Hamiltonian Quantum Dynamics With Separability Constraints

Abstract

Schroedinger equation on a Hilbert space $\mathcal{H}$, represents a linear Hamiltonian dynamical system on the space of quantum pure states, the projective Hilbert space $P\mathcal{H}$. Separable states of a bipartite quantum system form a special submanifold of $P\mathcal{H}$. We analyze the Hamiltonian dynamics that corresponds to the quantum system constrained on the manifold of separable states, using as an important example the system of two interacting qubits. The constraints introduce nonlinearities which render the dynamics nontrivial. We show that the qualitative properties of the constrained dynamics clearly manifest the symmetry of the qubits system. In particular, if the quantum Hamilton's operator has not enough symmetry, the constrained dynamics is nonintegrable, and displays the typical features of a Hamiltonian dynamical system with mixed phase space. Possible physical realizations of the separability constraints are discussed.

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• Relations between different notions of degrees of freedom of a quantum system and its classical model
• Phase space hybrid theory of quantum measurement with nonlinear and stochastic dynamics
• Orbits of hybrid systems as qualitative indicators of quantum dynamics
• Nonlinear evolution of coarse-grained quantum systems with generalized purity constraints
• Cloning in nonlinear Hamiltonian quantum and hybrid mechanics
• Constrained quantum dynamics
• Space of events and the time observable