Georges Parfionov | Searcharxiv

arXiv2010

Husimi coordinates of multipartite separable states

A parametrization of multipartite separable states in a finite-dimensional Hilbert space is suggested. It is proved to be a diffeomorphism between the set of zero-trace operators and the interior of the set of separable density operators. The result is applicable to any tensor product decomposition of the state space. An analytical criterion for separability of density operators is established in terms of the boundedness of a sequence of operators.

quant-ph↗

arXiv2009

Guessing Quantum Ensemble Using Laplace Principle

For a mixed quantum state with density matrix $ρ$ there are infinitely many ensembles of pure quantum states, which average to $ρ$. Starting from Laplace principle of insufficient reason (not to give \emph{a priori} preference to any particular state), we derive a `natural' distribution of pure states averaging to $ρ$, which is `more spread' than all the others.

quant-ph↗

arXiv2002

Macroscpoic Quantum Game

The game in which acts of participants don't have an adequate description in terms of Boolean logic and classical theory of probabilities is considered. The model of the game interaction is constructed on the basis of a non-distributive orthocomplemented lattice. Mixed strategies of the participants are calculated by the use of probability amplitudes according to the rules of quantum mechanics. A scheme of quantization of the payoff function is proposed and an algorithm for the search of Nash equilibrium is given. It is shown that differently from the classical case in the quantum situation a discrete set of equilibrium is possible.

quant-ph↗

arXiv2002

Can the game be quantum?

The game in which acts of participants don't have an adequate description in terms of Boolean logic and classical theory of probabilities is considered. The model of the game interaction is constructed on the basis of a non-distributive orthocomplemented lattice. Mixed strategies of the participants are calculated by the use of probability amplitudes according to the rules of quantum mechanics. A scheme of quantization of the payoff function is proposed and an algorithm for the search of Nash equilibrium is given. It is shown that differently from the classical case in the quantum situation a discrete set of equilibrium is possible.

quant-ph↗