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This paper presents two realizations of linear quantum systems for covariance assignment corresponding to pure Gaussian states. The first one is called a cascade realization; given any covariance matrix corresponding to a pure Gaussian…
Motivated by queueing systems with heterogeneous parallel servers, we consider a class of structured multi-dimensional Markov processes whose state space can be partitioned into two parts: a finite set of boundary states and a structured…
The contact process is a paradigmatic classical stochastic system displaying critical behavior even in one dimension. It features a non-equilibrium phase transition into an absorbing state that has been widely investigated and shown to…
Correlated, non-Markovian noise is present in many solid-state systems employed as hosts for quantum information technologies, significantly complicating the realistic theoretical description of these systems. In this regime, the effects of…
The quantum process framework is devised as a generalization of quantum theory to incorporate indefinite causal structure. In this short paper we point out a restriction in forming products of processes: there exist both classical and…
The set of two-body reduced states of translation invariant, infinite quantum spin chains can be approximated from inside and outside using matrix product states and marginals of finite systems, respectively. These lead to hierarchies of…
We introduce a theoretical framework for resource-efficient characterization and control of non-Markovian open quantum systems, which naturally allows for the integration of given, experimentally motivated, control capabilities and…
We consider filtering for a continuous-time, or asynchronous, stochastic system where the full distribution over states is too large to be stored or calculated. We assume that the rate matrix of the system can be compactly represented and…
In this paper, we present a formalism for representing infinite systems in quantum mechanics by employing a strategy that embraces divergences rather than avoiding them. We do this by representing physical quantities such as inner products,…
In this paper a system-oriented formalism of Quantum Information Processing is presented. Its form resembles that of standard signal processing, although further complexity is added in order to describe pure quantum-mechanical effects and…
Fluctuation dissipation theorems connect the linear response of a physical system to a perturbation to the steady-state correlation functions. Until now, most of these theorems have been derived for finite-dimensional systems. However, many…
We propose an extension of the input-output feedback linearization for a class of multivariate systems that are not input-output linearizable in a classical manner. The key observation is that the usual input-output linearization problem…
We develop a switched predictor-feedback law, which achieves global asymptotic stabilization of linear systems with input delay and with the plant and actuator states available only in (almost) quantized form. The control design relies on a…
We review the subject of perfect state transfer; how one designs the (fixed) interactions of a chain of spins so that a quantum state, initially inserted on one end of the chain, is perfectly transferred to the opposite end in a fixed time.…
The purpose of this paper is to show how a class of classical linear stochastic systems can be physically implemented using quantum optical components. Quantum optical systems typically have much higher bandwidth than electronic devices,…
Based on a established relation in Refs.~\cite{Guo:2023ecc,Guo:2024zal,Guo:2024pvt} that relates the integrated correlation functions for a trapped system to the infinite volume scattering phase shifts through a weighted integral, we…
We introduce a hierarchy of linear systems for showing that a given subspace of pure quantum states is entangled (i.e., contains no product states). This hierarchy outperforms known methods already at the first level, and it is complete in…
The formalism developed in Refs.\cite{Guo:2023ecc,Guo:2024zal} that connects integrated correlation function of a trapped two-particle system to infinite volume scattering phase shift is further extended to coupled-channel systems in the…
The standard quantum formalism introduced at the undergraduate level treats measurement as an instantaneous collapse. In reality however, no physical process can occur over a truly infinitesimal time interval. A more subtle investigation of…
The generic behavior of quantum systems has long been of theoretical and practical interest. Any quantum process is represented by a sequence of quantum channels. We consider general ergodic sequences of stochastic channels with arbitrary…