Mode Representations of Linear Passive Quantum Systems
نویسندگان
چکیده
There has been much interest in modeling open quantum linear passive systems as a fundamental class of quantum control systems. Quantum linear passive systems are parameterized by triple G ∼ (S,C,Ω) consisting of an input-to-output scattering matrix S, an input-system coupling matrix C, a Hamiltonian matrix Ω for normal modes. The purpose of this paper is to characterize these systems using recent techniques in effective mode representations. It is first shown that the Hurwitz stability of G is equivalent to that the state-space realization in terms of C and Ω is minimal. Then the dimension of minimal realization, namely the number of system oscillators, is characterized by C and Ω. A special form of minimal realization is proposed, based on which a spectral measure is defined and is used to derive a chain-mode representation of G ∼ (S,C,Ω). Another representation, the so-called independentoscillator representation, is also proposed; then the uniqueness of and equivalence between these two representations are established. The dissipativity of the quantum linear passive system G ∼ (S,C,Ω) is investigated, and it is shown that G is lossless bounded if and only if it can be written in a fractional linear from in terms of a lossless positive function Σ, and it turns out that the specific form of Σ that generates a genuine quantum system is given by the chain-mode (or equivalently the independentoscillator) representation.
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تاریخ انتشار 2013