274 research outputs found
Non-commutative Markov chains and multi-analytic operators
We study a model of repeated interaction between quantum systems which can be
thought of as a non-commutative Markov chain. It is shown that there exists an
outgoing Cuntz scattering system associated to this model which induces an
input-output formalism with a transfer function corresponding to a
multi-analytic operator, in the sense of multivariate operator theory. Finally
we show that observability for this system is closely related to the scattering
theory of non-commutative Markov chains.Comment: 19 page
Weak Markov Processes as Linear Systems
A noncommutative Fornasini-Marchesini system (a multi-variable version of a
linear system) can be realized within a weak Markov process (a model for
quantum evolution). For a discrete time parameter the resulting structure is
worked out systematically and some quantum mechanical interpretations are
given. We introduce subprocesses and quotient processes and then the notion of
a -extension for processes which leads to a complete classification of
all the ways in which processes can be built from subprocesses and quotient
processes. We show that within a -extension we have a cascade of
noncommutative Fornasini-Marchesini systems. We study observability in this
setting and as an application we gain new insights into stationary Markov
chains where observability for the system is closely related to asymptotic
completeness in a scattering theory for the chain.Comment: Expanded version v2 (43 pages) with substantial additions and
improvements compared to v1. More details and examples, in particular in
sections 3, 4 and 7. Also changes in terminology, compare Def. 3.1, 4.2, 6.4,
page 33. To appear in the journal: Mathematics of Control, Signals, and
Systems (MCSS
Full control by locally induced relaxation
We demonstrate a scheme for controlling a large quantum system by acting on a
small subsystem only. The local control is mediated to the larger system by
some fixed coupling Hamiltonian. The scheme allows to transfer arbitrary and
unknown quantum states from a memory on the large system (``upload access'') as
well as the inverse (``download access''). We study sufficient conditions of
the coupling Hamiltonian and give lower bounds on the fidelities for
downloading and uploading.Comment: 4 pages, 2 figure
Quantum MERA Channels
Tensor networks representations of many-body quantum systems can be described
in terms of quantum channels. We focus on channels associated with the
Multi-scale Entanglement Renormalization Ansatz (MERA) tensor network that has
been recently introduced to efficiently describe critical systems. Our approach
allows us to compute the MERA correspondent to the thermodynamic limit of a
critical system introducing a transfer matrix formalism, and to relate the
system critical exponents to the convergence rates of the associated channels.Comment: 4 pages, 2 figure
Characteristic Functions for Ergodic Tuples
Motivated by a result on weak Markov dilations, we define a notion of
characteristic function for ergodic and coisometric row contractions with a
one-dimensional invariant subspace for the adjoints. This extends a definition
given by G. Popescu. We prove that our characteristic function is a complete
unitary invariant for such tuples and show how it can be computed.Comment: 22 pages, changes made after referee's comments, to appear in
Integral Equations and Operator Theor
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