Related papers: Matrix Product States approach to non-Markovian pr…
Recently remarkable progress in quantum technology has been witnessed. In view of this it is important to investigate an open quantum system as a model of such quantum devices. Quantum devices often require extreme conditions such as very…
We study the non-Markovian quantum interference phenomenon of a multi-state atomic system coupled to a bosonic dissipative environment by using the exact master equations derived in this paper. Two examples involving four-level systems with…
We give a probabilistic characterization of the set of measures that can be represented by the matrix product ansatz. By suitably enlarging the state space, we show that a probability measure can be described in terms of non negative…
In this paper, the aim is to develop a quantum counterpart to classical Markov decision processes (MDPs). Firstly, we provide a very general formulation of quantum MDPs with state and action spaces in the quantum domain, quantum…
Calculating the degree of non-Markovianity of a dissipative process is a difficult task, even for the dynamics of a single qubit, given the complex maximization problem. In this work, focusing on the entanglement-based quantifier of…
We present and test a protocol to learn the matrix-product operator (MPO) representation of an experimentally prepared quantum state. The protocol takes as an input classical shadows corresponding to local randomized measurements, and…
We develop a numerical method based on matrix product states for simulating quantum many-body systems at finite temperatures without importance sampling and evaluate its performance in spin 1/2 systems. Our method is an extension of the…
The concept of stochastic matrix product states is introduced and a natural form for the states is derived. This allows to define the analogue of Schmidt coefficients for steady states of non-equilibrium stochastic processes. We discuss a…
Stochastic processes on topological vector spaces over non-Archimedean fields and with transition measures having values in non-Archimedean fields are defined and investigated. For this the non-Archimedean analog of the Kolmogorov theorem…
Non-Markovian processes have recently become a central topic in the study of open quantum systems. We realize experimentally non-Markovian decoherence processes of single photons by combining time delay and evolution in a…
Matrix product states are useful representations for a large variety of naturally occurring quantum states. Studying their typical properties is important for understanding universal behavior, including quantum chaos and thermalization, as…
We present a state-interaction approach for matrix product state (MPS) wave functions in a nonorthogonal molecular orbital basis. Our approach allows us to calculate for example transition and spin-orbit coupling matrix elements between…
We study the dynamics of classical and quantum systems undergoing a continuous measurement of position by schematizing the measurement apparatus with an infinite set of harmonic oscillators at finite temperature linearly coupled to the…
Generators of Markov processes on a countable state space can be represented as finite or infinite matrices. One key property is that the off-diagonal entries corresponding to jump rates of the Markov process are non-negative. Here we…
This paper reveals the intrinsic structure of Matrix Product States (MPS) by establishing their deep connection to entangled hidden Markov models (EHMMs). It is demonstrated that a significant class of MPS can be derived as the outcomes of…
Matrix product density operators (MPDOs) are an important class of states with interesting properties. Consequently, it is important to understand how to prepare these states experimentally. One possible way to do this is to design an open…
We use projection methods to construct (global) quantum states with prescribed reduced (marginal) states, and possibly with some special properties such as having specific eigenvalues, having specific rank and extreme von Neumann or Renyi…
A wide class of exact master equations for a multiple qubit system can be explicitly constructed by using the corresponding exact non-Markovian quantum state diffusion equations. These exact master equations arise naturally from the quantum…
We construct measures for the non-Markovianity of quantum evolution with a physically meaningful interpretation. We first provide a general setting in the framework of channel capacities and propose two families of meaningful quantitative…
An operator equality on the entropy production for general quantum Markovian master equations is derived without resorting quantum stochastic trajectory and priori quantum definition of entropy production. We find that, the equality can be…