrices form the group P($2^w$), isomorphic to the symmetric group {\bf S}$_{2^w}$. The permutation group P($n$),…

An efficient and intuitive framework for universal quantum computation is presented that uses pairs of spin-1/2 particles to form logical qubits and a single physical interaction, Heisenberg exchange, to produce all gate operations. Only…

We describe the notion of a quantum family of maps of a quantum space and that of a quantum commutant of such a family. Quantum commutants are quantum semigroups defined by a certain universal property. We give a few examples of these…

The set of correlations between particles in multipartite quantum systems is larger than those in classical systems. Nevertheless, it is subject to restrictions by the underlying quantum theory. In order to better understand the structure…

Quantum particles can be obtained from a classical probability distribution in phase space by a suitable coarse graining, whereby simultaneous classical information about position and momentum can be lost. For a suitable time evolution of…

We introduce twisted permutation-equivariant GW-invariants, and compute them in terms of untwisted ones. The computation is based on Grothendieck-like RR formula corresponding to Adams' operations from K-theory to itself, and the result can…

Quantum permutation matrices and quantum magic squares are generalizations of permutation matrices and magic squares, where the entries are no longer numbers but elements from arbitrary (non-commutative) algebras. The famous Birkhoff--von…

Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…