Interaction-free evolving states of a bipartite system

Abstract

We show that two interacting physical systems may admit entangled pure or nonseparable mixed states evolving in time as if the mutual interaction Hamiltonian were absent. In this paper we define these interaction-free evolving (IFE) states and characterize their existence for a generic binary system described by a time-independent Hamiltonian. A comparison between IFE subspace and the decoherence-free subspace is reported. The set of all pure IFE states is explicitly constructed for a nonhomogeneous spin-star-system model

Interaction free and decoherence free states

“…One might wonder whether one can relax commutation of H 0 and H I and still have states satisfying condition (1). Recently it has been found [1] a positive answer to this question in the bipartite scenario.…”

“…Note, that when [H 0 , H I ] = 0, that is H defines a non-demolition Hamiltonian model, each eigenvector of H I , i.e. H I ψ α = αψ α , satisfies (1). Indeed, one has e −iHt ψ α = e −iH 0 t e −iH I t ψ α = e −iαt e −iH 0 t ψ α .…”

“…Recently it has been found [1] a positive answer to this question in the bipartite scenario. It was shown [1] that in the Hilbert space of some closed bipartite systems there exists a non-empty subspace H IFE of H constituted by eigenvectors of H I generally evolving as if H I were a c-number.…”

“…Recently it has been found [1] a positive answer to this question in the bipartite scenario. It was shown [1] that in the Hilbert space of some closed bipartite systems there exists a non-empty subspace H IFE of H constituted by eigenvectors of H I generally evolving as if H I were a c-number. The states belonging to H IFE have been called InteractionFree Evolving states (IFE states in short) and when they belong to the kernel of H I , they evolve as if the two subsystems of S were fully decoupled.…”

“…Generally speaking an IFE state is a non separable mixed state of S unitarily evolving in H under the action of H 0 only and necessary a sufficient condition for the existence of pure or mixed IFE states of a given bipartite closed system have been reported in Ref. [1]. In this paper we generalize the concept of IFE states problem to arbitrary "systems" whose dynamics is characterized by a linear first order homogeneous differential equation whose generator L allows to a natural splitting L = A + B.…”